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+Project Gutenberg (https://www.gutenberg.org) public repository for
+eBook #53740 (https://www.gutenberg.org/ebooks/53740)
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-The Project Gutenberg EBook of The Telescope, by Louis Bell
-
-This eBook is for the use of anyone anywhere in the United States and most
-other parts of the world at no cost and with almost no restrictions
-whatsoever.  You may copy it, give it away or re-use it under the terms of
-the Project Gutenberg License included with this eBook or online at
-www.gutenberg.org.  If you are not located in the United States, you'll have
-to check the laws of the country where you are located before using this ebook.
-
-
-
-Title: The Telescope
-
-Author: Louis Bell
-
-Release Date: December 16, 2016 [EBook #53740]
-
-Language: English
-
-Character set encoding: UTF-8
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-*** START OF THIS PROJECT GUTENBERG EBOOK THE TELESCOPE ***
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-
-                             THE TELESCOPE
-
-
-
-
-                      _McGraw-Hill Book Co. Inc._
-
-                        PUBLISHERS OF BOOKS FOR
-
-                  Coal Age ▿ Electric Railway Journal
-              Electrical World ▿ Engineering News-Record
-             American Machinist ▿ Ingeniería Internacional
-                 Engineering & Mining Journal ▿ Power
-                 Chemical & Metallurgical Engineering
-                       Electrical Merchandising
-
-
-
-
- [Illustration: Galileo’s Telescopes. (_Frontispiece_) (_Bull. de la
- Soc. Astron. de France._)]
-
-
-
-
-                             THE TELESCOPE
-
-                                  BY
-
-                           LOUIS BELL, PH.D.
-
-   CONSULTING ENGINEER; FELLOW, AMERICAN ACADEMY OF ARTS & SCIENCES;
-     PAST-PRESIDENT, THE ILLUMINATING ENGINEERING SOCIETY; MEMBER,
-                     AMERICAN ASTRONOMICAL SOCIETY
-
-                             FIRST EDITION
-
-                    MCGRAW-HILL BOOK COMPANY, INC.
-                     NEW YORK: 370 SEVENTH AVENUE
-                  LONDON: 6 & 8 BOUVERIE ST., E. C. 4
-                                 1922
-
-
-
-
-                        COPYRIGHT, 1922, BY THE
-                    MCGRAW-HILL BOOK COMPANY, INC.
-
-                        THE MAPLE PRESS YORK PA
-
-
-
-
-PREFACE
-
-
-This book is written for the many observers, who use telescopes for
-study or pleasure and desire more information about their construction
-and properties. Not being a “handbook” in two or more thick quartos, it
-attempts neither exhaustive technicalities nor popular descriptions of
-great observatories and their work. It deals primarily with principles
-and their application to such instruments as are likely to come into
-the possession, or within reach, of students and others for whom the
-Heavens have a compelling call.
-
-Much has been written of telescopes, first and last, but it is for
-the most part scattered through papers in three or four languages,
-and quite inaccessible to the ordinary reader. For his benefit the
-references are, so far as is practicable, to English sources, and
-dimensions are given, regretfully, in English units. Certain branches
-of the subject are not here discussed for lack of space or because
-there is recent literature at hand to which reference can be made.
-Such topics are telescopes notable chiefly for their dimensions, and
-photographic apparatus on which special treatises are available.
-
-Celestial photography is a branch of astronomy which stands on its
-own feet, and although many telescopes are successfully used for
-photography through the help of color screens, the photographic
-telescope proper and its use belongs to a field somewhat apart,
-requiring a technique quite its own.
-
-It is many years, however, since any book has dealt with the telescope
-itself, apart from the often repeated accounts of the marvels it
-discloses. The present volume contains neither pictures of nebulæ nor
-speculations as to the habitibility of the planets; it merely attempts
-to bring the facts regarding the astronomer’s chief instrument of
-research somewhere within grasp and up to the present time.
-
-The author cordially acknowledges his obligations to the important
-astronomical journals, particularly the Astro-physical Journal,
-and Popular Astronomy in this country; The Observatory, and the
-publications of the Royal Astronomical Society in England; the
-Bulletin de la Société Astronomique de France; and the Astronomische
-Nachrichten; which, with a few other journals and the official reports
-of observatories form the body of astronomical knowledge. He also
-acknowledges the kindness of the various publishers who have extended
-the courtesy of illustrations, especially Macmillan & Co. and the
-Clarendon Press, and above all renders thanks to the many friends
-who have cordially lent a helping hand—the Director and staff of the
-Harvard Observatory, Dr. George E. Hale, C. A. R. Lundin, manager of
-the Alvan Clark Corporation, J. B. McDowell, successor of the Brashear
-Company, J. E. Bennett, the American representative of Carl Zeiss,
-Jena, and not a few others.
-
-  LOUIS BELL.
-
-  BOSTON, MASS.,
-  _February, 1922_.
-
-
-
-
-CONTENTS
-
-
-                                                          PAGE
-
-  PREFACE                                                  vii
-
-  CHAP.
-
-     I. THE EVOLUTION OF THE TELESCOPE                       1
-
-    II. THE MODERN TELESCOPE                                31
-
-   III. OPTICAL GLASS AND ITS WORKING                       57
-
-    IV. THE PROPERTIES OF OBJECTIVES AND MIRRORS            76
-
-     V. MOUNTINGS                                           98
-
-    VI. EYE-PIECES                                         134
-
-   VII. HAND TELESCOPES AND BINOCULARS                     150
-
-  VIII. ACCESSORIES                                        165
-
-    IX. THE TESTING AND CARE OF TELESCOPES                 201
-
-     X. SETTING UP AND HOUSING THE TELESCOPE               228
-
-    XI. SEEING AND MAGNIFICATION                           253
-
-  APPENDIX                                                 279
-
-  INDEX                                                    281
-
-
-
-
-THE TELESCOPE
-
-
-
-
-CHAPTER I
-
-THE EVOLUTION OF THE TELESCOPE
-
-
-In the credulous twaddle of an essay on the Lost Arts one may generally
-find the telescope ascribed to far antiquity. In place of evidence
-there is vague allusion of classical times or wild flights of fancy
-like one which argued from the Scriptural statement that Satan took
-up Christ into a high mountain and showed him all the kingdoms of the
-earth, that the Devil had a telescope—bad optics and worse theology.
-
-In point of fact there is not any indication that either in classical
-times, or in the black thousand years of hopeless ignorance that
-followed the fall of Roman civilization, was there any knowledge of
-optical instruments worth mentioning.
-
-The peoples that tended their flocks by night in the East alone kept
-alive the knowledge of astronomy, and very gradually, with the revival
-of learning, came the spirit of experiment that led to the invention of
-aids to man’s natural powers.
-
-The lineage of the telescope runs unmistakably back to spectacles, and
-these have an honorable history extending over more than six centuries
-to the early and fruitful days of the Renaissance.
-
-That their origin was in Italy near the end of the thirteenth century
-admits of little doubt. A Florentine manuscript letter of 1289 refers
-to “Those glasses they call spectacles, lately invented, to the great
-advantage of poor old men when their sight grows weak,” and in 1305
-Giordano da Rivalto refers to them as dating back about twenty years.
-
-Finally, in the church of Santa Maria Maggiore in Florence lay
-buried Salvino d’Amarto degli Armati, (obiit 1317) under an epitaph,
-now disappeared, ascribing to him the invention of spectacles. W.
-B. Carpenter, F. R. S., states that the inventor tried to keep the
-valuable secret to himself, but it was discovered and published before
-his death. At all events the discovery moved swiftly. By the early
-fourteenth century it had spread to the Low Countries where it was
-destined to lead to great results, and presently was common knowledge
-over all civilized Europe.
-
-It was three hundred years, however, between spectacles and the
-combination of spectacle lenses into a telescope, a lapse of time
-which to some investigators has seemed altogether mysterious. The
-ophthalmological facts lead to a simple explanation. The first
-spectacles were for the relief of presbyopia, the common and lamentable
-affection of advancing years, and for this purpose convex lenses of
-very moderate power sufficed, nor was material variation in power
-necessary. Glasses having a uniform focus of a foot and a half or
-thereabouts would serve every practical purpose, but would be no
-material for telescopes.
-
-Myopia was little known, its acquired form being rare in a period of
-general illiteracy, and glasses for its correction, especially as
-regards its higher degrees, probably came slowly and were in very small
-demand, so that the chance of an optical craftsman having in hand the
-ordinary convex lenses and those of strong negative curvature was
-altogether remote. Indeed it was only in 1575 that Maurolycus published
-a clear description of myopia and hypermetropia with the appropriate
-treatment by the use of concave and convex lenses. Until both of these,
-in quite various powers, were available, there was small chance of
-hitting upon an instrument that required their use in a highly special
-combination.
-
-At all events there is no definite trace of the discovery of telescopic
-vision until 1608 and the inventor of record is unquestionably one Jan
-Lippershey, a spectacle maker of Middelburg in Zeeland, a native of
-Wesel. On Oct. 2, 1608 the States-General took under consideration a
-petition which had been presented by Lippershey for a 30-year patent
-to the exclusive right of manufacture of an instrument for seeing at a
-distance, or for a suitable pension, under the condition that he should
-make the instrument only for his country’s service.
-
-The States General pricked up its ears and promptly appointed on Oct. 4
-a committee to test the new instrument from a tower of Prince Maurice’s
-palace, allotting 900 florins for the purchase of the invention should
-it prove good. On the 6th the committee reported favorably and the
-Assembly agreed to give Lippershey 900 florins for his instrument, but
-desired that it be arranged for use with both eyes.
-
-Lippershey therefore pushed forward to the binocular form and two
-months later, Dec. 9, he announced his success. On the 15th the new
-instrument was examined and pronounced good, and the Assembly ordered
-two more binoculars, of rock crystal, at the same price. They denied a
-patent on the ground that the invention was known to others, but paid
-Lippershey liberally as a sort of retainer to secure his exclusive
-services to the State. In fact even the French Ambassador, wishing to
-obtain an instrument from him for his King, had to secure the necessary
-authorization from the States-General.
-
-[Illustration: _Bull. de la Soc. Astron. de France._ FIG. 1.—Jan
-Lippershey, Inventor of the Telescope.]
-
-It is here pertinent to enquire what manner of optic tube Lippershey
-showed to back up his petition, and how it had come to public
-knowledge. As nearly as we may know these first telescopes were about a
-foot and a half long, as noted by Huygens, and probably an inch and a
-half or less in aperture, being constructed of an ordinary convex lens
-such as was used in spectacles for the aged, and of a concave glass
-suitable for a bad case of short sightedness, the only kind in that day
-likely to receive attention.
-
-It probably magnified no more than three or four diameters and was most
-likely in a substantial tube of firmly rolled, glued, and varnished
-paper, originally without provision for focussing, since with an eye
-lens of rather low power the need of adjustment would not be acute.
-
-As to the invention being generally known, the only definite attempt
-to dispute priority was made by James Metius of Alkmaar, who, learning
-of Lippershey’s petition, on Oct. 17, 1608, filed a similar one,
-alleging that through study and labor extending over a couple of years
-he, having accidentally hit upon the idea, had so far carried it out
-that his instrument made distant objects as distinct as the one lately
-offered to the States by a citizen and spectacle maker of Middelburg.
-
-He apparently did not submit an instrument, was politely told to
-perfect his invention before his petition was further considered,
-and thereafter disappears from the scene, whatever his merits. If he
-had actually noted telescopic vision he had neither appreciated its
-enormous importance nor laid the facts before others who might have
-done so.
-
-The only other contemporary for whom claims have been made is Zacharius
-Jansen, also a spectacle maker of Middelburg, to whom Pierre Borel,
-on entirely second hand information, ascribed the discovery of the
-telescope. But Borel wrote nearly fifty years later, after all the
-principals were dead, and the evidence he collected from the precarious
-memories of venerable witnesses is very conflicting and points to about
-1610 as the date when Jansen was making telescopes—like many other
-spectacle makers.[1]
-
- [1] There is a very strong probability that Jansen was the inventor of
- the compound microscope about the beginning of the seventeenth century.
-
-Borel also gave credence to a tale that Metius, seeking Jansen,
-strayed into Lippershey’s shop and by his inquiries gave the shrewd
-proprietor his first hint of the telescope, but set the date at 1610.
-A variation of this tale of the mysterious stranger, due to Hieronymus
-Sirturus, contains the interesting intimation that he may have been of
-supernatural origin—not further specified. There are also the reports,
-common among the ignorant or envious, that Lippershey’s discovery was
-accidental, even perhaps made by his children or apprentice.
-
-Just how it actually was made we do not know, but there is no reason to
-suppose that it was not in the commonplace way of experimenting with
-and testing lenses that he had produced, perhaps those made to meet a
-vicious case of myopia in one of his patrons.
-
-When the discovery was made is somewhat clearer. Plainly it antedated
-Oct. 2, and in Lippershey’s petition is a definite statement that an
-instrument had already been tested by some, at least, of the members of
-the States-General. A somewhat vague and gossipy note in the _Mercure
-Française_ intimates that one was presented to Prince Maurice “about
-September of the past year” (1608) and that it was shown to the Council
-of State and to others.
-
-Allowing a reasonable time between Lippershey’s discovery and the
-actual production of an example suitable for exhibition to the
-authorities, it seems likely that the invention dates back certainly
-into the summer of 1608, perhaps even earlier.
-
-At all events there is every indication that the news of it spread
-like wild-fire. Unless Lippershey were unusually careful in keeping
-his secret, and there are traditions that he was not, the sensational
-discovery would have been quickly known in the little town and every
-spectacle maker whose ears it reached would have been busy with it.
-
-If the dates given by Simon Marius in his _Mundus Jovialis_ be correct,
-a Belgian with an air of mystery and a glass of which one of the
-lenses was cracked, turned up at the Frankfort fair in the autumn of
-1608 and at last allowed Fuchs, a nobleman of Bimbach, to look through
-the instrument. Fuchs noted that it magnified “several” times, but
-fell out with the Belgian over the price, and returning, took up the
-matter with Marius, fathomed the construction, tried it with glasses
-from spectacles, attempted to get a convex lens of longer focus from a
-Nuremburg maker, who had no suitable tools, and the following summer
-got a fairly good glass from Belgium where such were already becoming
-common.
-
-With this Marius eventually picked up three satellites of Jupiter—the
-fourth awaited the arrival of a superior telescope from Venice. Early
-in 1609 telescopes “about a foot long” were certainly for sale in
-Paris, a Frenchman had offered one in Milan by May of that year, a
-couple of months later one was in use by Harriot in England, an example
-had reached Cardinal Borghese, and specimens are said to have reached
-Padua. Fig. 2 from the “_Mundus Jovialis_,” shows Marius with his
-“Perspicilium,” the first published picture of the new instrument.
-Early in 1610 telescopes were being made in England, but if the few
-reports of performance, even at this date, are trustworthy, the “Dutch
-trunk” of that period was of very indifferent quality and power, far
-from being an astronomical instrument.
-
-[Illustration: _The Observatory._ FIG. 2.—Simon Marius and his
-Telescope.]
-
-One cannot lay aside this preliminary phase of the evolution of the
-telescope without reference to the alleged descriptions of telescopic
-apparatus by Roger Bacon, (c. 1270), Giambattista della Porta (1558),
-and Leonard Digges (1571), details of which may be found in Grant’s
-_History of Physical Astronomy_ and many other works.
-
-Of these the first on careful reading conveys strongly the conviction
-that the author had a pretty clear idea of refraction from the
-standpoint of visual angle, yet without giving any evidence of
-practical acquaintance with actual apparatus for doing the things which
-he suggests.
-
-Given a suitable supply of lenses, it is reasonably certain that Bacon
-was clever enough to have devised both telescope and microscope, but
-there is no evidence that he did so, although his manifold activities
-kept him constantly in public view. It does not seem unlikely, however,
-that his suggestions in manuscripts, quite available at the time, may
-have led to the contemporaneous invention of spectacles.
-
-Porta’s comments sound like an echo of Bacon’s, plus a rather muddled
-attempt to imagine the corresponding apparatus. Kepler, certainly
-competent and familiar with the principles of the telescope, found his
-description entirely unintelligible. Porta, however, was one of the
-earliest workers on the _camera obscura_ and upon this some of his
-cryptic statements may have borne.
-
-Somewhat similar is the situation respecting Digges. His son makes
-reference to a Ms. of Roger Bacon as the source of the marvels he
-describes. The whole account, however, strongly suggests experiments
-with the _camera obscura_ rather than with the telescope.
-
-The most that can be said with reference to any of the three is that,
-if he by any chance fell upon the combination of lenses that gave
-telescopic vision, he failed to set down the facts in any form that
-could be or was of use to others. There is no reason to believe that
-the Dutch discovery, important as it was, had gone beyond the empirical
-observation that a common convex spectacle lens and a concave one of
-relatively large curvature could be placed in a tube, convex ahead,
-at such a distance apart as to give a clear enlarged image of distant
-objects.
-
-It remained for Galileo (1564-1647) to grasp the general principles
-involved and to apply them to a real instrument of research. It was in
-May 1609 that, on a visit to Venice, he heard reports that a Belgian
-had devised an instrument which made distant objects seem near, and
-this being quickly confirmed by a letter from Paris he awakened to the
-importance of the issue and, returning to Padua, is said to have solved
-the problem the very night of his arrival.
-
-Next day he procured a plano-convex and a plano-concave lens, fitted
-them to a lead tube and found that the combination magnified three
-diameters, an observation which indicates about what it was possible
-to obtain from the stock of the contemporary spectacle maker.[2] The
-relation between the power and the foci of the lenses he evidently
-quickly fathomed for his next recorded trial reached about eight
-diameters.
-
- [2] The statement by Galileo that he “fashioned” these first lenses
- can hardly be taken literally if his very speedy construction is to be
- credited.
-
-With this instrument he proceeded to Venice and during a month’s stay,
-August, 1609, exhibited it to the senators of the republic and throngs
-of notables, finally disclosing the secret of its construction and
-presenting the tube itself to the Doge sitting in full council. This
-particular telescope was about twenty inches long and one and five
-eighths inches in aperture, showing plainly that Galileo had by this
-time found, or more likely made, an eye lens of short focus, about
-three inches, quite probably using a well polished convex lens of the
-ordinary sort as objective.
-
-[Illustration: _Lodge “Pioneers of Science.”_ FIG. 3.—Galileo.]
-
-Laden with honors he returned to Padua and settled down to the hard
-work of development, grinding many lenses with his own hands and
-finally producing the instrument magnifying some 32 times, with which
-he began the notable succession of discoveries that laid the foundation
-of observational astronomy. This with another of similar dimensions is
-still preserved at the Galileo Museum in Florence, and is shown in the
-Frontispiece. The larger instrument is forty-nine inches long and an
-inch and three quarters aperture, the smaller about thirty-seven inches
-long and of an inch and five-eighths aperture. The tubes are of paper,
-the glasses still remain, and these are in fact the first astronomical
-telescopes.
-
-Galileo made in Padua, and after his return to Florence in the autumn
-of 1610, many telescopes which found their way over Europe, but quite
-certainly none of power equalling or exceeding these.
-
-In this connection John Greaves, later Savilian Professor of Astronomy
-at Oxford, writing from Sienna in 1639, says: “Galileus never made but
-two good glasses, and those were of old Venice glass.” In these best
-telescopes, however, the great Florentine had clearly accomplished a
-most workmanlike feat. He had brought the focus of his eye lens down to
-that usual in modern opera glasses, and has pushed his power about to
-the limit for simple lenses thus combined.
-
-The lack of clear and homogeneous glass, the great difficulty
-of forming true tools, want of suitable commercial abrasives,
-impossibility of buying sheet metals or tubing (except lead), and
-default of now familiar methods of centering and testing lenses, made
-the production of respectably good instruments a task the difficulty of
-which it is hard now to appreciate.
-
-The services of Galileo to the art were of such profound importance,
-that his form of instrument may well bear his name, even though his
-eyes were not the first that had looked through it. Such, too, was the
-judgment of his contemporaries, and it was by the act of his colleagues
-in the renowned Acaddemia dei Lincei, through the learned Damiscianus,
-that the name “Telescope” was devised and has been handed down to us.
-
-A serious fault of the Galilean telescope was its very small field of
-view when of any considerable power. Galileo’s largest instrument had
-a field of but 7′15″, less than one quarter the moon’s diameter. The
-general reason is plain if one follows the rays through the lenses as
-in Fig. 4 where _AB_ is the distant object, _o_ the objective, _e_ the
-eye lens, _ab_ the real image in the absence of _e_, and _a′b′_ the
-virtual magnified image due to _e_.
-
-It will be at once seen that the axes of the pencils of rays from
-all parts of the object, as shown by the heavy lines, act as if they
-diverged from the optical center of the objective, but diverging
-still more by refraction through the concave eye lens _e_, fall
-mostly outside the pupil of the observer’s eye. In fact the field is
-approximately measured by the angle subtended by the pupil from the
-center of _o_.
-
-To the credit of the Galilean form may be set down the convenient
-erect image, a sharp, if small, field somewhat bettered by a partial
-compensation of the aberrations of the objective by the concave eye
-lens, and good illumination. For a distant object the lenses were
-spaced at the difference of their focal lengths, and the magnifying
-power was the ratio of these, _f_{o}/f_{e}_.
-
-[Illustration: FIG. 4.—Diagram of Galileo’s Telescope.]
-
-But the difficulty of obtaining high power with a fairly sizeable
-field was ultimately fatal and the type now survives only in the
-form of opera and field glasses, usually of 2 to 5 power, and in an
-occasional negative eye lens for erecting the image in observatory
-work. Practically all the modern instruments have achromatic objectives
-and commonly achromatic oculars.
-
-[Illustration: FIG. 5.—Diagram of Kepler’s Telescope.]
-
-The necessary step forward was made by Johann Kepler (1571-1630), the
-immortal discoverer of the laws of planetary motion. In his _Dioptrice_
-(1611) he set forth the astronomical telescope, substantially, save for
-the changes brought by achromatism, as it has been used ever since.
-His arrangement was that of Fig. 5 in which the letters have the same
-significance as in Fig. 4.
-
-There are here three striking differences from the Galilean form.
-There is a real image in the front focus of the eye lens _e_, the rays
-passing it are refracted inwards instead of outwards, to the great
-advantage of the field, and any object placed in the image plane will
-be magnified together with the image. The first two points Kepler
-fully realized, the third he probably did not, though it is the basis
-of the micrometer. The lenses _o_ and _e_ are obviously spaced at the
-sum of their focal lengths, and as before the magnifying power is the
-ratio of these lengths, the visible image being inverted.
-
-Kepler, so far as known, did not actually use the new telescope, that
-honor falling about half a dozen years later, to Christopher Scheiner,
-a Jesuit professor of mathematics at Ingolstadt, best known as a very
-early and most persistent, not to say verbose, observer of sun spots.
-His _Rosa Ursina_ (1630) indicates free use of Kepler’s telescope for
-some years previously, in just what size and power is uncertain.[3]
-Fontana of Naples also appears to have been early in the field.
-
- [3] Scheiner also devised a crude parallactic mount which he used
- in his solar observations, probably the first European to grasp the
- principle of the equatorial. It was only near the end of the century
- that Roemer followed his example, and both had been anticipated by
- Chinese instruments with sights.
-
-But the new instrument despite its much larger field and far greater
-possibilities of power, brought with it some very serious problems.
-With increased power came greatly aggravated trouble from spherical
-aberration and chromatic aberration as well, and the additive
-aberrations of the eye lens made matters still worse. The earlier
-Keplerian instruments were probably rather bad if the drawings of
-Fontana from 1629 to 1636 fairly represent them.
-
-If one may judge from the course of developments, the first great
-impulse to improvement came with the publication of Descartes’
-(1596-1650) study of dioptrics in 1637. Therein was set forth much of
-the theory of spherical aberration and astronomers promptly followed
-the clues, practical and impractical, thus disclosed.
-
-Without going into the theory of aberrations the fact of importance
-to the improvement of the early telescope is that the longitudinal
-spherical aberration of any simple lens is directly proportional to its
-thickness due to curvature. Hence, other things being equal, the longer
-the focus for the same aperture the less the spherical aberration both
-absolutely and relatively to the image. Further, although Descartes
-knew nothing of chromatic aberration, and the colored fringe about
-objects seen through the telescope must then have seemed altogether
-mysterious, it, also, was greatly relieved by lengthening the focus.
-
-For the chromatic circle produced by a simple lens of given diameter
-has a radial width substantially irrespective of the focal length. But
-increasing the focal length increases in exact proportion the size
-of the image, correspondingly decreasing the relative effect of the
-chromatic error.
-
-Descartes also suggested several designs of lenses which would be
-altogether free of spherical aberration, formed with elliptical or
-hyperbolic curvature, and for some time fruitless efforts were made to
-realize this in practice. It was in fact to be near a century before
-anyone successfully figured non-spherical surfaces. It was spherical
-quite as much as chromatic aberration that drove astronomers to long
-telescopes.
-
-Meanwhile the astronomical telescope fell into better hands than those
-of Scheiner. The first fully to grasp its possibilities was William
-Gascoigne, a gallant young gentleman of Middleton, Yorkshire, born
-about 1620 (some say as early as 1612) and who died fighting on the
-King’s side at Marston Moor, July 2, 1644. To him came as early as
-1638 the inspiration of utilizing the real focus of the objective for
-establishing a telescopic sight.
-
-[Illustration: FIG. 6.—Diagram of Terrestrial Ocular.]
-
-This shortly took the form of a genuine micrometer consisting of a pair
-of parallel blades in the focus, moved in opposite directions by a
-screw of duplex pitch, with a scale for whole revolutions, and a head
-divided into 100 parts for partial revolutions. With this he observed
-much from 1638 to 1643, measured the diameters of sun, moon and planets
-with a good degree of precision, and laid the foundations of modern
-micrometry. He was equipped by 1639 with what was then called a large
-telescope.
-
-His untimely death, leaving behind an unpublished treatise on optics,
-was a grave loss to science, the more since the manuscript could not be
-found, and, swept away by the storms of war, his brilliant work dropped
-out of sight for above a score of years.
-
-Meanwhile De Rheita (1597-1660), a Capuchin monk, and an industrious
-and capable investigator, had been busy with the telescope, and in
-1645 published at Antwerp a somewhat bizarre treatise, dedicated to
-Jesus Christ, and containing not a little practical information. De
-Rheita had early constructed binoculars, probably quite independently,
-had lately been diligently experimenting with Descartes’ hyperbolic
-lens, it is needless to say without much success, and was meditating
-work on a colossal scale—a glass to magnify 4,000 times.
-
-But his real contribution to optics was the terrestrial ocular. This
-as he made it is shown in Fig. 6 where _a b_ is the image formed by
-the objective in front of the eye lens r, s and t two equal lenses
-separated by their focal lengths and _a′ b′_ the resultant reinverted
-image. This form remained in common use until improved by Dolland more
-than a century later.
-
-[Illustration: FIG. 7.—Johannes Hevelius.]
-
-A somewhat earlier form ascribed to Father Scheiner had merged the two
-lenses forming the inverting system of Fig. 6, into a single lens used
-at its conjugate foci.
-
-Closely following De Rheita came Johannes Hevelius (1611-1687) of
-Danzig, one of the really important observers of the seventeenth
-century. His great treatise _Selenographia_ published in 1647 gives us
-the first systematic study of the moon, and a brief but illuminating
-account of the instruments of the time and their practical construction.
-
-At this time the Galilean and Keplerian forms of telescope were in
-concurrent use and Hevelius gives directions for designing and making
-both of them. Apparently the current instruments were not generally
-above five or six feet long and from Hevelius’ data would give not
-above 30 diameters in the Galilean form. There is mention, however, of
-tubes up to 12 feet in length, and of the advantage in clearness and
-power of the longer focus plano-convex lens. Paper tubes, evidently
-common, are condemned, also those of sheet iron on account of their
-weight, and wood was to be preferred for the longer tubes.
-
-Evidently Hevelius had at this time no notion of the effect of the
-plano-convex form of lens as such in lessening aberration, but he
-mentions a curious form of telescope, actually due to De Rheita, in
-which the objective is double, apparently of two plano-convex lenses,
-the weaker ahead, and used with a concave eye lens. If properly
-proportioned such a doublet would have less than a quarter the
-spherical aberration of the equivalent double convex lens.
-
-Hevelius also mentions the earlier form of re-inverting telescope above
-referred to, and speaks rather highly of its performance. To judge from
-his numerous drawings of the moon made in 1643 and 1644, his telescopes
-were much better than those of Scheiner and Fontana, but still woefully
-lacking in sharp definition.
-
-Nevertheless the copper plates of the _Selenographia_, representing
-every phase of the moon, placed the lunar details with remarkable
-accuracy and formed for more than a century the best lunar atlas
-available. One acquires an abiding respect for the patience and skill
-of these old astronomers in seeing how much they did with means utterly
-inadequate.
-
-One may get a fair idea of the size, appearance, and mounting of
-telescopes in this early day from Fig. 8, which shows a somewhat
-advanced construction credited by Hevelius to a suggestion in
-Descartes’ _Dioptrica_. Appearances indicate that the tube was
-somewhere about six feet long, approximately two inches in aperture,
-and that it had a draw tube for focussing. The offset head of the mount
-to allow observing near the zenith is worth an extra glance.
-
-Incidentally Hevelius, with perhaps pardonable pride, also explains the
-“Polemoscope,” a little invention of his own, made, he tells us, in
-1637. It is nothing else than the first periscope, constructed as shown
-in Fig. 9, a tube _c_ with two right angled branches, a fairly long
-one _e_ for the objective _f_, a 45° mirror at _g_, another at _a_,
-and finally the concave ocular at _b_. It was of modest size, of tubes
-1⅔ inch in diameter, the longer tube being 22 inches and the upper
-branch 8 inches, a size well suited for trench or parapet.
-
-[Illustration: FIG. 8.—A Seventh Century Astronomer and his Telescope.]
-
-Even in these days of his youth Hevelius had learned much of practical
-optics as then known, had devised and was using very rational methods
-of observing sun-spots by projection in a darkened room, and gives
-perhaps the first useful hints at testing telescopes by such solar
-observations and on the planets. He was later to do much in the
-development and mounting of long telescopes and in observation,
-although, while progressive in other respects, he very curiously never
-seemed to grasp the importance of telescopic sights and consistently
-refused to use them.
-
-Telescope construction was now to fall into more skillful hands.
-Shortly after 1650 Christian Huygens (1629-1695), and his accomplished
-brother Constantine awakened to a keen interest in astronomy and
-devised new and excellent methods of forming accurate tools and of
-grinding and polishing lenses.
-
-[Illustration: FIG. 9.—The first Periscope.]
-
-By 1655 they had completed an instrument of 12 feet focus with which
-the study of Saturn was begun, Titan the chief satellite discovered,
-and the ring recognized. Pushing further, they constructed a telescope
-of 23 feet focal length and 2⅓ inches aperture, with which four
-years later Christian Huygens finally solved the mystery of Saturn’s
-ring.
-
-Evidently this glass, which bore a power of 100, was of good defining
-quality, as attested by a sketch of Mars late in 1695 showing plainly
-Syrtis Major, from observation of which Huygens determined the rotation
-period to be about 24 hours.
-
-The Huygens brothers were seemingly the first fully to grasp the
-advantage of very long focus in cutting down the aberrations, the
-aperture being kept moderate. Their usual proportions were about as
-indicated above, the aperture being kept somewhere nearly as the square
-root of the focus in case of the larger glasses.
-
-In the next two decades the focal length of telescopes was pushed
-by all hands to desperate extremes. The Huygens brothers extended
-themselves to glasses up to 210 feet focus and built many shorter ones,
-a famous example of which, of 6 inches aperture and 123 feet focal
-length, presented to the Royal Society, is still in its possession.
-Auzout produced even longer telescopes, and Divini and Campani,
-in Rome, of whom the last named made Cassini’s telescopes for the
-Observatory of Paris, were not far behind. The English makers were
-similarly busy, and Hevelius in Danzig was keeping up the record.
-
-[Illustration: FIG. 10.—Christian Huygens.]
-
-Clearly these enormously long telescopes could not well be mounted
-in tubes and the users were driven to aerial mountings, in which the
-objective was at the upper end of a spar or girder and the eye piece at
-the lower. Figure 11 shows an actual construction by Hevelius for an
-objective of 150 feet focal length.
-
-In this case the main support was a T beam of wooden planks well braced
-together. Additional stiffness was given by light wooden diaphragms
-at short intervals with apertures of about 8 inches next to the
-objective, and gradually increasing downwards. The whole was lined up
-by equalizing tackle in the vertical plane, and spreaders with other
-tackle at the joints of the 40foot sections of the main beam. The mast
-which supported the whole was nearly 90 feet high.
-
-So unwieldly and inconvenient were these long affairs that, quite apart
-from their usual optical imperfections, it is little wonder that they
-led to no results commensurate with their size. In fact nearly all the
-productive work was done with telescopes from 20 to 35 feet long, with
-apertures roughly between 2 and 3 inches.
-
-[Illustration: FIG. 11.—Hevelius’ 150-foot Telescope.]
-
-Dominique Cassini to be sure, scrutinizing Saturn in 1684 with
-objectives by Campani, of 100 and 136 feet focus picked up the
-satellites Tethys and Dione, but he had previously found Iapetus with
-a 17-foot glass, and Rhea with one of 34 feet. The longer glasses
-above mentioned had aerial mounts but the smaller ones were in tubes
-supported on a sort of ladder tripod. A 20-foot objective, power 90,
-gave Cassini the division in Saturn’s ring.
-
-A struggle was still being kept up for the non-spherical curves urged
-by Descartes. It is quite evident that Huygens had a go at them,
-and Hevelius thought at one time that he had mastered the hyperbolic
-figure, but his published drawings give no indication that he had
-reduced spherical aberration to any perceptible degree. At this time
-the main thing was to get good glass and give it true figure and
-polish, in which Huygens and Campani excelled, as the work on Saturn
-witnesses.
-
-These were the days of the dawn of popular astronomy and many a
-gentleman was aroused to at least a casual interest in observing the
-Heavens. Notes Pepys in his immortal _Diary_: “I find Reeves there, it
-being a mighty fine bright night, and so upon my leads, though very
-sleepy, till one in the morning, looking on the moon and Jupiter, with
-this twelve foot glass, and another of six foot, that he hath brought
-with him to-night, and the sights mighty pleasant, and one of the
-glasses I will buy.”
-
-Little poor Pepys probably saw, by reason of his severe astigmatism,
-but astronomy was in the air with the impulse that comes to every
-science after a period of brilliant discovery. Another such stimulus
-came near the end of the eighteenth century, with the labors of Sir
-William Herschel.
-
-Just at this juncture comes one of the interesting episodes of
-telescopic history, the ineffectual and abandoned experiments on
-reflecting instruments.
-
-[Illustration: FIG. 12.—Gregory’s Diagram of his Telescope.]
-
-In 1663 James Gregory (1638-1675) a famous Scottish mathematician,
-published his _Optica Promota_, in which he described the rather
-elegant construction which bears his name, a perforated parabolic
-mirror with an elliptical mirror forward of the focus returning an
-image to the ocular through the perforation. It was convenient in that
-it gave an erect image, and it was sound theoretically, and, as the
-future proved, practically, but the curves were quite too much for the
-contemporary opticians. Figure 12 shows the diagrammatic construction
-as published.
-
-The next year Gregory started Reive, a London optician, doubtless the
-same mentioned by Pepys, on the construction of a 6 foot telescope.
-This rather ambitious effort failed of material success through the
-inability of Reive to give the needed figures to the mirrors,[4] and of
-it nothing further appears until the ingenious Robert Hooke (1635-1703)
-executed in 1674 a Gregorian, apparently without any notable results.
-There is a well defined tradition that Gregory himself was using one in
-1675, at the time of his death, but the invention then dropped out of
-sight.
-
- [4] He attempted to polish them on cloth, which in itself was
- sufficient to guarantee failure.
-
-No greater influence on the art attended the next attempt at a
-reflector, by Isaac Newton (1643-1727). This was an early outcome of
-his notable discovery of the dispersion of light by prisms, which led
-him to despair of improving refracting telescopes and turned his mind
-to reflectors.
-
-Unhappily in an experiment to determine whether refraction and
-dispersion were proportional he committed the singular blunder of
-raising the refractive index of a water-filled prism to equality
-with glass by dissolving sugar of lead in it. Without realizing the
-impropriety of thus varying two quite unknown quantities at once in
-his crucial experiment, he promptly jumped to the conclusion that
-refraction and dispersion varied in exact proportion in all substances,
-so that if two prisms or lenses dispersed light to the same extent they
-must also equally refract it. It would be interesting to know just how
-the fact of his bungling was passed along to posterity. As a naïve
-apologist once remarked, it was not to be found in his “_Optics_.” But
-Sir David Brewster and Sir John Herschel, both staunch admirers of the
-great philosopher, state the fact very positively. If one may hazard a
-guess it crept out at Cambridge and was passed along, perhaps to Sir
-William Herschel, via the unpublished history of research that is rich
-in picturesque details of the mare’s nests of science. At all events a
-mistake with a great name behind it carries far, and the result was to
-delay the production of the achromatic telescope by some three quarters
-of a century.
-
-Turning from refractors he presented to the Royal Society just after
-his election as Fellow in 1672, the little six-inch model of his device
-which was received with acclamation and then lay on the shelf without
-making the slightest impression on the art, for full half a century.
-
-Newton, by dropping the notion of direct view through the tube,
-hit upon by far the simplest way of getting the image outside it,
-by a plane mirror a little inside focus and inclined at 45°, but
-injudiciously abandoned the parabolic mirror of his original paper
-on dispersion. His invention therefore as actually made public was
-of the combination with a spherical concave mirror of a plane mirror
-of elliptical form at 45°, a construction which in later papers he
-defended as fully adequate.[5]
-
- [5] In Fig 13, _A_ is the support of the tube and focussing screw, _B_
- the main mirror, an inch in diameter, _CD_ the oblique mirror, _E_ the
- principal focus, _F_ the eye lens, and _G_ the member from which the
- oblique mirror is carried.
-
-[Illustration: FIG. 13.—Newton’s Model of his Reflector.]
-
-His error in judgment doubtless came from lack of practical
-astronomical experience, for he assumed that the whole real trouble
-with existing telescopes was chromatic aberration, which in fact
-worried the observer little more than the faults due to other causes,
-since the very low luminosity toward the ends of the spectrum
-enormously lessens the indistinctness due to dispersion.
-
-As a matter of fact the long focus objective of small aperture did very
-creditable work, and its errors would not compare unfavorably with
-those of a spherical concave mirror of the wide aperture planned by
-Newton. Had he actually made one of his telescopes of fair dimensions
-and power the definition would infallibly have been wrecked by the
-aberrations due to spherical figure.[6]
-
- [6] In fact a “four foot telescope of Mr. Newton’s invention” brought
- before the Royal Society two weeks after his original paper, proved
- only fair in quality, was returned somewhat improved at the next
- meeting, and then was referred to Mr. Hooke to be perfected as far as
- might be, after which nothing more was heard of it.
-
-[Illustration: FIG. 14.—De Bercé’s sketch of Cassegrain’s Telescope.]
-
-It is quite likely that appreciation of this, and the grave doubts
-of both Newton and Huygens as to obtaining a proper parabolic curve
-checked further developments. About the beginning of the year 1672
-M. Cassegrain communicated to M. de Bercé a design for a reflecting
-telescope, which eventually found its way into the _Philosophical
-Transactions_ of May in that year, after previous publication in the
-_Journal des Sçavans_. Figure 14 shows de Bercé’s rough original
-sketch. It differed from Gregory’s construction in that the latter’s
-elliptical concave mirror placed outside the main focus, was replaced
-by a convex mirror placed inside focus. The image was therefore
-inverted.
-
-The inventor is referred to in histories of science as “Cassegrain,
-a Frenchman.” He was in fact Sieur Guillaume Cassegrain, sculptor in
-the service of Louis Quatorze, modeller and founder of many statues.
-In 1666 he was paid 1200 livres for executing a bust of the King
-modelled by Bertin, and later made many replicas from the antique for
-the decoration of His Majesty’s gardens at Versailles. He disappeared
-from the royal records in 1684 and probably died within a year or two
-of that date.
-
-At the period here concerned he apparently, like de Bercé, was of
-Chartres. Familiar with working bronzes and with the art of the
-founder, he was a very likely person to have executed specula. Although
-there is no certainty that he actually made a telescope, a contemporary
-reference in the _Journal des Sçavans_ speaks of his invention as a
-“petite lunette d’approche,” and one does not usually suggest the
-dimensions of a thing non-existent. How long he had been working upon
-it prior to the period about the beginning of 1672 when he disclosed
-the device to de Bercé is unknown.
-
-Probably Newton’s invention was the earlier, but the two were
-independent, and it was somewhat ungenerous of Newton to criticise
-Cassegrain, as he did, for using spherical mirrors, on the strength of
-de Bercé’s very superficial description, when he himself considered the
-parabolic needless.
-
-However, nothing further was done, and the devices of Gregory, Newton
-and Cassegrain went together into the discard for some fifty years.
-
-These early experiments gave singularly little information about
-material for mirrors and methods of working it, so little that those
-who followed, even up to Lord Rosse, had to work the problems out
-for themselves. We know from his original paper that Newton used
-bell-metal, whitened by the addition of arsenic, following the lore of
-the alchemists.
-
-These speculative worthies used to alloy copper with arsenic, thinking
-that by giving it a whitish cast they had reached a sort of half way
-point on the road to silver. Very silly at first thought, but before
-the days of chemical analysis, when the essential properties of the
-metals were unknown, the way of the scientific experimenter was hard.
-
-What the “steely matter, imployed in London” of which Newton speaks in
-an early paper was, we do not know—very likely one of the hard alloys
-much richer in tin than is ordinary bell-metal. Nor do we know to what
-variety of speculum metal Huygens refers in his correspondence with
-Newton.
-
-As to methods of working it Newton only disclosed his scheme of
-pitch-polishing some thirty years after this period, while it is
-a matter of previous record, that Huygens had been in the habit of
-polishing his true tools on pitch from some date unknown. Probably
-neither of them originated the practice. Opticians are a peculiarly
-secretive folk and shop methods are likely to be kept for a long time
-before they leak out or are rediscovered.
-
-Modern speculum metal is substantially a definite compound of four
-atoms copper and one tin (SnCu_{4}), practically 68 per cent copper and
-32 per cent tin, and is now, as it was in all previous modifications, a
-peculiarly mean material to cast and work. Thus exit the reflector.
-
-The long telescope continued to grow longer with only slow improvement
-in quality, but the next decade was marked by the introduction of
-Huygens’ eyepiece, an immense improvement over the single lens which
-had gone before, and with slight modifications in use today.
-
-[Illustration: FIG. 15.—Diagram of Huygens’ Eyepiece.]
-
-This is shown in section in Fig. 15. It consists of a field lens _A_,
-plano-convex, and an eye lens _B_ of one-third the focal length, the
-two being placed at the difference of their focal lengths apart with
-(in later days) a stop half way between them. The eye piece is pushed
-inside the main focus until the rays which fall on the field lens focus
-through the eye lens.
-
-The great gain from Huygens’ view-point was a very much enlarged
-clear field—about a four-fold increase—and in fact the combination is
-substantially achromatic, particularly important now when high power
-oculars are needed.
-
-Still larger progress was made in giving the objective a better form
-with respect to spherical aberration, the “crossed” lens being rather
-generally adopted. This form is double convex, and if of ordinary
-glass, with the rear radius six times the front radius, and gives even
-better results than a plano-convex in its best position-plane side to
-the rear. Objectives were rated on focal length for the green rays,
-that is, the bright central part of the spectrum, the violet rays of
-course falling short and the red running beyond.
-
-To give customary dimensions, a telescope of 3 inches aperture, with
-magnifying power of 100, would be of about 30 feet focus with the
-violet nearly 6 inches short and the red a similar amount long. It is
-vast credit to the early observers that with such slender means they
-did so much. But in fact the long telescope had reached a mechanical
-_impasse_, so that the last quarter of the seventeenth century and the
-first quarter of the next were marked chiefly by the development of
-astronomy of position with instruments of modest dimensions.
-
-[Illustration: FIG. 16.—The First Reflector. John Hadley, 1722.]
-
-In due time the new order came and with astounding suddenness. Just
-at the end of 1722 James Bradley (1692-1762) measured the diameter of
-Venus with an objective of 212 ft. 3 in. focal length; about three
-months later John Hadley (1682-1744) presented to the Royal Society
-the first reflecting telescope worthy the name, and the old order
-practically ended.
-
-John Hadley should in fact be regarded as the real inventor of the
-reflector in quite the same sense that Mr. Edison has been held, _de
-jure_ and _de facto_, the inventor of the incandescent electric lamp.
-Actually Hadley’s case is the stronger of the two, for the only things
-which could have been cited against him were abandoned experiments
-fifty years old. Moreover he took successfully the essential step at
-which Gregory and Newton had stumbled or turned back—parabolizing his
-speculum.
-
-The instrument he presented was of approximately 6 inches aperture and
-62⅝ inches focal length, which he had made and tested some three
-years previously; on a substantial alt-azimuth mount with slow motions.
-He used the Newtonian oblique mirror and the instrument was provided
-with both convex and concave eye lenses, with magnifications up to
-about 230.
-
-The whole arrangement is shown in Fig. 16 which is for the most part
-self explanatory. It is worth noting that the speculum is positioned
-in the wooden tube by pressing it forward against three equidistant
-studs by three corresponding screws at the rear, that a slider moved
-by a traversing screw in a wide groove carries the small mirror and
-the ocular, that there is a convenient door for access to the mirror,
-and also a suitable finder. The motion in altitude is obtained by a
-key winding its cord against gravity. That in azimuth is by a roller
-support along a horizontal runway carried by an upright, and is
-obtained by the key with a cord pull off in one direction, and in the
-other, by springs within the main upright, turning a post of which the
-head carries cheek pieces on which rest the trunnions of the tube.
-
-A few months later this telescope was carefully tested, by Bradley and
-the Rev. J. Pound, against the Huygens objective of 123 feet focus
-possessed by the Royal Society, and with altogether satisfactory
-results. Hadley’s reflector would show everything which could be
-seen by the long instrument, bearing as much power and with equal
-definition, though somewhat lessened light. In particular they saw
-all five satellites of Saturn, Cassini’s division, which the inventor
-himself had seen the previous year even in the northern edge of the
-ring beyond the planet, and the shadow of the ring upon the ball.
-
-The casting of the large speculum was far from perfect, with many spots
-that failed to take polish, but the figure must have been rather good.
-A spherical mirror of these dimensions would give an aberration blur
-something like twenty times the width of Cassini’s division, and the
-chance of seeing all five satellites with it would be negligibly small.
-
-Further, Hadley presently disclosed to others not only the method he
-used in polishing and parabolizing specula, but his method of testing
-for true figure by the aberrations disclosed as he worked the figure
-away from the sphere—a scheme frequently used even to this day.
-
-The effect of Hadley’s work was profound. Under his guidance others
-began to produce well figured mirrors, in particular Molyneux and
-Hawksbee; reflecting telescopes became fairly common; and in the
-beginning of the next decade James Short, (1710-1768), possessed of
-craftsmanship that approached wizardry, not only fully mastered the
-art of figuring the paraboloid, but at once took up the Gregorian
-construction with its ellipsoidal small mirror, with much success.
-
-His specula were of great relative aperture, F/4 to F/6, and from the
-excellent quality of his metal some of them have retained their fine
-polish and definition after more than a century. He is said to have
-gone even up to 12 inches in diameter. His exact methods of working
-died with him. Even his tools he ordered to be destroyed before his
-death.
-
-The Cassegrain reflector, properly having a parabolic large mirror and
-a hyperbolic small one, seems very rarely to have been made in the
-eighteenth century, though one certainly came into the hands of Ramsden
-(1735-1800).
-
-Few refractors for astronomical use were made after the advent of the
-reflector, which was, and is, however, badly suited for the purposes of
-a portable spy-glass, owing to trouble from stray light. The refractor
-therefore permanently held its own in this function, despite its length
-and uncorrected aberrations.
-
-Relief was near at hand, for hardly had Short started on his notable
-career when Chester Moor Hall, Esq. (1704-1771) a gentleman of Essex,
-designed and caused to be constructed the first achromatic telescope,
-with an objective of crown and flint glass. He is stated to have been
-studying the problem for several years, led to it by the erroneous
-belief (shared by Gregory long before) that the human eye was an
-example of an achromatic instrument.
-
-Be this as it may Hall had his telescopes made by George Bast of
-London at least as early as 1733, and according to the best available
-evidence several instruments were produced, one of them of above 2
-inches aperture on a focal length of about 20 inches (F/8) and further,
-subsequently such instruments were made and sold by Bast and other
-opticians.
-
-These facts are clear and yet, with knowledge of them among London
-workmen as well as among Hall’s friends, the invention made no
-impression, until it was again brought to light, and patented, by the
-celebrated John Dolland (1706-1761) in the year 1758.
-
-Physical considerations give a clue to this singular neglect. The only
-glasses differing materially in dispersion available in Hall’s day
-were the ordinary crown, and such flint as was in use in the glass
-cutting trade,—what we would now know as a light flint, and far from
-homogeneous at that.
-
-[Illustration: _Lodge “Pioneers of Science.”_ FIG. 17.—John Dolland.]
-
-Out of such material it was practically very hard (as the Dollands
-quickly found) to make a double objective decently free from spherical
-aberration, especially for one working, as Hall quite assuredly did,
-by rule of thumb. With the additional handicap of flint full of faults
-it is altogether likely that these first achromatics, while embodying
-the correct principles, were not good enough to make effective headway
-against the cheaper and simpler spy-glass of the time.
-
-Dolland, although in 1753 he strongly supported Newton’s error in a
-Royal Society paper against Euler’s belief in achromatism, shifted his
-view a couple of years later and after a considerable period of skilful
-and well ordered experimenting published his discovery of achromatism
-early in 1758, for which a patent was granted him April 19, while in
-the same year the Royal Society honored him with the Copley medal. From
-that time until his death, late in 1761, he and his son Peter Dolland
-(1730-1820) were actively producing achromatic glasses.
-
-The Dollands were admirable craftsmen and their early product was
-probably considerably better than were Hall’s objectives but they felt
-the lack of suitable flint and soon after John Dolland’s death, about
-1765, the son sought relief in the triple objective of which an early
-example is shown in Fig. 18, and which, with some modifications, was
-his standard form for many years.
-
-[Illustration: FIG. 18.—Peter Dolland’s Triple Objective.]
-
-Other opticians began to make achromatics, and, Peter Dolland having
-threatened action for infringement, a petition was brought by 35
-opticians of London in 1764 for the annulment of John Dolland’s patent,
-alleging that he was not the original inventor but had knowledge of
-Chester Moor Hall’s prior work. In the list was George Bast, who in
-fact did make Hall’s objectives twenty five years before Dolland, and
-also one Robert Rew of Coldbath Fields, who claimed in 1755 to have
-informed Dolland of the construction of Hall’s objective.
-
-This was just the time when Dolland came to the right about face on
-achromatism, and it may well be that from Rew or elsewhere he may
-have learned that a duplex achromatic lens had really been produced.
-But his Royal Society paper shows that his result came from honest
-investigations, and at worst he is in about the position of Galileo a
-century and a half before.
-
-The petition apparently brought no action, perhaps because Peter
-Dolland next year sued Champneys, one of the signers, and obtained
-judgment. It was in this case that the judge (Lord Camden) delivered
-the oft quoted dictum: “It was not the person who locked up his
-invention in his scrutoire that ought to profit by a patent for
-such invention, but he who brought it forth for the benefit of the
-public.[7]”
-
- [7] Commonly, but it appears erroneously, ascribed to Lord Mansfield.
-
-This was sound equity enough, assuming the facts to be as stated, but
-while Hall did not publish the invention admittedly made by him, it had
-certainly become known to many. Chester Moor Hall was a substantial and
-respected lawyer, a bencher of the Inner Temple, and one is inclined
-to think that his alleged concealment was purely constructive, in his
-failing to contest Dolland’s claim.
-
-Had he appeared at the trial with his fighting blood up, there is every
-reason to believe that he could have established a perfectly good
-case of public use quite aside from his proof of technical priority.
-However, having clearly lost his own claims through _laches_, he not
-improbably was quite content to let the tradesmen fight it out among
-themselves. Hall’s telescopes were in fact known to be in existence as
-late as 1827.
-
-As the eighteenth century drew toward its ending the reflecting
-telescope, chiefly in the Gregorian form, held the field in
-astronomical work, the old refractor of many draw tubes was the
-spy-glass of popular use, and the newly introduced achromatic was the
-instrument of “the exclusive trade.” No glass of suitable quality for
-well corrected objectives had been produced, and that available was not
-to be had in discs large enough for serious work. A 3-inch objective
-was reckoned rather large.
-
-
-
-
-CHAPTER II
-
-THE MODERN TELESCOPE
-
-
-The chief link between the old and the new, in instrumental as well
-as observational astronomy, was Sir William Herschel (1738-1822). In
-the first place he carried the figuring of his mirrors to a point not
-approached by his predecessors, and second, he taught by example the
-immense value of aperture in definition and grasp of light. His life
-has never been adequately written, but Miss Clerke’s “_The Herschels
-and Modern Astronomy_” is extremely well worth the reading as a record
-of achievement that knew not the impossible.
-
-[Illustration: _Miss Clerke’s Herschel & Modern Astronomy_
-(_Macmillan_). FIG. 19.—Sir William Herschel.]
-
-He was the son of a capable band-master of Hanover, brought up as a
-musician, in a family of exceptional musical abilities, and in 1757
-jumped his military responsibilities and emigrated to England, to the
-world’s great gain. For nearly a decade he struggled upward in his art,
-taking meanwhile every opportunity for self education, not only in the
-theory of music but in mathematics and the languages, and in 1767 we
-find him settled in fashionable Bath, oboist in a famous orchestra, and
-organist of the Octagon Chapel. His abilities brought him many pupils,
-and ultimately he became director of the orchestra in which he had
-played, and the musical dictator of the famous old resort.
-
-In 1772 came his inspiration in the loan of a 2-foot Gregorian
-reflector, and a little casual star-gazing with it. It was the opening
-of the kingdom of the skies, and he sought to purchase a telescope of
-his own in London, only to find the price too great for his means.
-(Even a 2-foot, of 4½ inches aperture, by Short was listed at
-five-and-thirty guineas.) Then after some futile attempts at making a
-plain refractor he settled down to hard work at casting and polishing
-specula.
-
-Although possessed of great mechanical abilities the difficult
-technique of the new art long baffled him, and he cast and worked some
-200 small discs in the production of his first successful telescopes,
-to say nothing of a still greater number in larger sizes in his
-immediately subsequent career.
-
-As time went on he scored a larger proportion of successes, but at the
-start good figure seems to have been largely fortuitous. Inside of a
-couple of years, however, he had mastered something of the art and
-turned out a 5-foot instrument which seems to have been of excellent
-quality, followed later by a 7-foot (aperture 6¼ inches) even
-better, and then by others still bigger.
-
-The best of Herschel’s specula must have been of exquisite figure. His
-7-foot was tested at Greenwich against one of Short’s of 9½ inches
-aperture much to the latter’s disadvantage. His discovery with the
-7-foot, of the “Georgium Sidus” (Uranus) in 1781 won him immediate fame
-and recognition, beside spurring him to greater efforts, especially in
-the direction of larger apertures, of which he had fully grasped the
-importance.
-
-In 1782 he successfully completed a 12-inch speculum of 20 feet focus,
-followed in 1788 by an 18-inch of the same length. The previous year he
-first arranged his reflector as a “front view” telescope—the so-called
-Herschelian. Up to this time he, except for a few Gregorians, had used
-Newton’s oblique mirror.
-
-The heavy loss of light (around 40 per cent) in the second reflection
-moved him to tilt the main mirror so as to throw the focal point
-to the edge of the aperture where one could look downward upon the
-image through the ocular as shown in Fig. 20. Here _SS_ is the great
-speculum, _O_ the ocular and _i_ the image formed near the rim of the
-tube. In itself the tilting would seriously impair the definition, but
-Herschel wisely built his telescopes of moderate relative aperture
-(F/10 to F/20), so that this difficulty was considerably lessened,
-while the saving of light, amounting to nearly a stellar magnitude, was
-important.
-
-Meanwhile he was hard at work on his greatest mirror, of 48 inches
-clear aperture and 40 feet focal length, the father of the great line
-of modern telescopes. It was finished in the summer of 1789. The
-speculum was 49½ inches in over-all diameter, 3½ inches thick
-and weighed as cast 2118 lbs. The completion of this instrument, which
-would rank as large even today, was made notable by the immediate
-discovery of two new satellites of Saturn, Enceladus and Mimas.
-
-It also proved of very great value in sweeping for nebulæ, but its
-usefulness seems to have been much limited by the flexure of the mirror
-under its great weight, and by its rapid tarnishing. It required
-repolishing, which meant refiguring, at least every two years, a
-prodigious task.[8]
-
- [8] This was probably due not only to unfavorable climate, but to the
- fact that Herschel, with all his ingenuity, does not appear to have
- mastered the casting difficulty, and was constrained to make his big
- speculum of Cu 75 per cent, Sn 25 per cent, a composition working
- rather easily and taking beautiful, but far from permanent, polish.
- He never seems to have used practically the SnCu_{4} formula, devised
- empirically by Mudge (Phil. Trans. _67_, 298), and in quite general
- use thereafter up to the present time.
-
-[Illustration: FIG. 20.—Herschel’s Front View Telescope.]
-
-It was used as a front view instrument and was arranged as shown in
-Fig. 21. Obviously the front view form has against it the mechanical
-difficulty of supporting the observer up to quite the full focal length
-of the instrument in air, a difficulty vastly increased were the
-mount an equatorial one, so that for the great modern reflectors the
-Cassegrain form, looked into axially upward, and in length only a third
-or a quarter of the principal focus, is almost universal.
-
-As soon as the excellent results obtained by Herschel became generally
-known, a large demand arose for his telescopes, which he filled in so
-far as he could spare the time from his regular work, and not the
-least of his services to science was the distribution of telescopes
-of high quality and consequent strong stimulus to general interest in
-astronomy.
-
-Two of his instruments, of 4-and 7-feet focus respectively, fell into
-the worthy hands of Schröter at Lilienthal and did sterling service in
-making his great systematic study of the lunar surface. At the start
-even Herschel’s 7-foot telescope brought 200 guineas, and the funds
-thus won he promptly turned to research.
-
-[Illustration: _Miss Clerke’s Herschel & Modern Astronomy_
-(_Macmillan_). FIG. 21.—Herschel’s Forty-foot Telescope.]
-
-We sometimes think of the late eighteenth century as a time of license
-unbounded and the higher life contemned, but Herschel wakened a general
-interest in unapplied science that has hardly since been equalled
-and never surpassed. Try to picture social and official Washington
-rushing to do honor to some astronomer who by luck had found the
-trans-Neptunian planet; the diplomatic corps crowding his doors, and
-his very way to the Naval Observatory blocked by the limousines of
-the curious and admiring, and some idea may be gained of what really
-happened to the unassuming music master from Bath who suddenly found
-himself famous.
-
-Great as were the advances made by Herschel the reflector was destined
-to fall into disuse for many years. The fact was that the specula had
-to be refigured, as in the case of the great 40-foot telescope, quite
-too often to meet the requirements of the ordinary user, professional
-or amateur. Only those capable of doing their own figuring could keep
-their instruments conveniently in service.
-
-Sir W. Herschel always had relays of specula at hand for his smaller
-instruments, and when his distinguished son, Sir John F. W. Herschel,
-went on his famous observing expedition to the Cape of Good Hope in
-1834-38 he took along his polishing machine and three specula for his
-20-foot telescope. And he needed them indeed, for a surface would
-sometimes go bad even in a week, and regularly became quite useless in
-2 or 3 months.
-
-Makers who used the harder speculum metal, very brittle and scarcely
-to be touched by a file, fared better, and some small mirrors, well
-cared for, have held serviceable polish for many years. Many of these
-instruments of Herschel’s time, too, were of very admirable performance.
-
-Some of Herschel’s own 7-foot telescopes give evidence of exquisite
-figure and he not only commonly used magnifying powers up to some 80
-per inch of aperture, a good stiff figure for a telescope old or new,
-but went above 2,000, even nearly to 6,000 on one of his 6½-inch
-mirrors without losing the roundness of the star image. “Empty
-magnification” of course, gaining no detail whatever, but evidence of
-good workmanship.
-
-Many years later the Rev. W. R. Dawes, the famous English observer, had
-a 5-inch Gregorian, commonly referred to as “The Jewel,” on which he
-used 430 diameters, and pushed to 2,000 on Polaris without distortion
-of the disc. Comparing it with a 5-foot (approximately 4-inch aperture)
-refractor, he reports the Gregorian somewhat inferior in illuminating
-power; “But in sharpness of definition, smallness of discs of stars,
-and hardness of outline of planets it is superior.” All of which shows
-that while methods and material may have improved, the elders did not
-in the least lack skill.
-
-The next step forward, and a momentous one, was to be taken in the
-achromatic refractor. Its general principles were understood, but clear
-and homogeneous glass, particularly flint glass, was not to be had in
-pieces of any size. “Optical glass,” as we understand the term, was
-unknown.
-
-It is a curious and dramatic fact that to a single man was due not only
-the origin of the art but the optical glass industry of the world.
-If the capacity for taking infinite pains be genius, then the term
-rightfully belongs to Pierre Louis Guinand. He was a Swiss artisan
-living in the Canton of Neuchatel near Chaux-de-Fonds, maker of bells
-for repeaters, and becoming interested in constructing telescopes
-imported some flint glass from England and found it bad.
-
-He thereupon undertook the task of making better, and from 1784 kept
-steadily at his experiments, failure only spurring him on to redoubled
-efforts. All he could earn at his trade went into his furnaces, until
-gradually he won success, and his glass began to be heard of; for by
-1799 he was producing flawless discs of flint as much as 6 inches in
-diameter.
-
-What is more, to Guinand is probably due the production of the denser,
-more highly refractive flints, especially valuable for achromatic
-telescopes. The making of optical glass has always been an art rather
-than a science. It is one thing to know the exact composition of a
-glass and quite another to know in what order and proportion the
-ingredients went into the furnace, to what temperature they were
-carried, and for how long, and just how the fused mass must be treated
-to free the products from bubbles and striæ.
-
-Even today, though much has been learned by scientific investigation
-in the past few years, it is far from easy to produce two consecutive
-meltings near enough in refractive power to be treated as optically
-identical, or to produce large discs optically homogeneous. What
-Guinand won by sheer experience was invaluable. He was persuaded in
-1805 to move to Munich and eventually to join forces with Fraunhofer,
-an association which made both the German optical glass industry and
-the modern refractor.
-
-He returned to Switzerland in 1814 and continued to produce perfect
-discs of larger and larger dimensions. One set of 12 inches worked up
-by Cauchoix in Paris furnished what was for some years the world’s
-largest refractor.
-
-Guinaud died in 1824, but his son Henry, moving to Paris, brought
-his treasure of practical knowledge to the glass works there, where
-it has been handed down, in effect from father to son, gaining
-steadily by accretion, through successive firms to the present one of
-Parra-Mantois.
-
-Bontemps, one of the early pupils of Henry Guinand, emigrated to
-England at the Revolution of 1848 and brought the art to the famous
-firm of Chance in Birmingham. Most of its early secrets have long
-been open, but the minute teachings of experience are a tremendously
-valuable asset even now.
-
-[Illustration: FIG. 22.—Dr. Joseph von Fraunhofer, the Father of
-Astrophysics.]
-
-To Fraunhofer, the greatest master of applied optics in the nineteenth
-century, is due the astronomical telescope in substantially its
-present form. Not only did he become under Guinand’s instruction
-extraordinarily skillful in glass making but he practically devised the
-art of working it with mathematical precision on an automatic machine,
-and the science of correctly designing achromatic objectives.
-
-The form which he originated (Fig. 23) was the first in which the
-aberrations were treated with adequate completeness, and, particularly
-for small instruments, is unexcelled even now. The curvatures here
-shown are extreme, the better to show their relations. The front radius
-of the crown is about 2½ times longer than the rear radius, the
-front of the flint is slightly flatter than the back of the crown, and
-the rear of the flint is only slightly convex.
-
-Fraunhofer’s workmanship was of the utmost exactness and it is not
-putting the case too strongly to say that a first class example
-of the master’s craft, in good condition, would compare well in
-color-correction, definition, and field, with the best modern
-instruments.
-
-[Illustration: FIG. 23.]
-
-The work done by the elder Struve at Dorpat with Fraunhofer’s first
-large telescope (9.6 inches aperture and 170 inches focal length) tells
-the story of its quality, and the Königsberg heliometer, the first of
-its class, likewise, while even today some of his smaller instruments
-are still doing good service.
-
-It was he who put in practice the now general convention of a relative
-aperture of about F/15, and standardized the terrestrial eyepiece into
-the design quite widely used today. The improvements since his time
-have been relatively slight, due mainly to the recent production of
-varieties of optical glass unknown a century ago. Fraunhofer was born
-in Straubing, Bavaria, March 6, 1787. Self-educated like Herschel, he
-attained to an extraordinary combination of theoretical and practical
-knowledge that went far in laying the foundations of astrophysics.
-
-The first mapping of the solar spectrum, the invention of the
-diffraction grating and its application to determining the wave
-length of light, the first exact investigation of the refraction
-and dispersion of glass and other substances, the invention of the
-objective prism, and its use in studying the spectra of stars and
-planets, the recognition of the correspondence of the sodium lines to
-the D lines in the sun, and the earliest suggestion of the diffraction
-theory of resolution later worked out by Lord Rayleigh and Professor
-Abbé, make a long list of notable achievements.
-
-To these may be added his perfecting of the achromatic telescope, the
-equatorial mounting and its clockwork drive, the improvement of the
-heliometer, the invention of the stage micrometer, several types of
-ocular micrometers, and the automatic ruling engine.
-
-He died at the height of his creative powers June 7, 1826, and lies
-buried at Munich under the sublime ascription, by none better earned,
-_Approximavit Sidera_.
-
-From Fraunhofer’s time, at the hands of Merz his immediate successor,
-Cauchoix in France, and Tully in England, the achromatic refractor
-steadily won its way. Reflecting telescopes, despite the sensational
-work of Lord Rosse on his 6-foot mirror of 53 feet focus (unequalled
-in aperture until the 6-foot of the Dominion Observatory seventy years
-later), and the even more successful instrument of Mr. Lassell (4 feet
-aperture, 39 feet focus), were passing out of use, for the reason
-already noted, that repolishing meant refiguring and the user had to be
-at once astronomer and superlatively skilled optician.
-
-These large specula, too, were extremely prone to serious flexure
-and could hardly have been used at all except for the equilibrating
-levers devised by Thomas Grubb about 1834, and used effectively on the
-Rosse instrument. These are in effect a group of upwardly pressing
-counterbalanced planes distributing among them the downward component
-of the mirror’s weight so as to keep the figure true in any position of
-the tube.
-
-Such was the situation in the 50’s of the last century, when the
-reflector was quite unexpectedly pushed to the front as a practical
-instrument by almost simultaneous activity in Germany and France. The
-starting point in each was Liebig’s simple chemical method of silvering
-glass, which quickly and easily lays on a thin reflecting film capable
-of a beautiful polish.
-
-The honor of technical priority in its application to silvering
-telescope specula worked in glass belongs to Dr. Karl August Steinheil
-(1801-1870) who produced about the beginning of 1856 an instrument
-of 4-inch aperture reported to have given with a power of 100 a
-wonderfully good image. The publication was merely from a news item in
-the “_Allgemeine Zeitung_” of Augsburg, March 24, 1856, so it is little
-wonder that the invention passed for a time unnoticed.
-
-Early the next year, Feb. 16, 1857, working quite independently,
-exactly the same thing was brought before the French Academy of
-Sciences by another distinguished physicist, Jean Bernard Léon
-Foucault, immortal for his proof of the earth’s rotation by the
-pendulum experiment, his measurement of the velocity of light, and the
-discovery of the electrical eddy currents that bear his name.
-
-[Illustration: FIG. 24.—Dr. Karl August Steinheil. FIG. 25.—Jean
-Bernard Léon Foucault. The Inventors of the Silver-on-Glass Reflector.]
-
-To Foucault, chiefly, the world owes the development of the modern
-silver-on-glass reflector, for not being a professional optician he
-had no hesitation in making public his admirable methods of working
-and testing, the latter now universally employed. It is worth noting
-that his method of figuring was, physically, exactly what Jesse
-Ramsden (1735-1800) had pointed out in 1779, (Phil. Tr. 1779, 427)
-geometrically. One of Foucault’s very early instruments mounted
-equatorially by Sécrétan is shown in Fig. 26.
-
-[Illustration: FIG. 26.—Early Foucault Reflector.]
-
-The immediate result of the admirable work of Steinheil and Foucault
-was the extensive use of the new reflector, and its rapid development
-as a convenient and practical instrument, especially in England in
-the skillful hands of With, Browning, and Calver. Not the least of
-its advantages was its great superiority over the older type in
-light-grasp, silver being a better reflector than speculum metal in
-the ratio of very nearly 7 to 5. From this time on both refractors and
-reflectors have been fully available to the user of telescopes.
-
-In details of construction both have gained somewhat mechanically.
-As we have seen, tubes were often of wood, and not uncommonly the
-mountings also. At the present time metal work of every kind being more
-readily available, tubes and mountings of telescopes of every size are
-quite universally of metal, save for the tripod-legs of the portable
-instruments. The tubes of the smaller refractors, say 3 to 5 inches in
-aperture, are generally of brass, though in high grade instruments this
-is rapidly being replaced by aluminum, which saves considerable weight.
-Tubes above 5 or 6 inches are commonly of steel, painted or lacquered.
-The beautifully polished brass of the smaller tubes, easily damaged
-and objectionably shiny, is giving way to a serviceable matt finish
-in hard lacquer. Mountings, too, are now more often in iron and steel
-or aluminum than in brass, the first named quite universally in the
-working parts, for which the aluminum is rather soft.
-
-The typical modern refractor, even of modest size, is a good bit more
-of a machine than it looks at first glance. In principle it is outlined
-in Fig. 5, in practice it is much more complex in detail and requires
-the nicest of workmanship. In fact if one were to take completely apart
-a well-made small refractor, including its optical and mechanical parts
-one would reckon up some 30 to 40 separate pieces, not counting screws,
-all of which must be accurately fitted and assembled if the instrument
-is to work properly.
-
-[Illustration: FIG. 27.—Longitudinal Section of Modern Refractor.]
-
-Fig. 27 shows such an instrument in section from end to end, as one
-would find it could he lay it open longitudinally.
-
-_A_ is the objective cap covering the objective _B_ in its adjustable
-cell _C_, which is squared precisely to the axis of the main tube _D_.
-Looking along this one finds the first of the diaphragms, _E_.
-
-These are commonly 3 to 6 in number spaced about equally down the tube,
-and are far more important than they look. Their function is not to
-narrow the beam of light that reaches the ocular, but to trap light
-which might enter the tube obliquely and be reflected from its sides
-into the ocular, filling it with stray glare.
-
-No amount of simple blackening will answer the purpose, for even dead
-black paint such as opticians use reflects at very oblique incidence
-quite 10 to 20 per cent of the beam. The importance of both diaphragms
-and thorough blackening has been realized for at least a century and a
-half, and one can hardly lay too much stress upon the matter.
-
-The diaphragms should be so proportioned that, when looking up the
-tube from the edge of an aperture of just the size and position of
-the biggest lens in the largest eyepiece, no part of the edge of the
-objective is cut off, and no part of the side of the tube is visible
-beyond the nearest diaphragm.
-
-Going further down the tube past a diaphragm or two one comes to
-the clamping screws _F_. These serve to hold the instrument to its
-mounting. They may be set in separate bases screwed in place on the
-inside of the tube, or may be set in the two ends of a lengthwise strap
-thus secured. They are placed at the balance point as nearly as may be,
-generally nearer the eye end than the objective.
-
-Then, after one or more diaphragms, comes the guide ring _G_, which
-steadies the main draw tube _H_, and the rack _I_ by which it is moved
-for the focussing in turning the milled head of the pinion _J_. The end
-ring _K_ of the main tube furnishes the other bearing of _H_, and both
-_G_ and _K_ are commonly recessed for accurately fitted cloth lining
-rings _L_, _L_, to give the draw tube the necessary smoothness of
-motion.
-
-For the same reason _I_ and _J_ have to be cut and fitted with the
-utmost exactness so as to work evenly and without backlash. _H_ is
-fitted at its outer end with a slide ring and tube _M_, generally again
-cloth lined to steady the sliding eyepiece tube _N_. This is terminated
-by the spring collar _O_, in which fits the eyepiece _P_, generally of
-the two lens form; and finally comes the eyepiece cap _Q_ set at the
-proper distance from the eye lens and with an aperture of carefully
-determined size.
-
-One thus gets pretty well down in the alphabet without going much into
-the smaller details of construction. Both objective mount and ocular
-are somewhat complex in fact, and the former is almost always made
-adjustable in instruments of above 3 or 4 inches aperture, as shown in
-Fig. 28, the form used by Cooke, the famous maker of York, England.
-Unless the optical axis of the objective is true with the tube bad
-images result.
-
-[Illustration: FIG. 28.—Adjustable Cell for Objective.]
-
-To the upper end of the tube is fitted a flanged counter-cell _c_, to
-an outward flange _f_, tapped for 3 close pairs of adjusting screws as
-_s__{1}, _s__{11} spaced at 120° apart. The objective cell itself, _b_,
-is recessed for the objective which is held in place by an interior
-or exterior ring _d_. The two lenses of the achromatic objective are
-usually very slightly separated by spacers, either tiny bits of tinfoil
-120° apart, or a very thin ring with its upper edge cut down save at 3
-points.
-
-This precaution is to insure that the lenses are quite uniformly
-supported instead of touching at uncertain points, and quite usually
-the pair as a whole rests below on three corresponding spacers. Of each
-pair of adjusting screws one as 1 in the pair _s__{11} is threaded to
-push the counter cell out, the adjacent one, 2, to pull it in, so that
-when adjustment is made the objective is firmly held. Of the lenses
-that form the objective, the concave flint is commonly at the rear and
-the convex crown in front.
-
-At the eye end the ocular ordinarily consists of two lenses each
-burnished into a brass screw ring, a tube, flange, cap, and diaphragm
-arranged as shown in Fig. 29. There are many varieties of ocular as
-will presently be shown, but this is a typical form. Figure 30 shows
-a complete modern refractor of four inches aperture on a portable
-equatorial stand with slow motion in right ascension and diagonal eye
-piece.
-
-Reflectors, used in this country less than they deserve, are, when
-properly mounted, likewise possessed of many parts. The smaller ones,
-such as are likely to come into the reader’s hands, are almost always
-in the Newtonian form, with a small oblique mirror to bring the image
-outside the tube.
-
-[Illustration: FIG. 29.—The Eye-Piece and its Fittings.]
-
-The Gregorian form has entirely vanished. Its only special merit was
-its erect image, which gave it high value as a terrestrial telescope
-before the days of achromatics, but from its construction it was almost
-impossible to keep the field from being flooded with stray light, and
-the achromatic soon displaced it. The Cassegranian construction on
-the other hand, shorter and with aberrations much reduced, has proved
-important for obtaining long equivalent focus in a short mount, and is
-almost universally applied to large reflectors, for which a Newtonian
-mirror is also generally provided.
-
-Figure 31 shows in section a typical reflector of the Newtonian form.
-Here _A_ is the main tube, fitted near its outer end with a ring _B_
-carrying the small elliptical mirror _C_, which is set at 45° to the
-axis of the tube. At the bottom of the tube is the parabolic main
-mirror _D_, mounted in its cell _E_. Just opposite the 45° small mirror
-is a hole in the tube to which is fitted the eye piece mounting _F_,
-carrying the eyepiece _G_, fitted to a spring collar _H_, screwed into
-a draw tube _I_, sliding in its mounting and brought to focus by the
-rack-and-pinion _J_.
-
-[Illustration: FIG. 30.—Portable Equatorial Refractor (Brashear).]
-
-At _K_, _K_, are two rings fixed to the tube and bearing smoothly
-against the rings _L L_ rigidly fixed to the bar _M_ carried by the
-polar axis of the mount. The whole tube can therefore be rotated about
-its axis so as to bring the eye piece into a convenient position for
-observation. One or more handles, _N_, are provided for this purpose.
-
-[Illustration: FIG. 31.—Longitudinal Section of Newtonian Reflector.]
-
-Brackets shown in dotted lines at _O_, _O_, carry the usual finder,
-and a hinged door _P_ near the lower end of the tube enables one to
-remove or replace the close fitting metal cover that protects the
-main mirror when not in use. Similarly a cover is fitted to the small
-mirror, easily reached from the upper end of the tube. The proportions
-here shown are approximately those commonly found in medium sized
-instruments, say 7 to 10 inches aperture. The focal ratio is somewhere
-about _F_/6, the diagonal mirror is inside of focus by about the
-diameter of the main mirror, and its minor axis is from ⅕ to ¼ that
-diameter.
-
-[Illustration: FIG. 32.—Reflector with Skeleton Tube (Brashear).]
-
-Note that the tube is not provided with diaphragms. It is merely
-blackened as thoroughly as possible, although stray light is quite as
-serious here as in a refractor. One could fit diaphragms effectively
-only in a tube of much larger diameter than the mirror, which would be
-inconvenient in many ways.
-
-A much better way of dealing with the difficulty is shown in Fig. 32 in
-which the tube is reduced to a skeleton, a construction common in large
-instruments. Nothing is blacker than a clear opening into the darkness
-of night, and in addition there can be no localized air currents, which
-often injure definition in an ordinary tube.
-
-[Illustration: FIG. 33.]
-
-Instruments by different makers vary somewhat in detail. A good type of
-mirror mounting is that shown in Fig. 33, and used for many years past
-by Browning, one of the famous English makers. Here the mirror _A_, the
-back of which is made accurately plane, is seated in its counter-cell
-_B_, of which a wide annulus _F_, _F_, is also a good plane, and is
-lightly held in place by a retaining ring. This counter cell rests
-in the outer cell _C_ on three equidistant studs regulated by the
-concentric push-and-pull adjusting screws _D_, _D_, _E_, _E_. The outer
-cell may be solid, or a skeleton for lightness and better equalization
-of temperature.
-
-Small specula may be well supported on any flat surface substantial
-enough to be thoroughly rigid, with one or more thicknesses of soft,
-thick, smooth cloth between, best of all Brussels carpet. Such was the
-common method of support in instruments of moderate dimensions prior
-to the day of glass specula. Sir John Herschel speaks of thus carrying
-specula of more than a hundred-weight, but something akin to Browning’s
-plan is generally preferable.
-
-There is also considerable variety in the means used for supporting
-the small mirror centrally in the tube. In the early telescopes it was
-borne by a single stiff arm which was none too stiff and produced by
-diffraction a long diametral flaring ray in the images of bright stars.
-
-A great improvement was introduced by Browning more than a half century
-ago, in the support shown in Fig. 34. Here the ring _A_, (_B_, Fig.
-31) carries three narrow strips of thin spring steel, _B_, extending
-radially inward to a central hub which carries the mirror _D_, on
-adjusting screws _E_. Outside the ring the tension screws _C_ enable
-the mirror to be accurately centered and held in place. Rarely, the
-mirror is replaced by a totally reflecting right angled prism which
-saves some light, but unless for small instruments is rather heavy and
-hard to obtain of the requisite quality and precision of figure. A
-typical modern reflector by Brashear, of 6 inches aperture, is shown in
-Fig. 35, complete with circles and driving clock, the latter contained
-in the hollow iron pier, an arrangement usual in American-made
-instruments.
-
-[Illustration: FIG. 34.—Support of Diagonal Mirror (Browning.)]
-
-Recent reflectors, particularly in this country, have four supporting
-strips instead of three, which gives a little added stiffness, and
-produces in star images but four diffraction rays instead of the six
-produced by the three strip arrangement, each strip giving a diametral
-ray.
-
-In some constructions the ring _A_ is arranged to carry the eyepiece
-fittings, placed at the very end of the tube and arranged for rotating
-about the optical axis of the telescope. This allows the ocular to
-be brought to any position without turning the whole tube. In small
-instruments a fixed eyepiece can be used without much inconvenience if
-located on the north side of the tube (in moderate north latitudes).
-
-Reflectors are easily given a much greater relative aperture than
-is practicable in a single achromatic objective. In fact they are
-usually given apertures of _F_/5 to _F_/8 and now and then are pushed
-to or even below _F_/3. Such mirrors have been successfully used for
-photography;[9] and less frequently for visual observation, mounted
-in the Cassegranian form, which commonly increases the virtual focal
-length at least three or four times. A telescope so arranged, with an
-aperture of a foot or more as in some recent examples, makes a very
-powerful and compact instrument.
-
- [9] An _F_/3 mirror of 1_m_ aperture by Zeiss was installed in the
- observatory at Bergedorf in 1911, and a similar one by Schaer is
- mounted at Carre, near Geneva.
-
-[Illustration: FIG. 35.—Small Equatorially Mounted Reflector.]
-
-This is the form commonly adopted for the large reflectors of recent
-construction, a type being the 60-inch telescope of the Mount Wilson
-Observatory of which the primary focus is 25¼ feet and the ordinary
-equivalent focus as a Cassegranian 80 feet.
-
-Comparatively few small reflectors have been made or used in the United
-States, although the climatic conditions here are more favorable
-than in England, where the reflector originated and has been very
-fully developed. The explanation may lie in our smaller number of
-non-professional active astronomers who are steadily at observational
-work, and can therefore use reflectors to the best advantage.
-
-The relative advantages of refractors and reflectors have long been
-a matter of acrimonious dispute. In fact, more of the genuine _odium
-theologicum_ has gone into the consideration of this matter than
-usually attaches to differences in scientific opinion. A good many
-misunderstandings have been due to the fact that until recently few
-observers were practically familiar with both instruments, and the
-professional astronomer was a little inclined to look on the reflector
-as fit only for amateurs. The comparison is somewhat clarified at
-present by the fact that the old speculum metal reflector has passed
-out of use, and the case now stands as between the ordinary refracting
-telescope such as has just been described, and the silver-on-glass
-reflector discussed immediately thereafter.
-
-The facts in the case are comparatively simple. Of two telescopes
-having the same clear aperture, one a reflector and the other a
-refractor, each assumed to be thoroughly well figured, as it can
-be in fact today, the theoretical resolving power is the same, for
-this is determined merely by the aperture, so that the only possible
-difference between the two would be in the residual imperfection in the
-performance of the refractor due to its not being perfectly achromatic.
-This difference is substantially a negligible one for many, but not
-all, purposes.
-
-Likewise, the general definition of the pair, assuming first-class
-workmanship, would be equal. Of the two, the single surface of the
-mirror is somewhat more difficult to figure with the necessary
-precision than is any single surface of the refractor, but reflectors
-can be, and are, given so perfect a parabolic figure that the image is
-in no wise inferior to that produced by the best refractors, and the
-two types of telescopes will stand under favorable circumstances the
-same proportional magnifying powers.
-
-The mirror is much more seriously affected by changes of temperature
-and by flexure than is the objective, since in the former case the
-successive surfaces of the two lenses in the achromatic combination
-to a considerable extent compensate each other’s slight changes of
-curvature, which act only by still slighter changes of refraction,
-while the mirror surface stands alone and any change in curvature
-produces double the defect on the reflected ray.
-
-It is therefore necessary, as we shall see presently, to take
-particular precautions in working with a reflecting telescope, which
-is, so to speak, materially more tender as regards external conditions
-than the refractor. As regards light-grasp, the power of rendering
-faint objects visible, there is more room for honest variety of
-opinion. It was often assumed in earlier days that a reflector was not
-much brighter than a refractor of half the aperture, _i.e._, of one
-quarter the working area.
-
-This might have been true in the case of an old speculum metal
-reflector in bad condition, but is certainly a libel on the
-silver-on-glass instrument, which Foucault on the other hand claimed to
-be, aperture for aperture, brighter than the refractor. Such a relation
-might in fact temporarily exist, but it is far from typical.
-
-The real relation depends merely on the light losses demonstrably
-occurring in the two types of telescopes. These are now quite well
-known. The losses in a refractor are those due to absorption of light
-in the two lenses, plus those due to the four free surfaces of these
-lenses. The former item in objectives of moderate size aggregates
-hardly more than 2 to 3 per cent. The latter, assuming the polish to be
-quite perfect, amount to 18 to 20 per cent of the incident light, for
-the glasses commonly used.
-
-The total light transmitted is therefore not over 80 per cent of the
-whole, more often somewhat under this figure. For example, a test by
-Steinheil of one of Fraunhofer’s refractors gave a transmission of 78
-per cent, and other tests show similar results.
-
-The relation between the light transmitted by glass of various
-thickness is very simple. If unit thickness transmits m per cent of the
-incident light then n units in thickness will pass m^n per cent. Thus
-if one half inch passes .98, two inches will transmit .98^4, or .922.
-Evidently the bigger the objective the greater the absorptive loss.
-If the loss by reflection at a single surface leaves m per cent to be
-transmitted then n surfaces will transmit m^n. And m being usually
-about .95, the four surfaces of an objective let pass nearly .815, and
-the thicker objective as a whole transmits approximately 75 per cent.
-
-As to the reflector the whole relation hinges on the coefficient of
-reflection from a silvered surface, under the circumstances of the
-comparison.
-
-In the case of a reflecting telescope as a whole, there are commonly
-two reflections from silver and if the coefficient of reflection is
-m then the total light reflected is m². Now the reflectivity of a
-silver-on-glass film has been repeatedly measured. (Chant Ap. J. 21,
-211) found values slightly in excess of 95 per cent, Rayleigh (Sci.
-Papers 2, 4) got 93.9, Zeiss (Landolt u. Bornstein, Tabellen) about
-93.0 for light of average wave length.
-
-Taking the last named value, a double reflection would return
-substantially 86.5 per cent of the incident light. No allowance is
-here made for any effect of selective reflection, since for the bright
-visual rays, which alone we are considering, there is very slight
-selective effect. In the photographic case it must be taken into
-account, and the absorption in glass becomes a serious factor in the
-comparison, amounting for the photographic rays to as much as 30 to 40
-per cent in large instruments. Now in comparing reflector and refractor
-one must subtract the light stopped by the small mirror and its
-supports, commonly from 5 to 7 per cent. One is therefore forced to the
-conclusion that with silver coatings fresh and very carefully polished
-reflector and refractor will show for equal aperture equal light grasp.
-
-But as things actually go even fresh silver films are quite often below
-.90 in reflectivity and in general tarnish rather rapidly, so that in
-fact the reflector falls below the refractor by just about the amount
-by which the silver films are out of condition. For example Chant (loc.
-cit.) found after three months his reflectivity had fallen to .69. A
-mirror very badly tarnished by fifteen weeks of exposure to dampness
-and dust, uncovered, was found by the writer down to a scant .40.
-
-The line of Fig. 36 shows the relative equivalent apertures of
-refractors corresponding to a 10 inch reflector at coefficients of
-reflection for a single silvered surface varying from .95 to .50 at
-which point the film would be so evidently bad as to require immediate
-renewal. The relation is obviously linear when the transmission of the
-objective is, as here, assumed constant. The estimates of skilled
-observers from actual comparisons fall in well with the line, showing
-reflectivities generally around .80 to .85 for well polished films in
-good condition.
-
-The long and short of the situation is that a silvered reflector
-deteriorates and at intervals varying from a few months to a year or
-two depending on situation, climate, and usage, requires repolishing
-or replacement of the film. This is a fussy job, but quickly done if
-everything goes well.
-
-[Illustration: FIG. 36.—Relative Light-grasp of Reflector and
-Refractor.]
-
-As to working field the reflector as ordinarily proportioned is at a
-disadvantage chiefly because it works at _F_/5 or _F_/6 instead of
-at _F_/15. At equal focal ratios there is no substantial difference
-between reflector and refractor in this respect, unless one goes into
-special constructions, as in photographic telescopes.
-
-In two items, first cost and convenience in observing, the reflector
-has the advantage in the moderate sizes. Roughly, the reflector simply
-mounted costs about one half to a quarter the refractor of equal light
-grasp and somewhat less resolving power, the discrepancy getting bigger
-in large instruments (2 feet aperture and upwards).
-
-As to case of observing, the small refractor is a truly neck-wringing
-instrument for altitudes above 45° or thereabouts, just the situation
-in which the equivalent reflector is most convenient. In considering
-the subject of mounts these relations will appear more clearly.
-
-Practically the man who is observing rather steadily and can give his
-telescope a fixed mount can make admirable use of a reflector and will
-not find the perhaps yearly or even half yearly re-silvering at all
-burdensome after he has acquired the knack—chiefly cleanliness and
-attention to detail.
-
-If, like many really enthusiastic amateurs, he can get only an
-occasional evening for observing, and from circumstances has to use a
-portable mount set up on his lawn, or even roof, when fortune favors
-an evening’s work, he will find a refractor always in condition,
-easy to set up, and requiring a minimum of time to get into action.
-The reflector is much the more tender instrument, with, however, the
-invaluable quality of precise achromatism, to compensate for the extra
-care it requires for its best performance. It suffers more than the
-refractor, as a rule, from scattered light, for imperfect polish of the
-film gives a field generally presenting a brighter background than the
-field of a good objective. After all the preference depends greatly on
-the use to which the telescope is to be put. For astrophysical work
-in general, Professor George E. Hale, than whom certainly no one is
-better qualified to judge, emphatically endorses the reflector. Most
-large observatories are now-a-days equipped with both refractors and
-reflectors.
-
-
-
-
-CHAPTER III
-
-OPTICAL GLASS AND ITS WORKING
-
-
-Glass, one of the most remarkable and useful products of man’s
-devising, had an origin now quite lost in the mists of antiquity. It
-dates back certainly near a thousand years before the Christian era,
-perhaps many centuries more. Respecting its origin there are only
-traditions of the place, quite probably Syria, and of the accidental
-melting together of sand and soda. The product, sodium silicate,
-readily becomes a liquid, i.e., “water-glass,” but the elder Pliny, who
-tells the story, recounts the later production of a stable vitreous
-body by the addition of a mineral which was probably a magnesia
-limestone.
-
-This combination would give a good permanent glass, whether the story
-is true or not, and very long before Pliny’s time glass was made in
-great variety of composition and color. In fact in default of porcelain
-glass was used in Roman times relatively more than now. But without
-knowledge of optics there was no need for glass of optical quality,
-it was well into the Renaissance before its manufacture had reached a
-point where anything of the sort could be made available even in small
-pieces, and it is barely over a century since glass-making passed
-beyond the crudest empiricism.
-
-Glass is substantially a solid solution of silica with a variety of
-metallic oxides, chiefly those of sodium, potassium, calcium and lead,
-sometimes magnesium, boron, zinc, barium and others.
-
-By itself silica is too refractory to work easily, though silica
-glass has some very valuable properties, and the alkaline oxides in
-particular serve as the fluxes in common use. Other oxides are added to
-obtain various desired properties, and some impurities may go with them.
-
-The melted mixture is thus a somewhat complex solution containing
-frequently half a dozen ingredients. Each has its own natural melting
-and vaporizing point, so that while the blend remains fairly uniform
-it may tend to lose some constituent while molten, or in cooling to
-promote the crystallization of another, if held too near its particular
-freezing point. Some combinations are more likely to give trouble from
-this cause than others, and while a very wide variety of oxides can
-be coerced into solution with silica, a comparatively limited number
-produce a homogeneous and colorless glass useful for optical purposes.
-
-Many mixtures entirely suitable for common commercial purposes are
-out of the question for lens making, through tendency to surface
-deterioration by weathering, lack of homogeneous quality, or
-objectionable coloration. A very small amount of iron in the sand used
-at the start gives the green tinge familiar in cheap bottles, which
-materially decreases the transparency. The bottle maker often adds
-oxide of manganese to the mixture, which naturally of itself gives the
-glass a pinkish tinge, and so apparently whitens it by compensating the
-one absorption by another. The resulting glass looks all right on a
-casual glance, but really cuts off a very considerable amount of light.
-
-A further difficulty is that glass differs very much in its degree of
-fluidity, and its components sometimes seem to undergo mutual reactions
-that evolve persistent fine bubbles, besides reacting with the fireclay
-of the melting pot and absorbing impurities from it.
-
-The molten glass is somewhat viscous and far from homogeneous. Its
-character suggests thick syrup poured into water, and producing streaks
-and eddies of varying density. Imagine such a mixture suddenly frozen,
-and you have a good idea of a common condition in glass, transparent,
-but full of striæ. These are frequent enough in poor window glass, and
-are almost impossible completely to get rid of, especially in optical
-glass of some of the most valuable varieties.
-
-The great improvement introduced by Guinand was constant stirring of
-the molten mass with a cylinder of fire clay, bringing bubbles to the
-surface and keeping the mass thoroughly mixed from its complete fusion
-until, very slowly cooling, it became too viscous to stir longer.
-
-The fine art of the process seems to be the exact combination of
-temperature, time, and stirring, suitable for each composition of the
-glass. There are, too, losses by volatilization during melting, and
-even afterwards, that must be reckoned with in the proportions of the
-various materials put into the melting, and in the temperatures reached
-and maintained.
-
-One cannot deduce accurately the percentage mixture of the raw
-materials from an analysis of the glass, and it is notorious that the
-product even of the best manufacturers not infrequently fails to run
-quite true to type. Therefore the optical properties of each melting
-have carefully to be ascertained, and the product listed either as a
-very slight variant from its standard type, or as an odd lot, useful,
-but quite special in properties. Some of these odd meltings in fact
-have optical peculiarities the regular reproduction of which would be
-very desirable.
-
-The purity of the materials is of the utmost importance in producing
-high grade glass for optical or other purposes. The silica is usually
-introduced in the form of the purest of white sand carrying only a few
-hundredths of one per cent of impurities in the way of iron, alumina
-and alkali. The ordinary alkalis go in preferably as carbonates, which
-can be obtained of great purity; although in most commercial glass the
-soda is used in the form of “salt-cake,” crude sodium sulphate.
-
-Calcium, magnesium, and barium generally enter the melt as carbonates,
-zinc and lead as oxides. Alumina, like iron, is generally an impurity
-derived from felspar in the sand, but occasionally enters intentionally
-as pure natural felspar, or as chemically prepared hydrate. A few
-glasses contain a minute amount of arsenic, generally used in the
-form of arsenious acid, and still more rarely other elements enter,
-ordinarily as oxides.
-
-Whatever the materials, they are commonly rather fine ground and very
-thoroughly mixed, preferably by machinery, before going into the
-furnaces. Glass furnaces are in these days commonly gas fired, and
-fall into two general classes, those in which the charge is melted
-in a huge tank above which the gas flames play, and those in which
-the charge is placed in crucibles or pots open or nearly closed,
-directly heated by the gas. In the tank furnaces the production is
-substantially continuous, the active melting taking place at one end,
-where the materials are introduced, while the clear molten glass flows
-to the cooler end of the tank or to a cooler compartment, whence it is
-withdrawn for working.
-
-The ordinary method of making optical glass is by a modification of
-the pot process, each pot being fired separately to permit better
-regulation of the temperature.
-
-The pots themselves are of the purest of fire clay, of moderate
-capacity, half a ton or so, and arched over to protect the contents
-from the direct play of the gases, leaving a side opening sufficient
-for charging and stirring.
-
-The fundamental difference between the making of optical glass and the
-ordinary commercial varieties lies in the individual treatment of each
-charge necessary to secure uniformity and regularity, carried even to
-the extent of cooling each melting very slowly in its own pot, which
-is finally broken up to recover the contents. The tank furnaces are
-under heat week in and week out, may hold several hundred tons, and on
-this account cannot so readily be held to exactness of composition and
-quality.
-
-The optical glass works, too, is provided with a particularly efficient
-set of preheating and annealing kilns, for the heat treatment of pots
-and glass must be of the most careful and thorough kind.
-
-The production of a melting of optical glass begins with a very gradual
-heating of the pot to a bright red heat in one of the kilns. It is
-then transferred to its furnace which has been brought to a similar
-temperature, sealed in by slabs of firebrick, leaving its mouth easy of
-access, and then the heat is pushed up to near the melting temperature
-of the mixture in production, which varies over a rather wide range,
-from a moderate white heat to the utmost that a regenerative gas
-furnace can conveniently produce. After the heating comes the rather
-careful process of charging.
-
-The mixture is added a portion at a time, since the fused material
-tends to foam, and the raw material as a solid is more bulky than the
-fluid. The chemical reactions as the mass fuses are somewhat complex.
-In their simplest form they represent the formation of silicates.
-
-At high temperatures the silica acts as a fairly strong acid, and
-decomposes the fused carbonates of sodium and potassium with evolution
-of gas. This is the _rationale_ of the fluxing action of such alkaline
-substances of rather low melting point. Other mixtures act somewhat
-analogously but in a fashion commonly too complex to follow.
-
-The final result is a thick solution, and the chief concern of the
-optical glass maker is to keep it homogeneous, free from bubbles,
-and as nearly colorless as practicable. To the first two ends the
-temperature is pushed up to gain fluidity, and frequently substances
-are added (e.g., arsenic) which by volatility or chemical effect tend
-to form large bubbles from the entrained gases, capable of clearing
-themselves from the fluid where fine bubbles would remain. For the same
-purpose is the stirring process.
-
-The stirrer is a hard baked cylinder of fire clay fastened to an iron
-bar. First heated in the mouth of the pot, the stirrer is plunged in
-the molten glass and given a steady rotating motion, the long bar
-being swivelled and furnished with a wooden handle for the workman.
-This stirring is kept up pretty steadily while the heat is very slowly
-reduced until the mass is too thick to manage, the process taking, for
-various mixtures and conditions, from three or four hours to the better
-part of a day.
-
-[Illustration: FIG. 37.—Testing Optical Glass in the Rough.]
-
-Then begins the careful and tedious process of cooling. Fairly rapid
-until the mass is solid enough to prevent the formation of fresh striæ,
-the cooling is continued more slowly, in the furnace or after removal
-to the annealing oven, until the crucible is cool enough for handling,
-the whole process generally taking a week or more.
-
-Then the real trouble begins. The crucible is broken away and there is
-found a more or less cracked mass of glass, sometimes badly broken up,
-again furnishing a clear lump weighing some hundreds of pounds. This
-glass is then carefully picked over and examined for flaws, striæ and
-other imperfections.
-
-These can sometimes be chipped away with more or less breaking up of
-the mass. The inspection of the glass in the raw is facilitated by the
-scheme shown in elevation Fig. 37. Here _A_ is a tank with parallel
-sides of plate glass. In it is placed _B_ the rough block of glass, and
-the tank is then filled with a liquid which can be brought to the same
-refractive power as the glass, as in Newton’s disastrous experiment.
-When equality is reached for, say, yellow light, one can see directly
-through the block, the rays no longer being refracted at its surface,
-and any interior striæ are readily seen even in a mass a foot or more
-thick. Before adding the liquid a ray would be skewed, as _C_, _D_,
-_E_, _F_, afterwards it would go straight through; _C_, _D_, _G_, _H_.
-
-The fraction that passes inspection may be found to be from much less
-than a quarter to a half of the whole. This good glass is then ready
-for the next operation, forming and fine annealing. The final form to
-be reached is a disc or block, and the chunks of perfect glass are
-heated in a kiln until plastic, and then moulded into the required
-shapes, sometimes concave or convex discs suitable for small lenses.
-
-Then the blocks are transferred to a kiln and allowed to cool off very
-gradually, for several days or weeks according to the size of the
-blocks and the severity of the requirements they must meet. In the
-highest class of work the annealing oven has thermostatic control and
-close watch is kept by the pyrometer.
-
-It is clear that the chance of getting a large and perfect chunk from
-the crucible is far smaller than that of getting fragments of a few
-pounds, so that the production of a perfect disc for a large objective
-requires both skill and luck. Little wonder therefore that the price of
-discs for the manufacture of objectives increases substantially as the
-cube of the diameter.
-
-The process of optical glass making as here described is the customary
-one, used little changed since the days of Guinand. The great
-advances of the last quarter century have been in the production of
-new varieties having certain desirable qualities, and in a better
-understanding of the conditions that bring a uniform product of high
-quality. During the world war the greatly increased demand brought
-most extraordinary activity in the manufacture, and especially in the
-scientific study of the problems involved, both here and abroad. The
-result has been a long step toward quantity production, the discovery
-that modifications of the tank process could serve to produce certain
-varieties of optical glass of at least fair quality, and great
-improvements in the precision and rapidity of annealing.
-
-These last are due to the use of the electric furnace, the study of
-the strains during annealing under polarized light, and scientific
-pyrometry. It is found that cooling can be much hastened over certain
-ranges of temperature, and the total time required very greatly
-shortened. It has also been discovered, thanks to captured instruments,
-that some of the glasses commonly regarded as almost impossible to
-free from bubbles have in fact yielded to improved methods of treatment.
-
-Conventionally optical glass is of two classes, crown and flint.
-Originally the former was a simple compound of silica with soda and
-potash, sometimes also lime or magnesia, while the latter was rich
-in lead oxide and with less of alkali. The crown had a low index of
-refraction and small dispersion, the flint a high index and strong
-dispersion. Crown glass was the material of general use, while the
-flint glass was the variety used in cut glass manufacture by reason of
-its brilliancy due to the qualities just noted.
-
-[Illustration: FIG. 38.—The Index of Refraction.]
-
-The refractive index is the ratio between the sine of the angle of
-incidence on a lens surface and that of the angle of refraction in
-passing the surface. Fig. 38 shows the relation of the incident and
-refracted rays in passing from air into the glass lens surface _L_, and
-the sines of the angles which determine n, the conventional symbol for
-the index of refraction. Here _i_ is the angle of incidence and _r_
-the angle of refraction i.e. n = _s_/_s′_. The indices of refraction
-are usually given for specific colors representing certain lines
-in the spectrum, commonly _A_¹, the potassium line in the extreme
-red, _C_ the red line due to hydrogen, _D_ the sodium line, _F_ the
-blue hydrogen line and _G′_ the blue-violet line hydrogen line, and
-are distinguished as n_{_c_}, n_{_d_}, n_{_f_}, etc. The standard
-dispersion (dn) for visual rays is given as between _C_ and _F_, while
-the standard refractivity is taken for _D_, in the bright yellow part
-of the spectrum. (Note. For the convenience of those who are rusty on
-their trigonometry, Fig. 39 shows the simpler trigonometric functions
-of an angle. Thus the sine of the angle _A_ is, numerically, the length
-of the radius divided into the length of the line dropped from the end
-of the radius to the horizontal base line, i.e. _bc_/_Ob_, the tangent
-is _da_/_Ob_, and the cosine _Oc_/_Ob_.)
-
-Ordinarily the index of refraction of the crown was taken as about
-3/2, that of the flint as about 8/5. As time has gone on and
-especially since the new glasses from the Jena works were introduced
-about 35 years ago, one cannot define crowns and flints in any such
-simple fashion, for there are crowns of high index and flints of low
-dispersion.
-
-[Illustration: FIG.39.—The Simple Trigonometric Functions of an Angle.]
-
-The following table gives the optical data and chemical analyses of
-a few typical optical glasses. The list includes common crowns and
-flints, a typical baryta crown and light flint, and a telescope crown
-and flint for the better achromatization of objectives, as developed at
-the Jena works.
-
-The thing most conspicuous here as distinguishing crowns from flints
-is that the latter have greater relative dispersion in the blue, the
-former in the red end of the spectrum, as shown by the bracketed
-ratios. This as we shall see is of serious consequence in making
-achromatic objectives. In general, too, the values of ν for flints are
-much lower than for crowns, and the indices of refraction themselves
-commonly higher.
-
-As we have just seen, glass comes to the optician in blocks or discs,
-for miscellaneous use the former, three or four inches square and an
-inch think, more or less; for telescope making the latter. The discs
-are commonly some ten percent greater in diameter than the finished
-objective for which they are intended, and in thickness from 1/8
-to 1/10 the diameter. They are commonly well annealed and given a
-preliminary polish on both sides to facilitate close inspection.
-
-                  CHARACTERISTICS OF OPTICAL GLASSES
-
- ---------------+--------+--------+------+--------------------------+
-                |        |        |      |        Bracketed         |
-                |        |        |      |        numbers are       |
-                |        |   dn   |      |      proportions of dn   |
-     Glass      |  n__d_ | -----  |  ν   +--------+--------+--------+
-                |        | (F-C)  |      |  D-A´  |   F-D  |  G´-F  |
-                |        |        |      |  ----  |  ----  |  ----  |
-                |        |        |      |   dn   |   dn   |   dn   |
- ---------------+--------+--------+------+--------+--------+--------+
- Boro-silicate  | 1.5069 | .00813 | 62.3 | .00529 | .00569 | .00457 |
-   crown        |        |        |      | (.651) | (.701) | (.562) |
- Zinco-silicate | 1.5170 | .00859 | 60.2 | .00555 | .00605 | .00485 |
-  (hard) crown  |        |        |      | (.646) | (.704) | (.565) |
- Dense baryta   | 1.5899 | .00970 | 60.8 | .00621 | .00683 | .00546 |
-   crown        |        |        |      | (.640) | (.704) | (.563) |
- Baryta light   | 1.5718 | .01133 | 50.4 | .00706 | .00803 | .00660 |
-    flint       |        |        |      | (.623) | (.709) | (.582) |
- Common light   | 1.5710 | .01327 | 43.0 | .00819 | .00943 | .00791 |
-   flint        |        |        |      | (.617) | (.710) | (.596) |
- Common dense   | 1.6116 | .01638 | 37.3 | .00995 | .01170 | .00991 |
-   flint        |        |        |      | (.607) | (.714) | (.607) |
- Very dense     | 1.6489 | .01919 | 33.8 | .01152 | .01372 | .01180 |
-   flint        |        |        |      | (.600) | (.714) | (.615) |
- Densest flint  | 1.7541 | .02743 | 27.5 | .01607 | .01974 | .01730 |
-                |        |        |      | (.585) | (.720) | (.630) |
- [*]Telescope   | 1.5285 | .00866 | 61.0 | .00557 | .00610 | .00493 |
-  crown         |        |        |      | (.643) | (.705) | (.570) |
- [*]Telescope   | 1.5286 | .01025 | 51.6 | .00654 | .00723 | .00591 |
-   flint        |        |        |      | (.638) | (.705) | (.576) |
-
- [* Optical data close approximations only.]
-
- +------------------------------------------------------------------------
- |
- |              Analysis of glasses in percentages
- |
- +----+----+---+----+----+----+----+----+----+----+----+----+----+----+----
- | Si |B_2 |   |    |    |K_2 |Na_2|    |AL_2|As_2|As_2|Fe_2|Mn_2|Sb_2|
- | O_2| O_3|ZnO| PbO| BaO| O  | O  |CaO | O_3| O_5| O_3| O_3| O_3| O_3| MgO
- |    |    |   |    |    |    |    |    |    |    |    |    |    |    |
- +----+----+---+----+----+----+----+----+----+----+----+----+----+----+----
- |74.8| 5.9| --| -- | -- |7.11|11.3| -- | .75| -- | .06| -- | .06|    |
- |    |    |   |    |    |    |    |    |    |    |    |    |    |    |
- |65.4| 2.5|2.0| -- | 9.6|15.0| 5.0| -- | -- | -- | .4 | -- | .1 |    |
- |    |    |   |    |    |    |    |    |    |    |    |    |    |    |
- |37.5|15.0| --| -- |41.0| -- |    | -- |5.0 | 1.5|    |    |    |    |
- |    |    |   |    |    |    |    |    |    |    |    |    |    |    |
- |51.7| -- |7.0|10.0|20.0| 9.5| 1.5| -- | -- | .30|    |    |    |    |
- |    |    |   |    |    |    |    |    |    |    |    |    |    |    |
- |54.3| 1.5| --|33.0| -- | 8.0| 3.0| -- | -- | .20|    |    |    |    |
- |    |    |   |    |    |    |    |    |    |    |    |    |    |    |
- |54.8| -- | --|37.0| -- | 5.8|  .8| .60| .4 | -- | -- | .70| -- | -- | .20
- |    |    |   |    |    |    |    |    |    |    |    |    |    |    |
- |40.0| -- | --|52.6| -- | 6.5|  .5| -- | -- | .30| -- | -- | .09|    |
- |    |    |   |    |    |    |    |    |    |    |    |    |    |    |
- |29.3| -- | --|67.5| -- | 3.0|  --| -- | -- | -- | .20| -- | .04|    |
- |    |    |   |    |    |    |    |    |    |    |    | ---^--- |    |
- |55.2| -- | --| -- |22.0| 5.7| 7.5|5.9 | -- | -- | -- |   3.7   |    |
- |    |    |   |    |    |    |    |    |    |    |    |         |    |
- |59.9|12.7| --| -- | -- | 5.1| 3.5| -- | -- | -- | -- |   2.7   |16.1|
- |    |    |   |    |    |    |    |    |    |    |    |         |    |
- +----+----+---+----+----+----+----+----+----+----+----+---------+----+----
-
-The first step toward the telescope is the testing of these discs
-of glass, first for the presence or absence of striæ and other
-imperfections; second, for the perfection of the annealing. The maker
-has usually looked out for all the grosser imperfections before the
-discs left his works, but a much closer inspection is needed in order
-to make the best use of the glass.
-
-[Illustration: FIG. 40.—Testing Glass for Striæ.]
-
-Bad striæ are of course seen easily, as they would be in a window pane,
-but such gross imperfections are often in reality less damaging than
-the apparently slighter ones which must be searched for. The simplest
-test is to focus a good telescope on an artificial star, remove the
-eyepiece and bring the eye into its place.
-
-When the eye is in focus the whole aperture of the objective is
-uniformly filled with light, and if the disc to be tested be placed
-in front of it, any inequality in refraction will announce itself by
-an inequality of illumination. A rough judgment as to the seriousness
-of the defect may be formed from the area affected and the amount by
-which it affects the local intensity of illumination. Fig. 40 shows the
-arrangement for the test, _A_ being the eye, _B_ the objective and _C_
-the disc. The artificial star is conveniently made by setting a black
-bottle in the sun a hundred feet or so away and getting the reflection
-from its shoulder.
-
-[Illustration: FIG. 41.—The Mirror Test for Striæ.]
-
-A somewhat more delicate test, very commonly used, is shown in Fig.
-41. Here _A_ is a truly spherical mirror silvered on the front. At _B_
-very close to its centre of curvature is placed a lamp with a screen in
-front of it perforated with a hole 1/32 inch or so in diameter.
-
-The rays reflected from the mirror come back quite exactly upon
-themselves and when the eye is placed at _C_, their reflected focus,
-the whole mirror _A_ is uniformly lighted just as the lens was in Fig.
-40, with the incidental advantage that it is much easier and cheaper to
-obtain a spherical mirror for testing a sizeable disc than an objective
-of similar size and quality. Now placing the disc _D_ in front of the
-mirror, the light passing twice through it shows up the slightest stria
-or other imperfection as a streak or spot in the field. Its place is
-obvious and can be at once marked on the glass, but its exact position
-in the substance of the disc is not so obvious.
-
-To determine this, which may indicate that the fault can be ground out
-in shaping the lens, a modification of the first test serves well, as
-indeed it does for the general examination of large discs. Instead of
-using a distant artificial star and a telescope, one uses the lamp and
-screen, or even a candle flame ten feet or more away and a condensing
-lens of rather short focus, which may or may not be achromatic, so
-that the eye will get into its focus conveniently while the lens is
-held in the hand. Fig. 42 shows the arrangement. Here _A_ is the eye,
-_B_ the condensing lens, _C_ the disc and _D_ the source of light. The
-condensing lens may be held on either side of the disc as convenience
-suggests, and either disc or lens may be moved. The operation is
-substantially the examination of a large disc piecemeal, instead of all
-at once by the use of a big objective or mirror.
-
-[Illustration: FIG. 42.—Locating Striæ in the Substance of a Disc.]
-
-Now when a stria has been noted mark its location as to the surface,
-and, moving the eye a little, look for parallax of the fault with
-respect to the surface mark. If it appears to shift try a mark on the
-opposite surface in the same way. Comparison of the two inspections
-will show about where the fault lies with respect to the surfaces,
-and therefore what is the chance of working it out. Sometimes a look
-edgewise of the disc will help in the diagnosis.
-
-Numerous barely detectable striæ are usually worse than one or two
-conspicuous ones, for the latter frequently throw the light they
-transmit so wide of the focus that it does not affect the image, which
-could be greatly damaged by slight blurs of light that just miss focus.
-
-Given a disc that passes well the tests for striæ and the like the next
-step is to examine the perfection of the annealing, which in its larger
-aspect is revealed by an examination in polarized light.
-
-[Illustration: FIG. 43.—Testing a Disc in Polarized Light.]
-
-For this purpose the disc is set up against a frame placed on table or
-floor with a good exposure to skylight behind it, and inclined about
-35° from the vertical. Behind it is laid a flat shiny surface to serve
-as polarizer. Black enamel cloth smoothly laid, a glass plate backed
-with black paint, or even a smooth board painted with asphalt paint
-will answer excellently. Then holding a Nicol prism before the eye and
-looking perpendicular to the face of the disc, rotate the prism on its
-axis. Fig. 43 shows the arrangement, _A_ being the eye, _B_ the Nicol,
-_C_ the disc, and _D_ the polarizer behind it.
-
-If annealing has left no strain the only effect of rotating the Nicol
-will be to change the field from bright to dark and back again as if
-the disc were not there. Generally a pattern in the form of a somewhat
-hazy Maltese cross will appear, with its arms crossing the disc,
-growing darker and lighter alternately as the Nicol is turned.
-
-If the cross is strongly marked but symmetrical and well centered the
-annealing is fair—better as the cross is fainter and hazier—altogether
-bad if colors show plainly or if the cross is decentered or distorted.
-The test is extremely sensitive, so that holding a finger on the
-surface of the disc may produce local strain that will show as a faint
-cloudy spot.
-
-A disc free of striæ and noticeable annealing strains is usually, but
-not invariably, good, for too frequent reheating in the moulding or
-annealing process occasionally leaves the glass slightly altered, the
-effect extending, at worst, to the crystallization or devitrification
-to which reference has been made.
-
-Given a good pair of discs the first step towards fashioning them into
-an objective is roughing to the approximate form desired. As a guide
-to the shaping of the necessary curves, templets must be made from the
-designed curves of the objective as precisely as possible. These are
-laid out by striking the necessary radii with beam compass or pivoted
-wire and scribing the curve on thin steel, brass, zinc or glass. The
-two last are the easier to work since they break closely to form.
-
-From these templets the roughing tools are turned up, commonly from
-cast iron, and with these, supplied with carborundum or even sand, and
-water, the discs, bearing against the revolving tool, are ground to the
-general shape required. They are then secured to a slowly revolving
-table, bearing edgewise against a revolving grindstone, and ground
-truly circular and of the proper final diameter.
-
-At this point begins the really careful work of fine grinding, which
-must bring the lens very close to its exact final shape. Here again
-tools of cast iron, or sometimes brass, are used, very precisely
-brought to shape according to the templets. They are grooved on the
-face to facilitate the even distribution of the abrasive, emery or
-fine carborundum, and the work is generally done on a special grinding
-machine, which moves the tool over the firmly supported disc in a
-complicated series of strokes imitating more or less closely the
-strokes found to be most effective in hand polishing.
-
-In general terms the operator in handwork at this task supports the
-disc on a firm vertical post, by cementing it to a suitable holder, and
-then moves the tool over it in a series of straight or oval strokes,
-meanwhile walking around the post. A skilful operator watches the
-progress of his work, varies the length and position of his strokes
-accordingly, and, despite the unavoidable wear on the tool, can both
-keep its figure true and impart a true figure to the glass.
-
-[Illustration: FIG. 44.—Dr. Draper’s Polishing Machine.]
-
-The polishing machine, of which a type used by Dr. Draper is shown
-in Fig. 44, produces a similar motion, the disc slowly revolving and
-the rather small tool moving over it in oval strokes kept off the
-center. More often the tool is of approximately the same diameter as
-the disc under it. The general character of the motion is evident
-from the construction. The disc _a_ is chucked by _c c′_ on the bed,
-turned by the post _d_ and worm wheel _e_. This is operated from the
-pulleys, _i_, _g_, which drive through _k_, the crank _m_, adjustable
-in throw by the nuts _n_, _n′_, and in position of tool by the clamps
-_r_, _r_. The motion may be considerably varied by adjustment of the
-machine, always keeping the stroke from repeating on the same part of
-the disc, by making the period of the revolution and of the stroke
-incommensurable so far as may be. Even in spectacle grinding machines
-the stroke may repeat only once in hundreds of times, and even this
-frequency in a big objective would, if followed in the polishing, leave
-tool marks which could be detected in the final testing.
-
-In the fine grinding, especially near the end of the process, the
-templets do not give sufficient precision in testing the curves, and
-recourse is had to the spherometer, by which measurements down to about
-1/100000 inch can be consistently made.
-
-The next stage of operations is polishing, which transforms the grey
-translucency of the fine ground lens into the clear and brilliant
-surface which at last permits rigorous optical tests to be used for the
-final finish of the lens. This polishing is done generally on the fine
-grinding machine but with a very different tool and with rouge of the
-utmost fineness.
-
-The polishing tool is in any case ground true and is then faced with a
-somewhat yielding material to carry the charge of rouge. Cheap lenses
-are commonly worked on a cloth polisher, a texture similar to billiard
-cloth being suitable, or sometimes on paper worked dry.
-
-With care either may produce a fairly good surface, with, however, a
-tendency to polish out the minute hollows left by grinding rather than
-to cut a true surface clear down to their bottoms. Hence cloth or paper
-is likely to leave microscopic inequalities apparently polished, and
-this may be sufficient to scatter over the field a very perceptible
-amount of light which should go to forming the image. All first class
-objectives and mirrors are in fact polished on optician’s pitch. This
-is not the ordinary pitch of commerce but a substance of various
-composition, sometimes an asphaltic compound, again on a base of tar,
-or of resin brought to the right consistency by turpentine.
-
-Whatever the exact composition, the fundamental property is that
-the material, apparently fairly hard and even brittle when cold, is
-actually somewhat plastic to continued pressure. Sealing wax has
-something of this quality, for a stick which may readily be broken will
-yet bend under its own weight if supported at the ends.
-
-If the fine grinding process has been properly carried out the lens has
-received its correct form as nearly as gauges and the spherometer can
-determine it. The next step is to polish the surface as brilliantly
-and evenly as possible. To this end advantage is taken of the plastic
-quality already mentioned, that the glass may form its own tool.
-
-The base of the tool may be anything convenient, metal, glass or even
-wood. Its working surface is made as nearly of the right curvature as
-practicable and it is then coated with warm pitch to a thickness of an
-eighth of an inch more or less, either continuously or in squares, and
-while still slightly warm the tool is placed against the fine ground
-disc, the exact shape of which it takes.
-
-When cold the pitch surface can easily be cut out into squares or
-symmetrically pitted with a suitable tool, at once facilitating the
-distribution of the rouge and water that serves for polishing, and
-permitting delicate adjustment of the working curvature in a way about
-to be described.
-
-Fig. 45 shows the squared surface of the tool as it would be used for
-polishing a plane or very slightly convex or concave surface. Supplied
-with the thin abrasive paste, it is allowed to settle, cold, into its
-final contact with the glass, and then the process of polishing by hand
-or machine is started.
-
-The action of the tool must be uniform to avoid changing the shape of
-the lens. It can be regulated as it was in the grinding, by varying the
-length and character of the stroke, but even more delicately by varying
-the extent of surface covered by the pitch actually working on the
-glass.
-
-[Illustration: FIG. 45.—Tool for Flat Surface.]
-
-[Illustration: FIG. 46.—Tool for Concave Surface.]
-
-This is done by channeling or boring away pitch near the rim or center
-of the tool as the case may be. Fig. 46 shows a tool which has been
-thus treated so that the squares are progressively smaller near the
-periphery. Such a spacing tends to produce a concave surface from a
-flat tool or to increase the concavity from a curved one. Trimming down
-the squares towards the centre produces the opposite result.
-
-Broadly, the principle is that the tool cuts the more in the areas
-where the contact surfaces are the greater. This is not wholly by
-reason of greater abrading surface, but also because where the contact
-is greater in area the pitch settles less, from the diminished
-pressure, thus increasing the effective contact.
-
-Clearly the effect of trimming away is correlated with the form and
-length of stroke, and the temper of the pitch, and in fact it requires
-the wisdom of the serpent to combine these various factors so as to
-produce the perfectly uniform and regular action required in polishing.
-Now and then, at brief intervals, the operation is stopped to supply
-rouge and to avoid changing the conditions by the heat of friction.
-Especially must heating be looked out for in hand polishing of lenses
-which is often done with the glass uppermost for easier inspection of
-the work.
-
-Polishing, if the fine grinding has been judiciously done is, for
-moderate sized surfaces, a matter of only a few hours. It proceeds
-quite slowly at first while the hills are being ground down and then
-rather suddenly comes up brilliantly as the polisher reaches the
-bottoms of the valleys. Large lenses and mirrors may require many days.
-
-Now begins the final and extraordinarily delicate process of figuring.
-The lens or mirror has its appointed form as nearly as the most precise
-mechanical methods can tell—say down to one or two hundred-thousandths
-of an inch. From the optical standpoint the result may be thoroughly
-bad, for an error of a few millionths of an inch may be serious in the
-final performance.
-
-The periphery may be by such an amount longer or shorter in radius
-than it should be, or there may be an intermediate zone that has
-gone astray. In case of a mirror the original polishing is generally
-intended to leave a spherical surface which must be converted into
-a paraboloidal one by a change in curvature totalling only a few
-hundred-thousandths of an inch and seriously affected by much smaller
-variations.
-
-The figuring is done in a fashion very similar to the polishing. The
-first step is to find out by optical tests such as are described in
-Chapter IX the location of the errors existing after the polishing, and
-once found, they must be eliminated by patient and cautious work on the
-surface.
-
-Every optical expert has his own favorite methods of working out the
-figure. If there is a hollow zone the whole surface must be worked
-down to its level by repolishing; if, on the other hand, there is an
-annular hump, one may repolish with stroke and tool-face adapted to cut
-it down, or one may cautiously polish it out until it merges with the
-general level.
-
-Polishing is commonly done with tools of approximately the size of
-the work, but in figuring there is great difference of practice, some
-expert workers depending entirely on manipulation of a full sized
-tool, others working locally with small polishers, even with the ball
-of the thumb, in removing slight aberrations. In small work where the
-glass can be depended on for homogeneity and the tools are easily kept
-true the former method is the usual one, but in big objectives the
-latter is often easier and may successfully reach faults otherwise very
-difficult to eliminate.
-
-Among well known makers of telescopes the Clarks and their equally
-skilled successors the Lundins, father and son, developed the art
-of local retouching to a point little short of wizardry; the late
-Dr. Brashear depended almost entirely on the adroitly used polishing
-machine; Sir Howard Grubb uses local correction in certain cases,
-and in general the cautiously modified polisher; while some of the
-Continental experts are reported to have developed the local method
-very thoroughly.
-
-The truth probably is that the particular error in hand should
-determine the method of attack and that its success depends entirely
-on the skill of the operator. As to the perfection of the objectives
-figured in either way, no systematic difference due to the method of
-figuring can be detected by the most delicate tests.
-
-In any case the figuring operation is long and tedious, especially in
-large work where problems of supporting to avoid flexure arise, where
-temperature effects on tool and glass involve long delays between tests
-and correction, and where in the last resort non-spherical surfaces
-must often be resorted to in bringing the image to its final perfection.
-
-The final test of goodness is performance, a clean round image without
-a trace of spherical or zonal aberration and the color correction the
-best the glasses will allow. Constant and rigorous testing must be
-applied all through the process of figuring, and the result seems to
-depend on a combination of experience, intuition and tactual expertness
-rarely united in any one person.
-
-Sir Howard Grubb, in a paper to be commended to anyone interested in
-objectives, once forcibly said: “I may safely say that I have never
-finished any objective over 10 inches diameter, in the working of which
-I did not meet with some new experience, some new set of conditions
-which I had not met before, and which had then to be met by special and
-newly devised arrangements.”
-
-The making of reflecting telescopes is not much easier since although
-only one surface has to be worked, that one has to be figured with
-extraordinary care, flexure has to be guarded against at every stage
-of the working, and afterwards, temperature change is a busy foe,
-while testing for correct figure, the surface being non-spherical, is
-considerably more troublesome.
-
-An expert can make a good mirror with far less actual labor than an
-objective of similar aperture, but when one reads Dr. Henry Draper’s
-statement that in spite of knowing at first hand the methods and
-grinding machines of Lord Rosse and Mr. Lassell, he ground over a
-hundred mirrors, and spent three years of time, before he could get a
-correct figure with reasonable facility, one certainly gains a high
-respect for the skill acquired.
-
-This chapter is necessarily sketchy and not in the least intended to
-give the reader a complete account of technical glass manufacture,
-far less of the intricate and almost incommunicable art of making
-objectives and mirrors. It may however lead to a better understanding
-of the difference between the optical glass industry and the
-fabrication of commercial glass, and lead the reader to a fuller
-realization of how fine a work of art is a finished objective or mirror
-as compared with the crude efforts of the early makers or the hasty
-bungling of too many of their successors.
-
-For further details on making, properties and working of optical glass
-see:
-
- HOVESTADT: “Jenaer Glas.”
-
- ROSENHAIN: “Glass Manufacture.”
-
- SIR HOWARD GRUBB: “Telescopic Objectives and Mirrors: Their
- Preparation and Testing.” Nature _34_, 85.
-
- DR. HENRY DRAPER: “On the Construction of a Silvered Glass Telescope.”
- (Smithsonian Contributions to Knowledge, Vol. 34.)
-
- G. W. RITCHEY: On the Modern Reflecting Telescope and the Making and
- Testing of Optical Mirrors. (Smithsonian Contributions to Knowledge,
- Vol. 34.)
-
- LORD RAYLEIGH: Polishing of Glass Surfaces. (Proc. Opt. Convention,
- 1905, p. 73.)
-
- BOTTONE: “Lens Making for Amateurs.”
-
-
-
-
-CHAPTER IV
-
-THE PROPERTIES OF OBJECTIVES AND MIRRORS
-
-
-The path of the rays through an ordinary telescope has been shown in
-Fig. 5. In principle all the rays from a point in the distant object
-should unite precisely in a corresponding point in the image which is
-viewed by the eyepiece. Practically it takes very careful design and
-construction of the objective to make them meet in such orderly fashion
-even over an angular space of a single degree, and the wider the view
-required the more difficult the construction. We have spoken in the
-account of the early workers of their struggles to avoid chromatic and
-spherical aberrations, and it is chiefly these that still, in less
-measure, worry their successors.
-
-[Illustration: FIG. 47.—Chromatic Aberration of Convex Lens.]
-
-The first named is due to the fact that a prism does not bend light of
-all colors equally, but spreads them out into a spectrum; red refracted
-the least, violet the most. Since a lens may be regarded as an
-assemblage of prisms, of small angle near the centre and greater near
-the edge, it must on the whole and all over bend the blue and violet
-rays to meet on the axis nearer the rear surface than the corresponding
-red rays, as shown in Fig. 47. Here the incident ray _a_ is split up by
-the prismatic effect of the lens, the red coming to a focus at _r_, the
-violet at _v_.
-
-One can readily see this chromatic aberration by covering up most of a
-common reading glass with his hand and looking through the edge portion
-at a bright light, which will be spread out into a colored band.
-
-If the lens is concave the violet rays will still be the more bent,
-but now outwards, as shown in Fig. 48. The incident ray _a′_ is split
-up and the violet is bent toward _v_, proceeding as if coming straight
-from a virtual focus _v′_ in front of the lens, and nearer it than the
-corresponding red focus _r′_. Evidently if we could combine a convex
-lens, bending the violet inward too much, with a concave one, bending
-it outward too much, the two opposite variations might compensate each
-other so that red and violet would come to the same focus—which is the
-principle of the achromatic objective.
-
-[Illustration: FIG. 48.—Chromatic Aberration of Concave Lens.]
-
-If the refractive powers of the lenses were exactly proportional to
-their dispersive powers, as Newton erroneously thought, it is evident
-that the concave lens would pitch all the rays outwards to an amount
-which would annul both the chromatic variation and the total refraction
-of the convex lens, leaving the pair without power to bring anything
-to a focus. Fortunately flint glass as compared with crown glass has
-nearly double the dispersion between red and violet, and only about 20%
-greater refractive power for the intermediate yellow ray.
-
-Hence, the prismatic dispersive effect being proportional to the total
-curvature of the lens, the chromatic aberration of a crown glass
-lens will be cured by a concave flint lens of about half the total
-curvature, and, the refractions being about as 5 to 6, of ⅗ the total
-power.
-
-Since the “power” of any lens is the reciprocal of its focal length,
-a crown glass convex lens of focal length 3, and a concave flint lens
-of focal length 5 (negative) will form an approximately achromatic
-combination. The power of the combination will be the algebraic sum of
-the powers of the components so that the focal length of the pair will
-be about 5/2 that of the crown lens with which we started.
-
-To be more precise the condition of achromatism is
-
-  Σρδn + Σρ′δn′ = 0
-
-where ρ is the reciprocal of a radius and δn, or δn′, is the difference
-in refractive index between the rays chosen to be brought to exact
-focus together, as the red and the blue or violet.
-
-This conventional equation simply states that the sum of the
-reciprocals of the radii of the crown lens multiplied by the dispersion
-of the crown, must equal the corresponding quantity for the flint lens
-if the two total dispersions are to annul each other, leaving the
-combination achromatic. Whatever glass is used the power of a lens made
-of it is
-
-  P( = 1/_f_) = Σρ(n - 1)
-
-so that it will be seen that, other things being equal, a glass of high
-index of refraction tends to give moderate curves in an objective.
-Also, referring to the condition of achromatism, the greater the
-difference in dispersion between the two glasses the less curvatures
-will be required for a given focal length, a condition advantageous for
-various reasons.
-
-The determination of achromatism for any pair of glasses and focal
-length is greatly facilitated by employing the auxiliary quantity ν
-which is tabulated in all lists of optical glass as a short cut to a
-somewhat less manageable algebraic expression. Using this we can figure
-achromatism for unity focal length at once,
-
-  P = ν/(ν-ν′) P′ = ν′/(ν-ν′) ν = (n_{_D_}-1)/δn
-
-being the powers of the leading and following lenses respectively.
-The combined lens will bring the rays of the two chosen colors, as
-red and blue, to focus at the same point on the axis. It does not
-necessarily give to the red and blue images of an object the same exact
-size. Failure in this respect is known as chromatic difference of
-magnification, but the fault is small and may generally be neglected in
-telescope objectives.
-
-We have now seen how an objective may be made achromatic and of
-determinate focal length, but the solution is in terms of the sums of
-the respective curvatures of the crown and flint lenses, and gives no
-information about the radii of the individual surfaces. The relation
-between these is all-important in the final performance.
-
-[Illustration: FIG. 49.—Spherical Aberration of Convex Lens.]
-
-For in a convex lens with spherical surfaces the rays striking near the
-edge, of whatever color, are pitched inwards too much compared with
-rays striking the more moderate curvatures near the axis, as shown in
-Fig. 49. The ray _a′ b′_ thus comes to a focus shorter than the ray _a
-b_.
-
-This constitutes the fault of spherical aberration, which the
-old astronomers, following the suggestions of Descartes, tried
-ineffectually to cure by forming lenses with non-spherical surfaces.
-
-[Illustration: FIG. 50.—Spherical Aberration of Concave Lens.]
-
-Fig. 50 suggests the remedy, for the outer ray _a″_ is pitched out
-toward _b″_ as if it came from a focal point _c″_, while the ray
-nearer the center _a″′_ is much less bent toward _b″′_ as if it came
-from _c″′_. The spherical aberrations of a concave lens therefore,
-being opposite to those of a convex lens, the two must, at least to a
-certain extent, compensate each other as when combined in an achromatic
-objective.
-
-So in fact they do, and, if the curves that go to make up the total
-curvatures of the two are properly chosen, the total spherical
-aberration can be made negligibly small, at least on and near the
-axis. Taking into account this condition, therefore, at once gives
-us a clue to the distribution of the total curvatures and hence to
-the radii of the two lenses. Spherical aberration, however, involves
-not only the curvatures but the indices of refraction, so that exact
-correction depends in part on the choice of glasses wherewith to obtain
-achromatization.
-
-In amount spherical aberration varies with the square of the aperture
-and inversely with the cube of the focal length i.e. with a²/f³. It is
-reckoned as + when, as in Fig. 49, the rim rays come to the shorter
-focus, as-, when they come to the longer focus.
-
-In any event, since the spherical aberration of a lens may be varied in
-above the ratio of 4:1, for the same total power, merely by changing
-the ratio of the radii, it is evident that the two lenses being fairly
-correct in total curvature might be given considerable variations in
-curvature and still mutually annul the axial spherical aberration.
-
-Such is in fact the case, so that to get determinate forms for
-the lenses one must introduce some further condition or make some
-assumption that will pin down the separate curvatures to some definite
-relations. The requirement may be entirely arbitrary, but in working
-out the theory of objectives has usually been chosen to give the lens
-some real or hypothetical additional advantage.
-
-The commonest arbitrary requirement is that the crown glass lens
-shall be equiconvex, merely to avoid making an extra tool. This fixes
-one pair of radii, and the flint lens is then given the required
-compensating aberration choosing the easiest form to make. This results
-in the objective of Fig. 51.
-
-[Illustration: FIG. 51.—Objectives with Equiconvex Crown.]
-
-Probably nine tenths of all objectives are of this general form,
-equiconvex crown and nearly or quite plano-concave flint. The inside
-radii may be the same, in which case the lenses should be cemented,
-or they may differ slightly in either direction as _a_, Fig. 51
-with the front of the flint less curved than the rear of the crown,
-and _b_ where the flint has the sharper curve. The resulting lens if
-ordinary glasses are chosen gives excellent correction of the spherical
-aberration on the axis, but not much away from it, yielding a rather
-narrow sharp field. Only a few exceptional combinations of glasses
-relieve this situation materially.
-
-The identity of the inner radii so that the surfaces can be cemented
-is known historically as Clairault’s condition, and since it fixes two
-curvatures at identity somewhat limits the choice of glasses, while to
-get proper corrections demands quite wide variations in the contact
-radii for comparatively small variations in the optical constants of
-the glass.
-
-When two adjacent curves are identical they should be cemented,
-otherwise rays reflected from say the third surface of Fig. 51 will be
-reflected again from the second surface, and passing through the rear
-lens in almost the path of the original ray will come to nearly the
-same focus, producing a troublesome “ghost.” Hence the curvatures of
-the second and third surfaces when not cemented are varied one way or
-the other by two or three per cent, enough to throw the twice reflected
-rays far out of focus.
-
-In this case, as in most others, the analytical expression for the
-fundamental curvature to be determined turns up in the form of a
-quadratic equation, so that the result takes the form a ± b and there
-are two sets of radii that meet the requirements. Of these the one
-presenting the gentler curves is ordinarily chosen. Fig. 52 _a_ and
-_c_ shows the two cemented forms, thus related, for a common pair of
-crown and flint glasses, both cleanly corrected for chromatic and axial
-spherical aberration.
-
-Nearly a century ago Sir John Herschel proposed another defining
-condition, that the spherical aberration should be removed both for
-parallel incident rays and for those proceeding from a nearer point
-on the axis, say ten or more times the focal length in front of the
-objective. This condition had little practical value in itself, and its
-chief merit was that it approximated one that became of real importance
-if the second point were taken far enough away.
-
-[Illustration: FIG. 52.—Allied Forms of Cemented Objectives.]
-
-A little later Gauss suggested that the spherical aberration should be
-annulled for two different colors, much as the chromatic aberration is
-treated. And, being a mathematical wizard, he succeeded in working out
-the very intricate theory, which resulted in an objective approximately
-of the form shown in Fig. 53.
-
-It does not give a wide field but is valuable for spectroscopic work,
-where keen definition in all colors is essential. Troublesome to
-compute, and difficult to mount and center, the type has not been much
-used, though there are fine examples of about 9½ inches aperture at
-Princeton, Utrecht, and Copenhagen, and a few smaller ones elsewhere,
-chiefly for spectroscopic use.
-
-It was Fraunhofer who found and applied the determining condition of
-the highest practical value for most purposes. This condition was
-absence of _coma_, the comet shaped blur generally seen in the outer
-portions of a wide field.
-
-It is due to the fact that parallel oblique rays passing through
-the opposite rims of the lens and through points near its center do
-not commonly come to the same focus, and it practically is akin to
-a spherical aberration for oblique rays which greatly reduces the
-extent of the sharp field. It is reckoned + when the blur points
-outwards,-when it points inwards, and is directly proportional to the
-tangent of the obliquity and the square of the aperture, and inversely
-to the square of the focal length i.e. it varies with a²tan(u)/f².
-
-[Illustration: FIG. 53.—Gaussian Objective.]
-
-Just how Fraunhofer solved the problem is quite unknown, but solve it
-he did, and very completely, as he indicates in one of his later papers
-in which he speaks of his objective as reducing all the aberrations
-to a minimum, and as Seidel proved 30 years later in the analysis of
-one of Fraunhofer’s objectives. Very probably he worked by tracing
-axial and oblique rays through the objective form by trigonometrical
-computation, thus finding his way to a standard form for the glasses he
-used.[10]
-
- [10] More recently his condition proves to be quite the exact
- equivalent of Abbé’s _sine condition_ which states that the sine of
- the angle made with the optical axis by a ray entering the objective
- from a given axial point shall bear a uniform ratio to the sine of the
- corresponding angle of emergence, whatever the point of incidence.
- For parallel rays along the axis this reduces to the requirement that
- the sines of the angles of emergence shall be proportional to the
- respective distances of the incident rays from the axis.
-
-Fraunhofer’s objective, of which Fig. 54_a_ is an example worked by
-modern formulæ for the sine condition, gives very exact corrections
-over a field of 2°-3° when the glasses are suitably chosen and hence is
-invaluable for any work requiring a wide angle of view.
-
-With certain combinations of glasses the coma-free condition may
-be combined successfully with Clairault’s, although ordinarily
-the coma-free form falls between the two forms clear of spherical
-aberration, as in Fig. 52, _b_, which has its oblique rays well
-compensated but retains serious axial faults.
-
-[Illustration: FIG. 54.—The Fraunhofer Types.]
-
-Fraunhofer’s objective has for all advantageous combinations of glasses
-the front radius of the flint longer than the rear radius of the
-crown hence the two must be separated by spacers at the edge, which
-in small lenses in simple cells is slightly inconvenient. However,
-the common attempt to simplify mounting by making the front flint
-radius the shorter almost invariably violates the sine condition and
-reduces the sharp field, fortunately not a very serious matter for most
-astronomical work.
-
-The only material objection to the Fraunhofer type is the strong
-curvature of the rear radius of the crown which gives a form somewhat
-susceptible to flexure in large objectives. This is met in the
-flint-ahead form, developed essentially by Steinheil, and used in most
-of the objectives of his famous firm. Fig. 54_b_ shows the flint-ahead
-objective corresponding to Fig. 54_a_. Obviously its curves are
-mechanically rather resistant to flexure.[11]
-
- [11] It is interesting to note that in computing Fig. 54_a_ for the
- sine condition, the other root of the quadratic gave roughly the
- Gaussian form of Fig. 53.
-
-[Illustration: FIG. 55.—Clark Objective.]
-
-Mechanical considerations are not unimportant in large objectives, and
-Fig. 55, a highly useful form introduced by the Clarks and used in
-recent years for all their big lenses, is a case in point. Here there
-is an interval of about the proportion shown between the crown and
-flint components.
-
-This secures effective ventilation allowing the lenses to come quickly
-to their steady temperature, and enables the inner surfaces to be
-cleaned readily and freed of moisture. Optically it lessens the
-deviation from the sine condition otherwise practically inseparable
-from the equiconvex crown, reduces the chromatic difference of
-spherical aberration, and gives an easy way of controlling the color
-correction by slightly varying the separation of the lenses.
-
-One further special case is worth noting, that of annulling the
-spherical aberration for rays passing through the lens in both
-directions. By proper choice of glass and curvatures this can be
-accomplished to a close approximation and the resulting form is shown
-in Fig. 56. The front of the crown is notably flat and the rear of
-the flint conspicuously curved, the shape in fact being intermediate
-between Figs. 52_b_ and 52_c_. The type is useful in reading telescopes
-and the like, and for some spectroscopic applications.
-
-[Illustration: FIG. 56.—Corrected in Both Directions.]
-
-There are two well known forms of aberration not yet considered;
-astigmatism and curvature of field. The former is due to the fact that
-when the path of the rays is away from the axis, as from an extended
-object, those coming from a line radial to the axis, and those from a
-line tangent to a circle about the axis, do not come to the same focus.
-The net result is that the axial and tangential elements are brought to
-focus in two coaxial surfaces touching at the axis and departing more
-and more widely from each other as they depart from it. Both surfaces
-have considerable curvature, that for tangential lines being the
-sharper.
-
-It is possible by suitable choice of glasses and their curvatures
-to bring both image surfaces together into an approximate plane for
-a moderate angular space about the axis without seriously damaging
-the corrections for chromatic and spherical aberration. To do this
-generally requires at least three lenses, and photographic objectives
-thus designed (_anastigmats_) may give a substantially flat field over
-a total angle of 50° to 60° with corrections perfect from the ordinary
-photographic standpoint.
-
-If one demands the rigorous precision of corrections called for in
-astronomical work, the possible angle is very much reduced. Few
-astrographic lenses cover more than a 10° or 15° field, and the wider
-the relative aperture the harder it is to get an anastigmatically flat
-field free of material errors. Astigmatism is rarely noticeable in
-ordinary telescopes, but is sometimes conspicuous in eyepieces.
-
-Curvature of field results from the tendency of oblique rays in
-objectives, otherwise well corrected, to come to shorter focus than
-axial rays, from their more considerable refraction resulting from
-greatly increased angles of incidence. This applies to both the
-astigmatic image surfaces, which are concave toward the objective in
-all ordinary cases.
-
-Fortunately both these faults are negligible near the axis. They are
-both proportional to tan²{u}/f where u is the obliquity to the axis
-and f the focal length; turn up with serious effect in wide angled
-lenses such as are used in photography, but may generally be forgotten
-in telescopes of the ordinary _F_ ratios, like _F_/12 to _F_/16. So
-also one may commonly forget a group of residual aberrations of higher
-orders, but below about _F_/8 look out for trouble. Objectives of
-wider aperture require a very careful choice of special glasses or
-the sub-division of the curvatures by the use of three or more lenses
-instead of two. Fig. 57 shows a cemented triplet of Steinheil’s design,
-with a crown lens between two flints. Such triplets are made up to
-about 4 inches diameter and of apertures ranging from _F_/4 to _F_/5.
-
-[Illustration: FIG. 57.—Steinheil Triple Objective.]
-
-[Illustration: FIG. 58.—Tolles Quadruple Objective.]
-
-In cases of demand for extreme relative aperture, objectives composed
-of four cemented elements have now and then been produced. An example
-is shown in Fig. 58, a four-part objective of 1 inch aperture made
-by Tolles years ago for a small hand telescope. Its performance,
-although it worked at _F_/4, was reported to be excellent even up to 75
-diameters.
-
-The main difficulty with these objectives of high aperture is the
-relatively great curvature of field due to short focal length which
-prevents full utilization of the improved corrections off the axis.
-
-Distortion is similarly due to the fact that magnification is not quite
-the same for rays passing at different distances from the axis. It
-varies in general with the cube of the distance from the axis, and is
-usually negligible save in photographic telescopes, ordinary visual
-fields being too small to show it conspicuously.
-
-Distortion is most readily avoided by adopting the form of a
-symmetrical doublet of at least four lenses as in common photographic
-use. No simple achromatic pair gives a field wholly free of distortion
-and also of the ordinary aberrations, except very near the axis, and
-in measuring plates taken with such simple objectives corrections for
-distortion are generally required.
-
-At times it becomes necessary to depart somewhat from the objective
-form which theoretically gives the least aberrations in order to
-meet some specific requirement. Luckily one may modify the ratios of
-the curves very perceptibly without serious results. The aberrations
-produced come on gradually and not by jumps.
-
-[Illustration: FIG. 59.—“Bent” Objective.]
-
-A case in point is that of the so-called “bent” objective in which the
-curvatures are all changed symmetrically, as if one had put his fingers
-on the periphery and his thumbs on the centre of the whole affair, and
-had sprung it noticeably one way or the other.
-
-The corrections in general are slightly deteriorated but the field may
-be in effect materially flattened and improved. An extreme case is the
-photographic landscape lens. Figure 59 is an actual example from a
-telescope where low power and very large angular view were required.
-The objective was first designed from carefully chosen glass to meet
-accurately the sine condition. Even so the field, which covered an
-apparent angle of fully 40°, fell off seriously at the edge.
-
-Bearing in mind the rest of the system, the objective was then “bent”
-into the form given by the dotted lines, and the telescope then showed
-beautiful definition clear to the periphery of the field, without any
-visible loss in the centre.
-
-This spurious flattening cannot be pushed far without getting into
-trouble for it does not cure the astigmatic difference of focus, but
-it is sometimes very useful. Practically curvature of field is an
-outstanding error that cannot be remedied in objectives required to
-stand high magnifying powers, except by going to the anastigmatic forms
-similar to those used in photography.[12]
-
- [12] The curvature of the image is the thing which sets a limit to
- shortening the relative focus, as already noted, for the astigmatic
- image surfaces as we have seen, fall rapidly apart away from the
- axis, and both curvatures are considerable. The tangential is the
- greater, corresponding roughly to a radius notably less than ⅓ the
- focal length, while the radial fits a radius of less than ⅔ this
- length with all ordinary glasses, given forms correcting the ordinary
- aberrations. The curves are concave towards the objective except in
- “anastigmats” and some objectives having bad aberrations otherwise.
- Their approximate curvatures assuming a semiangular aperture for an
- achromatic objective not over say 5°, have been shown to be, to focus
- unity
-
- ρ_{r} = 1 + (1/(ν-ν′)(ν/n - ν′/n′)),
- and ρ_{t} = 3 + 1/(ν-ν′)(ν/n - ν′/n′)
-
- ρ_r and ρ_t being the respective reciprocals of the radii. The
- surfaces are really somewhat egg shaped rather than spherical as one
- departs from the axis.
-
-Aside from curvature the chief residual error in objectives is
-imperfection of achromatism. This arises from the fact that crown and
-flint glasses do not disperse the various colors quite in the same
-ratio. The crown gives slightly disproportionate importance to the
-red end of the spectrum, the flint to the violet end—the so-called
-“irrationality of dispersion.”
-
-Hence if a pair of lenses match up accurately for two chosen colors
-like those represented by the C and F lines, they will fail of mutual
-compensation elsewhere. Figure 60 shows the situation. Here the spectra
-from crown and flint glasses are brought to exactly the same extent
-between the C and F lines, which serve as landmarks.
-
-Clearly if two prisms or lenses are thus adjusted to the same
-refractions for C and F, the light passing through the combination will
-still be slightly colored in virtue of the differences elsewhere in the
-spectrum. These residual color differences produce what is known as the
-“secondary spectrum.”
-
-What this does in the case of an achromatic lens may be clearly seen
-from the figure; C and F having exactly the same refractions in the
-flint and crown, come to the same focus. For D, the yellow line of
-sodium, the flint lens refracts a shade the less, hence is not quite
-powerful enough to balance the crown, which therefore brings D to a
-focus a little shorter than C and F. On the other hand for A′ and G′,
-the flint refracts a bit more than the crown, overbalances it and
-brings these red and violet rays to a focus a little longer than the
-joint C and F focus.
-
-[Illustration: FIG. 60.—Irrationality of Dispersion.]
-
-The difference for D is quite small, roughly about 1/2000 of the focal
-length, while the red runs long by nearly three times that amount,
-the violet by about four. Towards the H line the difference increases
-rapidly and in large telescopes the actual range of focus for the
-various colors amounts to several inches.
-
-This difficulty cannot be avoided by any choice among ordinary pairs of
-glasses, which are nearly alike in the matter of secondary spectrum.
-In the latter part of the last century determined efforts were made to
-produce glasses that would give more nearly an equal run of dispersion,
-at first by English experimenters, and then with final success by
-Schott and Abbé at Jena.
-
-Both crown and flint had to be quite abnormal in composition,
-especially the latter, and the pair were of very nearly the same
-refractive index and with small difference in the quantity ν which
-we have seen determines the general amount of curvature. Moreover it
-proved to be extremely hard to get the crown quite homogeneous and
-it is listed by Schott with the reservation that it is not free from
-bubbles and striæ.
-
-Nevertheless the new glasses reduce the secondary spectrum greatly, to
-about ¼ of its ordinary value, in the average. It is difficult to
-get rid of the spherical aberration, however, from the sharp curves
-required and the small difference between the glasses, and it seems to
-be impracticable on this account to go to greater aperture than about
-_F_/20.
-
-Figure 61 shows the deeply curved form necessary even at half the
-relative aperture usable with common glasses. At _F_/20 the secondary
-spectrum from the latter is not conspicuous and Roe (Pop. Ast. _18_,
-193), testing side by side a small Steinheil of the new glasses, and a
-Clark of the old, of almost identical size and focal ratio, found no
-difference in their practical performance.
-
-Another attack on the same problem was more successfully made by H. D.
-Taylor. Realizing the difficulty found with a doublet objective of even
-the best matched of the new glasses, he adopted the plan of getting a
-flint of exactly the right dispersion by averaging the dispersions of a
-properly selected pair of flints formed into lenses of the appropriate
-relative curvatures.
-
-[Illustration: FIG. 61.—Apochromatic Doublet.]
-
-[Illustration: FIG. 62.—Apochromatic Triplet.]
-
-The resulting form of objective is made, especially, by Cooke of York,
-and also by Continental makers, and carries the name of “photo-visual”
-since the exactness of corrections is carried well into the violet,
-so that one can see and photograph at the same focus. The residual
-chromatic error is very small, not above 1/8 to 1/10 the ordinary
-secondary spectrum.
-
-By this construction it is practicable to increase the aperture to
-_F_/12 or _F_/10 while still retaining moderate curvatures and reducing
-the residual spherical aberration. There are a round dozen triplet
-forms possible, of which the best, adopted by Taylor, is shown in Fig.
-62. It has the duplex flint ahead—first a baryta light flint, then a
-borosilicate flint, and to the rear a special light crown. The two
-latter glasses have been under some suspicion as to permanence, but the
-difficulty has of late years been reported as remedied. Be that as it
-may, neither doublets nor triplets with reduced secondary spectrum have
-come into any large use for astronomical purposes. Their increased
-cost is considerable,[13] their aperture even in the triplet, rather
-small for astrophotography, and their achromatism is still lacking the
-perfection reached by a mirror.
-
- [13] The doublet costs about one and a half times, and the triplet
- more than twice the price of an ordinary achromatic of the same
- aperture.
-
-The matter of achromatism is further complicated by the fact that
-objectives are usually over-achromatized to compensate for the
-chromatic errors in the eyepiece, and especially in the eye. As a
-general rule an outstanding error in any part of an optical system can
-be more or less perfectly balanced by an opposite error anywhere else
-in the system—the particular point chosen being a matter of convenience
-with respect to other corrections.
-
-The eye being quite uncorrected for color the image produced even by
-a reflector is likely to show a colored fringe if at all bright, the
-more conspicuous as the relative aperture of the pupil increases. For
-low power eyepieces the emerging ray may quite fill a wide pupil and
-then the chromatic error is troublesome. Hence it has been the custom
-of skilled opticians, from the time of Fraunhofer, who probably started
-the practice, to overdo the correction of the objective just a little
-to balance the fault of the eye.
-
-What actually happens is shown in Fig. 63, which gives the results
-of achromatization as practiced by some of the world’s adepts. The
-shortest focus is in the yellow green, not far from the line D. The
-longest is in the violet, and F, instead of coinciding in focus with
-C as it is conventionally supposed to do, actually coincides with the
-deep and faint red near the line marked B. Hence the visible effect
-is to lengthen the focus for blue enough to make up for the tendency
-of the eye in the other direction. The resulting image then should
-show no conspicuous rim of red or blue. The actual adjustment of
-the color correction is almost wholly a matter of skilled judgment
-but Fig. 63 shows that of the great makers to be quite uniform. The
-smallest overcorrection is found in the Grubb objective, the largest
-in the Fraunhofer. The differences seem to be due mainly to individual
-variations of opinion as to what diameter of pupil should be taken as
-typical for the eye.
-
-The common practice is to get the best possible adjustment for a fairly
-high power, corresponding to a beam hardly 1/64 inch in diameter
-entering the pupil.
-
-In any case the bigger the pencil of rays utilized by the eye, i.e.,
-the lower the power, the more overcorrection must be provided, so that
-telescopes intended, like comet seekers, for regular use with low
-powers must be designed accordingly, either as respects objective or
-ocular.
-
-[Illustration: FIG. 63.—Achromatization Curves by Various Makers.
-1. Fraunhofer 2. Clark 3. Steinheil 4. Hastings-Brashear 5. Grubb ]
-
-The differences concerned in this chromatic correction for power are by
-no means negligible in observing, and an objective actually conforming
-to the C to F correction assumed in tables of optical glass would
-produce a decidedly unpleasant impression when used with various
-powers on bright objects. And the values for ν implied in the actual
-color correction are not immaterial in computing the best form for a
-proposed objective.
-
-1 is from Franunhofer’s own hands, the instrument of 9.6 inches
-aperture and 170 inches focus in the Berlin Observatory.
-
-2 The Clark refractor of the Lowell Observatory, 24 inches aperture and
-386 inches focal length. This is of the usual Clark form, crown ahead,
-with lenses separated by about ⅙ of their diameter.
-
-3 is a Steinheil refractor at Potsdam of 5.3 inches aperture, and 85
-inches focus.
-
-4 is from the fine equatorial at Johns Hopkins University, designed by
-Professor Hastings and executed by Brashear.
-
-The objective was designed with special reference to minimizing the
-spherical aberration not only for one chosen wave length but for all
-others, has the flint lens ahead, aperture 9.4 inches, focal length 142
-inches, and the lenses separated by ¼ inch in the final adjustment of
-the corrections.
-
-5 is from the Potsdam equatorial by Grubb, 8.5 inches aperture 124
-inches focus.
-
-The great similarity of the color curves is evident at a glance, the
-differences due to variations in the glass being on the whole much less
-significant than those resulting from the adjustment for power.
-
-Really very little can be done to the color correction without going to
-the new special glasses, the use of which involves other difficulties,
-and leaves the matter of adjustment for power quite in the air, to be
-brought down by special eye pieces. Now and then a melting of glass has
-a run of dispersion somewhat more favorable than usual, but there is
-small chance of getting large discs of special characteristics, and the
-maker has to take his chance, minute differences in chromatic quality
-being far less important than uniformity and good annealing.
-
-Regarding the aberrations of mirrors something has been said in Chap.
-I, but it may be well here to show the practical side of the matter by
-a few simple illustrations.
-
-Figure 64 shows the simplest form of concave mirror—a spherical
-surface, in this instance of 90° aperture, the better to show its
-properties. If light proceeded radially outward from _C_, the center of
-curvature of the surface, evidently any ray would strike the surface
-perpendicularly as at _a_ and would be turned squarely back upon
-itself, passing again through the center of curvature as indicated in
-the figure.
-
-A ray, however, proceeding parallel to the axis and striking the
-surface as at _bb_ will be deflected by twice the angle of incidence as
-is the case with all reflected rays. But this angle is measured by the
-radius _Cb_ from the center of curvature and the reflected ray makes an
-angle _CbF_ with the radius, equal to _FCb_. For points very near the
-axis _bF_, therefore, equals _FC_, and substantially also equals _cF_.
-Thus rays near the axis and parallel to it meet at _F_ the focus half,
-way from _c_ to _C_. The equivalent focal length of a spherical concave
-mirror of small aperture is therefore half its radius of curvature.
-
-[Illustration: FIG. 64.—Reflection from Concave Spherical Mirror.]
-
-But obviously for large angles of incidence these convenient equalities
-do not hold. As the upper half of the figure shows, the ray parallel
-to the axis and incident on the mirror 45° away at _e_ is turned
-straight down, for it falls upon a surface inclined to it by 45° and
-is therefore deflected by 90°, cutting the axis far inside the nominal
-focus, at _d_. Following up other rays nearer the axis it appears that
-there is no longer a focal point but a cusp-like focal surface, known
-to geometrical optics as a caustic and permitting no well defined image.
-
-A paraboloidal reflecting surface as in Fig. 65 has the property
-of bringing to a single point focus all rays parallel to its axis
-while quite failing of uniting rays proceeding from any point on its
-axis, since its curvature is changing all the way out from vertex
-to periphery. Here the parallel rays _a_, _a_, _a_, _a_ meeting
-the surface are reflected to the focus _F_, while in a perfectly
-symmetrical way the prolongation of these rays _a′_, _a′_, _a′_, _a′_
-if incident on the convex surface of the paraboloid would be reflected
-in _R_, _R′_, _R″_ _R″′_ just as if they proceeded from the same focus
-_F_.
-
-The difference between the spherical and parabolic curves is well shown
-in Fig. 66. Here are sections of the former, and in dotted lines of
-the latter. The difference points the moral. The parabola falls away
-toward the periphery and hence pushes outward the marginal rays. But
-it is of relatively sharper curvature near the center and pulls in the
-central to meet the marginal portion. In the actual construction of
-parabolic mirrors one always starts with a sphere which is easy to test
-for precision of figure at its center of curvature. Then the surface
-may be modified into a paraboloid lessening the curvature towards the
-periphery, or by increasing the curvature toward the center starting in
-this case with a sphere of a bit longer radius as in Fig. 66a.
-
-[Illustration: FIG. 65.—Reflection from Paraboloid.]
-
-[Illustration: FIG. 66_a_. FIG. 66_b_.
-Variation of Paraboloid from Sphere.]
-
-Practice differs in this respect, either process leading to the same
-result. In any case the departure from the spherical curve is very
-slight—a few hundred thousandths or at most ten thousandths of an inch
-depending on the size and relative focus of the mirror.
-
-Yet this small variation makes all the difference between admirable and
-hopelessly bad definition. However the work is done it is guided by
-frequent testing, until the performance shows that a truly parabolic
-figure has been reached. Its attainment is a matter of skilled judgment
-and experience.
-
-The weak point of the parabolic mirror is in dealing with rays coming
-in parallel but oblique to the axis. Figure 67 shows the situation
-plainly enough. The reflected rays _a′_, _a″_ no longer meet in a
-point at the focus _F_ but inside the focus for parallel rays, at _f_
-forming a surface of aberration. The practical effect is that the image
-rapidly deteriorates as the star passes away from the axis, taking on
-an oval character that suggests a bad case of astigmatism with serious
-complications from coma, which in fact is substantially the case.
-
-[Illustration: FIG. 67.—Aberration of Parabolic Mirror.]
-
-Even when the angular aperture is very small the focal surface is
-nevertheless a sphere of radius equal to one half the focal length, and
-the aberrations off the axis increase approximately as the square of
-the relative aperture, and directly as the angular distance from the
-axis.
-
-The even tolerably sharp field of the mirror is therefore generally
-small, rarely over 30′ of arc as mirrors are customarily proportioned.
-At the relative aperture usual with refractors, say F/15, the sharp
-fields of the two are quite comparable in extent. The most effective
-help for the usual aberrations[14] of the mirror is the adoption of the
-Cassegrain form, by all odds the most convenient for large instruments,
-with a hyperboloid secondary mirror.
-
- [14] A very useful treatment of the aberrations of parabolic mirrors
- by Poor is in Ap. J. 7, 114. In this is given a table of the maximum
- dimension of a star disc off the axis in reflectors of various
- apertures. This table condenses to the closely approximate formula
-
- a = lld/f²
-
- where a is the aberrational diameter of the star disc, in seconds of
- arc, d the distance from the axis in minutes of arc, f the denominator
- of the F ratio (F/8 &c.) and 11, a constant. Obviously the separating
- power of a telescope (see Chap. X) being substantially 4.″56/D where
- D is the diameter of objective or mirror in inches, the separating
- power will be impaired when a > 4.″56/D. In the photographic
- case the critical quantity is not 4.″56/D, but the maximum image
- diameter tolerable for the purpose in hand. mirror is the adoption
- of the Cassegrain form, by all odds the most convenient for large
- instruments, with a hyperboloidal secondary mirror.
-
-The hyperboloid is a curve of very interesting optical properties. Just
-as a spherical mirror returns again rays proceeding from its center of
-curvature without aberration, and the paraboloid sends from its focus
-a parallel axial beam free of aberration, or returns such a beam to an
-exact focus again, so a hyperboloid, Fig. 68, sends out a divergent
-beam free from aberration or brings it, returning, to an exact focus.
-
-Such a beam _a_, _a_, _a_, in fact behaves as if it came from and
-returned to a virtual conjugate focus _F′_ on the other side of the
-hyperbolic surface. And if the convex side be reflecting, converging
-rays _R_, _R_′, _R″_, falling upon it at _P_, _P′_, _P″_, as if headed
-for the virtual focus _F_, will actually be reflected to _F′_, now a
-real focus.
-
-This surface being convex its aberrations off the axis are of opposite
-sign to those due to a concave surface, and can in part at least, be
-made to compensate the aberrations of a parabolic main mirror. The
-rationale of the operation appears from comparison of Figs. 67 and 68.
-
-[Illustration: FIG. 68.—Reflection from Hyperboloid.]
-
-In the former the oblique rays _a_, _a′_ are pitched too sharply down.
-When reflected from the convex surface of Fig. 68 as a converging beam
-along _R_, _R′_, _R″_, they can nevertheless, if the hyperbola be
-properly proportioned, be brought down to focus at _F′_ conjugate to
-_F_, their approximate mutual point of convergence.
-
-Evidently, however, this compensation cannot be complete over a wide
-angle, when _F′_ spreads into a surface, and the net result is that
-while the total aberrations are materially reduced there is some
-residual coma together with some increase of curvature of field, and
-distortion. Here just as in the parabolizing of the large speculum
-the construction is substantially empirical, guided in the case of a
-skilled operator by a sort of insight derived from experience.
-
-Starting from a substantially spherical convexity of very nearly the
-required curvature the figure is gradually modified as in the earlier
-example until test with the truly parabolic mirror shows a flawless
-image for the combination. The truth is that no conic surface of
-revolution save the sphere can be ground to true figure by any rigorous
-geometrical method. The result must depend on the skill with which one
-by machine or hand can gauge minute departures from the sphere.
-
-Attempts have been made by the late Professor Schwarzchild and others
-to improve the corrections of reflectors so as to increase the field
-but they demand either very difficult curvatures imposed on both
-mirrors, or the interposition of lenses, and have thus far reached no
-practical result.
-
-
-REFERENCES
-
-  SCHWARZCHILD: Untersuchungen 2, Geom., Opt. II.
-  SAMPSON _Observatory 36_, 248.
-  CODDINGTON: “Reflexion and Refraction of Light.”
-  HERSCHEL: “Light.”
-  TAYLOR: “Applied Optics.”
-  SOUTHALL: “Geometrical Optics.”
-  MARTIN: _Ann. Sci. de l’Ecole Normale_, 1877, Supplement.
-  MOSER: _Zeit. f._ Instrumentenkunde, 1887.
-  HARTING: _Zeit. f. Inst._, 1899.
-  HARTING: _Zeit. f. Inst._, 1898.
-  VON HOEGH: _Zeit. f. Inst._, 1899.
-  STEINHEIL & VOIT: “Applied Optics.”
-  COLLECTED RESEARCHES, National Physical Laboratory, Vol. 14.
-  GLEICHEN: “Lehrbuch d. Geometrische Optik.”
-
-NOTE.—In dealing with optical formulæ look out for the algebraic signs.
-Writers vary in their conventions regarding them and it sometimes is
-as difficult to learn how to apply a formula as to derive it from the
-start. Also, especially in optical patents, look out for camouflage,
-as omitting to specify an optical constant, giving examples involving
-glasses not produced by any manufacturer, and even specifying curves
-leading to absurd properties. It is a good idea to check up the
-achromatization and focal length before getting too trustful of a
-numerical design.
-
-
-
-
-CHAPTER V
-
-MOUNTINGS
-
-
-A steady and convenient mounting is just as necessary to the successful
-use of the telescope as is a good objective. No satisfactory
-observations for any purpose can be made with a telescope unsteadily
-mounted and not provided with adjustments enabling it to be moved
-smoothly and easily in following a celestial object.
-
-Broadly, telescope mounts may be divided into two general classes,
-alt-azimuth and equatorial. The former class is, as its name suggests,
-arranged to be turned in azimuth about a vertical axis, and in altitude
-about a horizontal axis. Such a mounting may be made of extreme
-simplicity, but obviously it requires two motions in order to follow up
-any object in the field, for the apparent motion of the heavenly bodies
-is in circles about the celestial pole as an axis, and consequently
-inclined from the vertical by the latitude of the place of observation.
-
-Pointing a telescope with motions about a vertical and horizontal axis
-only, therefore means that, as a star moves in its apparent path, it
-will drift away from the telescope both in azimuth and in altitude, and
-require to be followed by a double motion.
-
-Alt-azimuth mounts may be divided into three general groups according
-to their construction. The first and simplest of them is the
-pillar-and-claw stand shown in Figure 69. This consists of a vertical
-pillar supported on a strong tripod, usually of brass or iron, and
-provided at its top with a long conical bearing carrying at its upper
-extremity a hinged joint, bearing a bar to which the telescope is
-screwed as shown in the illustration.
-
-If properly made the upper joint comprises a circular plate carrying
-the bar and held between two cheek pieces with means for taking up
-wear, and providing just enough friction to permit of easy adjustment
-of the telescope, which can be swung in altitude from near the zenith
-to the horizon or below, and turned around its vertical axis in any
-direction.
-
-When well made a stand of this kind is steady and smooth working,
-readily capable of carrying a telescope up to about 3 inches aperture.
-It needs for its proper use a firm sub-support for the three strong
-hinged legs of the pillar. This is conveniently made as a very solid
-stool with spreading legs, or a plank of sufficient size may be firmly
-bolted to a well set post.
-
-[Illustration: FIG. 69.—Table Mount with Slow Motion.]
-
-Thus arranged the mount is a very serviceable one for small
-instruments. Its stability, however, depends on the base upon which
-it is set. The writer once unwisely attempted to gain convenience by
-removing the legs of the stand and screwing its body firmly upon a very
-substantial tripod. The result was a complete failure in steadiness,
-owing to the rather long lever arm furnished by the height of the
-pillar; and the instrument, which had been admirably steady originally,
-vibrated abominably when touched for focussing.
-
-The particular stand here shown is furnished with a rack motion in
-altitude which is a considerable convenience in following. More
-rarely adjustable steadying rods attached to the objective end of the
-instrument are brought down to its base, but for a telescope large
-enough to require this a better mount is generally desirable.
-
-Now and then an alt-azimuth head of just the sort used in the
-pillar-and-claw stand is actually fitted on a tall tripod, but such an
-arrangement is usually found only in cheap instruments and for such
-tripod mountings other fittings are desirable.
-
-[Illustration: FIG. 70.—Alt-azimuth Mount, Clark Type T.]
-
-The second form of alt-azimuth mount, is altogether of more substantial
-construction. The vertical axis, usually tapered and carefully ground
-in its bearings, carries an oblique fork in which the telescope tube is
-carried on trunnions for its vertical motion. The inclination of the
-forked head enables the telescope to be pointed directly toward the
-zenith and the whole mount forms the head of a well made tripod.
-
-Figure 70 shows an excellent type of this form of mount as used
-for the Clark Type T telescope, designed for both terrestrial and
-astronomical observation. In this particular arrangement the telescope
-lies in an aluminum cradle carried on the trunnions, from which it can
-be readily removed by loosening the thumb screws and opening the cradle.
-
-[Illustration: FIG. 71.—Alt-azimuth with Full Slow Motions.]
-
-It can also be set longitudinally for balance in the cradle if any
-attachments are to be placed upon either end. Here the adjustment for
-the height of the instrument is provided both in the spread of the
-tripod and in the adjustable legs. So mounted a telescope of 3 or 4
-inches aperture is easily handled and capable of rendering very good
-service either for terrestrial or celestial work.
-
-Indeed the Clarks have made instruments up to 6 inches aperture,
-mounted for special service in this simple manner. For celestial use
-where fairly high powers may be required this or any similar mount can
-be readily furnished with slow motions either in azimuth or altitude or
-both.
-
-Figure 71 shows a 4¼ inch telescope and mount by Zeiss thus
-equipped. Some alt-azimuth mounts are also provided with a vertical
-rack motion to bring the telescope to a convenient height without
-disturbing the tripod. A good alt-azimuth mount such as is shown in
-Figs. 70 and 71 is by no means to be despised for use with telescopes
-of 3 or 4 inch aperture.
-
-The sole inconvenience to be considered is that of the two motions
-required in following. With well fitted slow motions this is not really
-serious for ordinary observing with moderate powers, for one can work
-very comfortably up to powers of 150 or 200 diameters keeping the
-object easily in view; but with the higher powers in which the field is
-very small, only a few minutes of arc, the double motion becomes rather
-a nuisance and it is extremely inconvenient even with low powers in
-sweeping for an object the place of which is not exactly known.
-
-There are in fact two distinct kinds of following necessary in
-astronomical observations. First, the mere keeping of the object
-somewhere in the field, and second, holding it somewhat rigorously in
-position, as in making close observations of detail or micrometrical
-measurements. When this finer following is necessary the sooner one
-gets away from alt-azimuth mounts the better.
-
-Still another form of alt-azimuth mount is shown in Fig. 72 applied for
-a Newtonian reflector of 6 or 8 inches aperture. Here the overhung fork
-carrying the tube on trunnions is supported on a stout fixed tripod, to
-which it is pivoted at the front, and it is provided at the rear with a
-firm bearing on a sector borne by the tripod.
-
-At the front a rod with sliding coarse, and screw fine, adjustment
-provides the necessary motion in altitude. The whole fork is swung
-about its pivot over the sector bearing by a cross screw turned by a
-rod with a universal joint.
-
-This mount strongly suggests the original one of Hadley, Fig. 16, and
-is most firm and serviceable. A reflector thus mounted is remarkably
-convenient in that the eyepiece is always in a most accessible
-position, the view always horizontal, and the adjustments always within
-easy reach of the observer.
-
-[Illustration: FIG. 72.—Alt-azimuth Newtonian Reflector.]
-
-Whenever it is necessary to follow an object closely, as in using
-a micrometer and some other auxiliaries, the alt-azimuth mount is
-troublesome and some modification adjustable by a single motion,
-preferably made automatic by clockwork, becomes necessary.
-
-The first step in this direction is a very simple one indeed. Suppose
-one were to tilt the azimuth axis so that it pointed to the celestial
-pole, about which all the stars appear to revolve. Then evidently
-the telescope being once pointed, a star could be followed merely by
-turning the tube about this tilted axis. Of course one could not easily
-reach some objects near the pole without, perhaps, fouling the mount,
-but in general the sky is within reach and a single motion follows the
-star, very easily if the original mount had a slow motion in azimuth.
-
-This is in fact the simplest form of equatorial mount, sometimes
-called parallactic. Figure 73 shows the principle applied to a small
-reflector. An oblique block with its angle adjusted to the co-latitude
-of the place drops the vertical axis into line with the pole, and the
-major part of the celestial vault is then within easy reach.
-
-It may be regarded as the transition step from the alt-azimuth to
-the true equatorial. It is rarely used for refractors, and the first
-attempt at a real equatorial mount was in fact made by James Short F.
-R. S. in mounting some of his small Gregorians.[15] As a matter of
-record this is shown, from Short’s own paper before the Royal Society
-in 1749, in Fig. 74.
-
- [15] Instruments with a polar axis were used by Scheiner as early
- as 1627; by Roemer about three quarters of a century later, and
- previously had been employed, using sights rather than telescopes, by
- the Chinese; but these were far from being equatorials in the modern
- sense.
-
-[Illustration: FIG. 73.—Parallactic Mount for Reflector.]
-
-A glance shows a stand apparently most complicated, but closer
-examination discloses that it is merely an equatorial on a table
-stand with a sweep in declination over a very wide arc, and quite
-complete arrangements for setting to the exact latitude and azimuth.
-The particular instrument shown was of 4 inches aperture and about 18
-inches long and was one of several produced by Short at about this
-epoch.
-
-[Illustration: FIG. 74.—Short’s Equatorial Mount.]
-
-In the instrument as shown there is first an azimuth circle _A A_
-supported on a base _B B B B_ having levelling screws in the feet.
-Immediately under the azimuth circle is mounted a compass needle for
-approximate orientation, and the circle is adjustable by a tangent
-screw _C_.
-
-Carried by the azimuth circle on a bearing supported by four pillars
-is a latitude circle _D D_ for the adjustment of the polar axis, with
-a slow motion screw _E_. The latitude circle carries a right ascension
-circle _F F_, with a slow motion _G_, and this in turn carries on four
-pillars the declination circle _H H_, and its axis adjustable by the
-slow motion _K_.
-
-To this declination circle is secured the Gregorian reflector _L L_
-which serves as the observing telescope. All the circles are provided
-with verniers as well as slow motions. And the instrument is, so to
-speak, a universal one for all the purposes of an equatorial, and when
-the polar axis is set vertical equally adapted for use as a transit
-instrument, theodolite, azimuth instrument, or level, since the circles
-are provided with suitable levels.
-
-This mount was really a very neat and complete piece of work for the
-purpose intended, although scarcely suitable for mounting any but a
-small instrument. A very similar construction was used later by Ramsden
-for a small refractor.
-
-It is obvious that the reach of the telescope when used as an
-equatorial is somewhat limited in the mount just described. In modern
-constructions the telescope is so mounted that it may be turned readily
-to any part of the sky, although often the polar axis must be swung
-through 180° in order to pass freely from the extreme southern to the
-extreme northern heavens.
-
-The two motions necessary are those in right ascension to follow the
-heavenly bodies in their apparent course, and in declination to reach
-an object at any particular angular distance from the pole.
-
-There are always provided adjustments in azimuth and for latitude over
-at least a small arc, but these adjustments are altogether rudimentary
-as compared with the wide sweep given by Short.
-
-The fundamental construction of the equatorial involves two axes
-working at right angles positioned like a capital T.
-
-The upright of the T is the polar axis, fitted to a sleeve and bearing
-the cross of the T, which is hollow and provides the bearing for the
-declination axis, which again carries at right angles to itself the
-tube of the telescope.
-
-When the sleeve which carries the upright of the T points to the pole
-the telescope tube can evidently be swung to cover an object at any
-altitude, and can then be turned on its polar axis so as to follow
-that object in its apparent diurnal motion. The front fork of a bicycle
-set at the proper angle with a cross axis replacing the handle bars has
-more than once done good service
-
-[Illustration: FIG. 75.—Section of Modern Equatorial.]
-
-in an emergency. Figure 75 shows in section a modern equatorial mount
-for a medium sized telescope.
-
-The mounting shown in Fig. 75, by Zeiss, is thoroughly typical of
-recent practice in instruments of moderate size. The general form of
-this equatorial comes straight down to us from Fraunhofer’s mounting
-of the Dorpat instrument. It consists essentially of two axes crossed
-exactly at right angles.
-
-P, the polar axis, is aligned exactly with the pole, and is supported
-on a hollow iron pier provided at its top with the latitude block L to
-which the bearings of P are bolted. D the declination axis supports the
-telescope tube T.
-
-The tube is counterpoised as regards the polar axis by the weight a,
-and as regards the declination axis by the weights b b. At A, the upper
-section of the pier can be set in exact azimuth by adjusting screws,
-and at the base of the lower section the screws at B. B. allow some
-adjustment in latitude. To such mere rudiments are the azimuth and
-altitude circles of Short’s mount reduced.
-
-At the upper end of the polar axis is fitted the gear wheel g, driven
-by a worm from the clockwork at C to follow the stars in their course.
-At the lower end of the same axis is the hour circle h, graduated for
-right ascension, and a hand wheel for quick adjustment in R. A.
-
-At d is the declination circle, which is read, and set, by the
-telescope t with a right angled prism at its upper end, which saves the
-observer from leaving the eye piece for small changes.
-
-F is the usual finder, which should be applied to every telescope of 3
-inches aperture and above. It should be of low power, with the largest
-practicable field, and has commonly an aperture ¼ or ⅕ that of the
-main objective, big enough to pick up readily objects to be examined
-and by its coarse cross wires to bring them neatly into the field. At m
-and n are the clamping screws for the right ascension and declination
-axes respectively, while o and p control the respective tangent screws
-for fine adjustment in R. A. and Dec. after the axes are clamped. This
-mount has really all the mechanical refinements needed in much larger
-instruments and represents the class of permanently mounted telescopes
-used in a fixed observatory.
-
-The ordinary small telescope is provided with a mount of the same
-general type but much simpler and, since it is not in a fixed
-observatory, has more liberal adjustments in azimuth and altitude
-to provide for changes of location. Figure 76 shows in some detail
-the admirable portable equatorial mounting used by the Clarks for
-instruments up to about 5 or 6 inches aperture.
-
-Five inches is practically the dividing line between portable and fixed
-telescopes. In fact a 5 inch telescope of standard construction with
-equatorial mounting is actually too heavy for practical portability
-on a tripod stand. The Clarks have turned out really portable
-instruments of this aperture, of relatively short focus and with
-aluminum tube fitted to the mounting standard for a 4 inch telescope,
-but the ordinary 5 inch equipment of the usual focal length deserves a
-permanent placement.
-
-In this mount the short tapered polar axis P is socketed between the
-cheeks A, and tightened in any required position by the hand screws B.
-The stout declination axis D bears the telescope and the counterweight
-C. Setting circles in R. A. and Dec., p and d respectively, are carried
-on the two axes, and each axis has a worm wheel and tangent screw
-operated by a universal joint to give the necessary slow motion.
-
-[Illustration: FIG. 76.—Clark Adjustable Equatorial Mount.]
-
-The worm wheels carry their respective axes through friction bearings
-and the counter poising is so exact that the instrument can be quickly
-swung to any part of the sky and the slow motion picked up on the
-instant. The wide sweep of the polar axis allows immediate conversion
-into an alt-azimuth for terrestrial use, or adjustment for any
-latitude. A graduated latitude arc is customarily engraved on one of
-the check pieces to facilitate this adjustment.
-
-Ordinarily portable equatorials on tripod mounts are not provided
-with circles, and have only a single slow motion, that in R. A. A
-declination circle, however, facilitates setting up the instrument
-accurately and is convenient for locating an object to be swept for in
-R. A. which must often be done if one has not sidereal time at hand. In
-Fig. 76 a thumb screw underneath the tripod head unclamps the mount so
-that it may be at once adjusted in azimuth without shifting the tripod.
-
-As a rule American stands for fixed equatorials have the clock drive
-enclosed in the hollow pillar which carries the equatorial head
-as shown in the reflector of Fig. 35, and in the Clark mount for
-refractors of medium size shown in Fig. 77. Here a neat quadrangular
-pillar carries an equatorial mounting in principle very much like Fig.
-76, but big enough to carry telescopes of 8 to 10 inches aperture.
-It has universal adjustment in latitude, so that it can be used in
-either hemisphere, the clock and its driving weight are enclosed in the
-pillar and slow motions are provided for finding in R. A. and Dec. The
-adjustment in azimuth is made by moving the pillar on its base-plate,
-which is bolted to the pier. The convenient connections for accurate
-following and the powerful clock make the mount especially good for
-photographic telescopes of moderate size and the whole equipment is
-most convenient and workmanlike. It is worth noting that the circles
-are provided with graduations that are plain rather than minute, in
-accordance with modern practice. In these days of celestial photography
-equatorials are seldom used for determining positions except with the
-micrometer, and graduated circles therefore, primarily used merely for
-finding, should be, above all things, easy to read.
-
-All portable mounts are merely simplifications of the observatory type
-of Fig. 75, which, with the addition of various labor saving devices is
-applied to nearly all large refractors and to many reflectors as well.
-
-There is a modified equatorial mount sometimes known as the “English”
-equatorial in which the polar axis is long and supported on two piers
-differing enough in height to give the proper latitude angle, the
-declination axis being about midway of the polar axis. A bit of the
-sky is cut off by the taller pier, and the type is not especially
-advantageous unless in supporting a very heavy instrument, too heavy to
-be readily overhung in the usual way.
-
-[Illustration: FIG. 77.—Universal Observatory Mount (Clark 9-inch).]
-
-In such case some form of the “English” mounting is very important to
-securing freedom from flexure and thereby the perfection of driving
-in R. A. so important to photographic work. The 72 inch Dominion
-Observatory reflector and the 100 inch Hooker telescope at Mt. Wilson
-are thus mounted, the former on a counterpoised declination axis
-crosswise the polar axis, the original “English” type; the latter on
-trunnions within a long closed fork which carries the polar bearings at
-its ends.
-
-[Illustration: FIG. 78.—English Equatorial Mount (Hooker 100-inch
-Telescope).]
-
-Figure 78 shows the latter instrument, of 100 inches clear aperture
-and of 42 feet principal focal length, increased to 135 feet when used
-as a Cassegrainian. It is the immense stability of this mount that has
-enabled it to carry the long cross girder bearing the interferometer
-recently used in measuring the diameters of the stars. Note the
-mercury-flotation drum at each end of the polar axis. The mirrors were
-figured by the skillful hands of Mr. Ritchey.
-
-[Illustration: FIG. 79.—English Equatorial Mount (72-inch Dominion
-Observatory Telescope).]
-
-Figure 79 gives in outline the proportions and mounting of the
-beautiful instrument in service at the Dominion Observatory, near
-Victoria, B. C. The mirror and its auxiliaries were figured by Brashear
-and the very elegant mounting was by Warner and Swasey. The main mirror
-is of 30 feet principal focus. The 20 inch hyperboloidal mirror extends
-the focus as a Cassagrainian to 108 feet. The mechanical stability
-of these English mounts for very large instruments has been amply
-demonstrated by this, as by the Hooker 100 inch reflector. They suffer
-less from flexure than the Fraunhofer mount where great weights are
-to be carried, although the latter is more convenient and generally
-useful for instruments of moderate size. It is hard to say too much of
-the mechanical skill that has made these two colossal telescopes so
-completely successful as instruments of research.
-
-[Illustration: FIG. 80.—Astrographic Mount with Bent Pier.]
-
-The inconvenience of having to swing the telescope tube to clear the
-pier at certain points in the R. A. following is often a serious
-nuisance in photographic work requiring long exposures, and may waste
-valuable time in visual work. Several recent forms of equatorial mount
-have therefore been devised to allow the telescope complete freedom of
-revolution in R. A., swinging clear of everything.
-
-One such form is shown in Fig. 80 which is a standard astrographic
-mount for a Brashear doublet and guiding telescope. The pier is
-strongly overhung in the direction of the polar axis far enough to
-allow the instrument to follow through for any required period, even
-to resuming operations on another night without a shift of working
-position.
-
-[Illustration: FIG. 81.—Open Fork Mounting.]
-
-Another form, even simpler and found to be extremely satisfactory even
-for rather large instruments, is the open polar fork mount. Here the
-polar axis of an ordinary form is continued by a wide and stiff casting
-in the form of a fork within which the tube is carried on substantial
-trunnions, giving it complete freedom of motion.
-
-The open fork mount in its simplest form, carrying a heliostat mirror,
-is shown in Fig. 81. Here _A_ is the fork, _B_ the polar axis, carried
-on an adjustable sector for variation in latitude, _C_ the declination
-axis carrying the mirror _D_ in its cell, _E_ the slow motion in
-declination, and _F_ that in R. A. Both axes can be unclamped for quick
-motion and the R. A. axis can readily be driven by clock or electric
-motor.
-
-The resemblance to the fully developed English equatorial mount of
-Fig. 78 is obvious, but the present arrangement gives entirely free
-swing to a short instrument, is conveniently adjustable, and altogether
-workmanlike. It can easily carry a short focus celestial camera up to 6
-or 8 inches aperture or a reflector of 4 or 5 feet focal length.
-
-In Fig. 173, Chap. X a pair of these same mounts are shown at Harvard
-Observatory. The nearer one, carrying a celestial camera, is exposed
-to view. It is provided with a slow motion and clamp in declination,
-and with an electric drive in R. A., quickly unclamped for swinging the
-camera. It works very smoothly, its weight is taken by a very simple
-self adjusting thrust bearing at the lower end of the polar axis, and
-altogether it is about the simplest and cheapest equatorial mount of
-first class quality that can be devised for carrying instruments of
-moderate length.
-
-Several others are in use at the Harvard Observatory and very similar
-ones of a larger growth carry the 24 inch Newtonian reflector there
-used for stellar photography and the 16 inch Metcalf photographic
-doublet.
-
-[Illustration: FIG. 82.—Mounting of Mt. Wilson 60-inch Reflector.]
-
-[Illustration: FIG. 83.—The 60-inch as Cassegrainian, F = 100′.]
-
-In fact the open fork mount, which was developed by the late Dr.
-Common, is very well suited to the mounting of big reflectors. It was
-first adapted by him to his 3 ft. reflector and later used for his
-two 5 ft. mirrors, and more recently for the 5 ft. instrument at Mt.
-Wilson, and a good many others of recent make. Dr. Common in order
-to secure the easiest possible motion in R. A. devised the plan of
-floating most of the weight assumed by the polar axis in mercury.
-
-Figure 82 is, diagrammatically, this fork mount as worked out by
-Ritchey for the 5′ Mt. Wilson reflector. Here A is the lattice tube, B
-the polar axis, C the fork and D the hollow steel drum which floats the
-axis in the mercury trough E. The great mirror is here shown worked as
-a simple Newtonian of 25 ft. focal length. As a matter of fact it is
-used much of the time as a Cassegranian.
-
-To this end the upper section of tube carrying the oblique mirror is
-removed and a shorter tube carrying any one of three hyperboloidal
-mirrors is put in its place. Fig. 83 is the normal arrangement for
-visual or photographic work on the long focus, 100 ft. The dotted lines
-show the path of the rays and it will be noticed that the great mirror
-is not perforated as in the usual Cassegrainian construction, but that
-the rays are brought out by a diagonal flat.
-
-Figure 84 is a similar arrangement used for stellar spectroscopy with
-a small flat and an equivalent focus of 80 ft. In Fig. 85 a radically
-different scheme is carried out. The hyperboloidal mirror now used
-gives an equivalent focus of 150 ft., and the auxiliary flat is
-arranged to turn on an axis parallel to the declination axis so as to
-send the reflected beam down the hollow polar axis into a spectrograph
-vault below the southern end of the axis. Obviously one cannot work
-near the pole with this arrangement but only through some 75° as
-indicated by the dotted lines. The fork mount is not at all universal
-for reflectors, as has already been seen, and Cassegrainian of moderate
-size are very commonly mounted exactly like refractors.
-
-[Illustration: FIG. 84.—The 60-inch as Cassegrainian, F = 80′.]
-
-[Illustration: FIG. 85.—The 60-inch as Polar Cassegrainian, F = 150′.]
-
-We now come to a group of mounts which have in common the fundamental
-idea of a fixed eyepiece, and incidentally better protection of the
-observer against the rigors of long winter nights when the seeing
-may be at its best but the efficiency of the observer is greatly
-diminished by discomfort. Some of the arrangements are also of value in
-facilitating the use of long focus objectives and mirrors and escaping
-the cost of the large domes which otherwise would be required.
-
-Perhaps the earliest example of the class is found in Caroline
-Herschel’s comet seeker, shown in Fig. 86. This was a Newtonian
-reflector of about 6 inches aperture mounted in a fashion that is
-almost self explanatory. It was, like all Herschel’s telescopes, an
-alt-azimuth but instead of being pivoted in altitude about the mirror
-or the center of gravity of the whole tube, it was pivoted on the
-eyepiece location and the tube was counterbalanced as shown so that it
-could be very easily adjusted in altitude while the whole frame turned
-in azimuth about a vertical post.
-
-Thus the observer could stand or sit at ease sweeping in a vertical
-circle, and merely had to move around the post as the azimuth was
-changed. The arrangement is not without advantages, and was many years
-later adopted with modifications of detail by Dr. J. W. Draper for
-the famous instrument with which he advanced so notably the art of
-celestial photography.
-
-The same fundamental idea of freeing the observer from continual
-climbing about to reach the eyepiece has been carried out in various
-equatorially mounted comet seekers. A very good example of the type
-is a big comet seeker by Zeiss, shown in Fig. 87. The fundamental
-principle is that the ocular is at the intersection of the polar and
-declination axis, the telescope tube being overhung well beyond the
-north end of the former and counterbalanced on the latter. The observer
-can therefore sit in his swivel chair and without stirring from it
-sweep rapidly over a very wide expanse of sky.
-
-This particular instrument is probably the largest of regular comet
-seekers, 8 inches in clear aperture and 52½ inches focal length
-with a triple objective to ensure the necessary corrections in
-using so great a relative aperture. In this figure 1 is the base
-with corrections in altitude and azimuth, 2 the counterpoise of the
-whole telescope on its base, 3 the polar axis and R. A. circle, 4
-the overhung declination axis and its circle, 5 the counterpoise in
-declination, 6 the polar counterpoise, and 7 the main telescope tube.
-The handwheel shown merely operates the gear for revolving the dome
-without leaving the observing chair.
-
-The next step beyond the eyepiece fixed in general position is so
-to locate it that the observer can be thoroughly protected without
-including the optical parts of the telescope in such wise as to injure
-their performance.
-
-One cannot successfully observe through an open window on account of
-the air currents due to temperature differences, and in an observatory
-dome, unheated as it is, must wait after the shutter is opened until
-the temperature is fairly steadied.
-
-Except for these comet seekers practically all of the class make use of
-one or two auxiliary reflections to bring the image into the required
-direction, and in general the field of possible view is somewhat
-curtailed by the mounting. This is less of a disadvantage than it would
-appear at first thought, for, to begin with, observations within 20°
-of the horizon or thereabouts are generally unsatisfactory, and the
-advantages of a stable and convenient long focus instrument are so
-notable as for many purposes quite to outweigh some loss of sky-space.
-
-[Illustration: FIG. 86.—Caroline Herschel’s Comet Seeker.]
-
-The simplest of the fixed eyepiece group is the polar telescope of
-which the rudiments are well shown in Fig. 88, a mount described by Sir
-Howard Grubb in 1880, and an example of which was installed a little
-later in the Crawford Observatory in Cork. Here the polar axis A is
-the main tube of the telescope, and in front of the objective B, is
-held in a fork the declination cradle and mirror C, by which any object
-within a wide sweep of declination can be brought into the field and
-held there by hand or clockwork through rotating the polar tube.
-
-[Illustration: FIG. 87.—Mounting of Large Comet Seeker.]
-
-Looked at from another slant it is a polar heliostat, of which the
-telescope forms the driving axis in R. A. The whole mount was a
-substantial casting on wheels which ran on a pair of rails. For use the
-instrument was rolled to a specially arranged window and through it
-until over its regular bearings on a pier just outside.
-
-A few turns of the wheel D lowered it upon these, and the back of the
-frame then closed the opening in the wall leaving the instrument in the
-open, and the eye end inside the room. The example first built was of
-only 4 inches aperture but proved its case admirably as a most useful
-and convenient instrument.
-
-This mount with various others of the fixed eyepiece class may be
-regarded as derived from the horizontal photoheliographs used at the
-1874 transit of Venus and subsequently at many total solar eclipses.
-Given an equatorially mounted heliostat like Fig. 81 and it is evident
-that the beam from it may be turned into a horizontal telescope placed
-in the meridian, (or for that matter in any convenient direction) and
-held there by rotation of the mirror in R. A., but also in declination,
-save in the case where the beam travels along the extension of the
-polar axis.
-
-[Illustration: FIG. 88.—Grubb’s Original Polar Telescope.]
-
-For the brief exposure periods originally needed and the slow variation
-of the sun in declination this heliostatic telescope was easily kept
-in adjustment. The original instruments were of 5 inches aperture and
-40 ft. focal length, and the 7 inch heliostat mirror was provided with
-ordinary equatorial clockwork. Set up with the telescope pointing along
-the polar axis no continuous variation in declination is needed and the
-clock drive holds the field steadily, as in any other equatorial.
-
-Figure 89 shows diagrammatically the 12 inch polar telescope used for
-more than twenty years past at the Harvard Observatory. The mount was
-designed by Mr. W. P. Gerrish of the Harvard staff and contains many
-ingenious features. Unlike Fig. 88 this is a fixed mount, with the
-eye-end comfortably housed in a room on the second floor of the main
-observatory building, and the lower bearing on a substantial pier to
-the southward.
-
-[Illustration: FIG. 89.—Diagram of Gerrish Polar Telescope.]
-
-In the figure, _A_ is the eye end, _B_ the main tube with the objective
-at its lower end and prolonged by a fork supported by the bearing _C_
-and _D_ is the declination mirror sending the beam upward. The whole
-is rotated in R. A. by an electric clock drive, and all the necessary
-adjustments are made from the eye end.
-
-A view of the exterior is shown in Fig. 90, with the mirror and
-objective uncovered. The rocking arm at the objective end, operated by
-a small winch beside the ocular, swings clear both mirror and objective
-caps in a few seconds, and the telescope is then ready for use. Its
-focal length is 16 ft. 10 inches and it gives a sweep in declination of
-approximately 80°. It gives excellent definition and has proved a most
-useful instrument.
-
-A second polar telescope was set up at the Harvard Observatory station
-in Mandeville, Jamaica, in the autumn of 1900. This was intended
-primarily for lunar photography and was provided with a 12 inch
-objective of 135 ft. 4 inches focal length and an 18 inch heliostat
-with electric clock drive.
-
-[Illustration: FIG. 90.—Gerrish Polar Telescope, Harvard Observatory.]
-
-Inasmuch as all instruments of this class necessarily rotate the image
-as the mirror turns, the tail-piece of this telescope is also mounted
-for rotation by a similar drive so that the image is stationary on the
-plate both in position and orientation. As Mandeville is in N. lat. 18°
-01′ the telescope is conveniently near the horizontal. The observatory
-of Yale University has a large instrument of this class, of 50 feet
-focal length, with a 15-inch photographic objective and a 10-inch
-visual guiding objective working together from the same heliostat.
-
-Despite its simplicity and convenience the polar telescope has an
-obvious defect in its very modest sweep in declination, only to be
-increased by the use of an exceptionally large mirror. It is not
-therefore remarkable that the first serious attempt at a fixed eyepiece
-instrument for general use turned to a different construction even at
-the cost of an additional reflection.
-
-This was the _equatorial coudé_ devised by M. Loewy of the Paris
-Observatory in 1882. (Fig. 91.) In the diagram A is the main tube
-which forms the polar axis, and B the eye end under shelter, with all
-accessories at the observer’s hand. But the tube is broken by the box
-casing C containing a mirror rigidly supported at 45° to the axis of
-the main tube and of the side tube D, which is counterbalanced and is
-in effect a hollow declination axis carrying the objective E at its
-outer end.
-
-[Illustration: FIG. 91.—Diagram of Equatorial Coudé.]
-
-In lieu of the telescope tube usually carried on this declination
-axis we have the 45° mirror, F, turning in a sleeve concentric with
-the objective, which, having a lateral aperture, virtually gives the
-objectives a full sweep in declination, save as the upper pier cuts it
-off. The whole instrument is clock driven in R. A., and has the usual
-circles and slow motions all handily manipulated from the eye end.
-
-The _equatorial coudé_ is undeniably complicated and costly, but
-as constructed by Henry Frères it actually performs admirably even
-under severe tests, and has been several times duplicated in French
-observatories. The first _coudé_ erected was of 10½ inches aperture
-and was soon followed by one of 23.6 inches aperture and 59 ft. focus,
-which is the largest yet built.
-
-Still another mounting suggestive of both the polar telescope and the
-_coudé_ is due to Sir Howard Grubb, Fig. 92. Here as in the _coudé_
-the upper part of the polar axis, _A_, is the telescope tube which
-leads into a solid casing _B_, about which a substantial fork, _C_, is
-pivoted. This fork is the extension of the side tube _D_, which carries
-the objective, and thus has free swing in declination through an angle
-limited by the roof of the observing room above, and the proximity of
-the horizon below.
-
-Its useful swing, as in the polar telescope, is limited by the
-dimensions of the mirror _E_, which receives the cone of rays from the
-objective and turns it up the polar tube to the eyepiece. This mirror
-is geared to turn at half the rate of the tube _D_ so that the angle _D
-E A_ is continually bisected.
-
-[Illustration: FIG. 92.—Grubb Modified Coudé.]
-
-In point of fact the sole gain in this construction is the reduction
-in the size of mirror required, by reason of the diminished size of
-the cone of rays when it reaches the mirror. The plan has been very
-successfully worked out in the fine astrographic telescope of the
-Cambridge Observatory of 12½ inches aperture and 19.3 ft. focal
-length.
-
-As in the other instruments of this general class the adjustments are
-all conveniently made from the eye end. The Cambridge instrument has a
-triple photo-visual objective of the form designed by Mr. H. D. Taylor
-and the side tube, when not in use, is turned down to the horizontal
-and covered in by a low wheeled housing carried on a track. The sky
-space covered is from 15° above the pole to near the horizontal.
-
-It is obvious that various polar and _coudé_ forms of reflector
-are quite practicable and indeed one such arrangement is shown in
-connection with the 60 inch Mt. Wilson reflector, but we are here
-concerned only with the chief types of mounting which have actually
-proved their usefulness. None of the arrangements which require the
-use of additional large reflecting surfaces are exempt from danger of
-impaired definition. Only superlatively fine workmanship and skill in
-mounting can save them from distortion and astigmatism due to flexure
-and warping of the mirrors, and such troubles have not infrequently
-been encountered.
-
-To a somewhat variant type belong several valuable constructions which
-utilize in the auxiliary reflecting system the cœlostat rather than
-the polar heliostat or its equivalent. The cœlostat is simply a plane
-mirror mounted with its plane fixed in that of a polar axis which
-rotates once in 48 hours, i.e., at half the apparent rate of the stars.
-
-[Illustration: FIG. 93.—Diagram of Snow Horizontal Telescope.]
-
-A telescope pointed at such a mirror will hold the stars motionless
-in its field as if the firmament were halted à la Joshua. But if a
-change of view is wanted the telescope must be shifted in altitude or
-azimuth or both. This is altogether inconvenient, so that as a matter
-of practice a second plane mirror is used to turn the steady beam from
-the cœlostat into any desired direction.
-
-By thus shifting the mirror instead of the telescope, the latter can be
-permanently fixed in the most convenient location, at the cost of some
-added expense and loss of light. Further, the image does not rotate as
-in case of the polar heliostat, which is often an advantage.
-
-An admirable type of the fixed telescope thus constituted is the Snow
-telescope at Mt. Wilson (Cont. from the Solar Obs. #2, Hale). Fig.
-93 from this paper shows the equipment in plan and elevation. The
-topography of the mountain top made it desirable to lay out the axis of
-the building 15° E. of N. and sloping downward 5° toward the N.
-
-At the right hand end of the figure is shown the cœlostat pier, 29 ft.
-high at its S end. This pier carries the cœlostat mirror proper, 30
-inches in diameter, on rails _a a_ accurately E. and W. to allow for
-sliding the instrument so that its field may clear the secondary mirror
-of 24 inches diameter which is on an alt-azimuth fork mounting and also
-slides on rails _b b_.
-
-The telescope here is a pair of parabolic mirrors each of 24 inches
-aperture and of 60 ft. and 145 ft. focus respectively. The beam from
-the secondary cœlostat mirror passes first through the spectrographic
-laboratory shown to the left of the main pier, and in through a long
-and narrow shelter house to one of these mirrors; the one of longest
-focus on longitudinal focussing rails _e e_, the other on similar rails
-_c c_, with provision for sliding sidewise at _d_ to clear the way for
-the longer beam.
-
-The ocular end of this remarkable telescope is the spectrographic
-laboratory where the beam can be turned into the permanently mounted
-instruments, for the details of which the original paper should be
-consulted. The purpose of this brief description is merely to show the
-beautiful facility with which a cœlostatic telescope may be adapted to
-astrophysical work. Obviously an objective could be put in the cœlostat
-beam for any purpose for which it might be desirable.
-
-Such in fact is the arrangement of the tower telescopes at the Mt.
-Wilson Observatory. In these instruments we have the ordinary cœlostat
-arrangement turned on end for the sake of getting the chief optical
-parts well above the ground where, removed from the heated surface,
-the definition is generally improved. To be sure the focus is at or
-near the ground level, but the upward air currents cause much less
-disturbance than the crosswise ones in the Snow telescope.
-
-The head of the first tower telescope is shown in Fig. 94.[16] A is the
-cœlostat mirror proper 17 inches in diameter and 12 inches thick, B
-the secondary mirror 12¾ inches in the shorter axis of the ellipse,
-22¼ inches in the longer, and also 12 inches thick. C is the 12
-inch objective of 60 ft. focus, and D the focussing gear worked by a
-steel ribbon from below.
-
- [16] Contributions from the Solar Obs. #23, Hale, which should be seen
- for details.
-
-[Illustration: FIG. 94.—Head of 60-inch Tower Telescope.]
-
-This instrument being for solar research the mirrors are arranged for
-convenient working with the sun fairly low on either horizon where the
-definition is at its best, and can be shifted accordingly, to the same
-end as in the Snow telescope. There is also provision for shifting the
-objective laterally at a uniform rate from below, to provide for the
-use of the apparatus as spectro-heliograph.
-
-The tower is of the windmill type and proved to be fairly steady
-in spite of its height, high winds being rare on Mt. Wilson. The
-great thickness of the mirrors in the effort to escape distortion
-deserves notice. They actually proved to be too thick to give thermal
-conductivity sufficient to prevent distortion.
-
-[Illustration: FIG. 95.—Porter’s Polar Reflector.]
-
-In the later 150′ tower telescope the mirrors are relatively less
-thick, and a very interesting modification has been introduced in
-the tower, in that it consists of a lattice member for member within
-another exterior lattice, so that the open structure is retained, while
-each member that supports the optical parts is shielded from the wind
-and sudden temperature change by its corresponding outer sheath.
-
-Still another form of mounting to give the observer access to a fixed
-eyepiece under shelter is found in the ingenious polar reflector by
-Mr. Russell W. Porter of which an example with main mirror of 16
-inches diameter and 15 ft. 6 inches focal length was erected by him
-a few years ago. Fig. 95 is entirely descriptive of the arrangement
-which from Mr. Porter’s account seems to have worked extremely well.
-The chief difficulty encountered was condensation of moisture on the
-mirrors, which in some climates is very difficult to prevent.
-
-[Illustration: FIG. 96.—Diagram of Hartness Turret Telescope.]
-
-It is interesting to note that Mr. Porter’s first plan was to use the
-instrument as a Herschelian with its focus thrown below the siderostat
-at _F′_, but the tilting of the mirror, which was worked at F/11.6,
-produced excessive astigmatism of the images, and the plan was
-abandoned in favor of the Newtonian form shown in the figure. At F/25
-or thereabouts the earlier scheme would probably have succeeded well.
-
-Still another fixed eyepiece telescope of daring and successful design
-is the turret telescope of the Hon. J. E. Hartness of which the
-inventor erected a fine example of 10 inch aperture at Springfield,
-Vermont. The telescope is in this case a refractor, and the feature of
-the mount is that the polar axis is expanded into a turret within which
-the observer sits comfortably, looking into the ocular which lies in
-the divided declination axis and is supplied from a reflecting prism in
-the main beam from the objective
-
-Figure 96 shows a diagram of the mount and observatory. Here _a_ is the
-polar turret, _bb_ the bearings of the declination axis, _c_ the main
-tube, d its support, and _e_ the ocular end. Optically the telescope is
-merely an ordinary refractor used with a right angled prism a little
-larger and further up the tube than usual. The turret is entered
-in this instance from below, through a tunnel from the inventor’s
-residence. The telescope as shown in Fig. 96 has a 10 inch Brashear
-objective of fine optical quality, and the light is turned into the
-ocular tube by a right angled prism only 2¾ inches in the face. This
-is an entirely practicable size for a reflecting prism and the light
-lost is not materially in excess of that lost in the ordinary “star
-diagonal” so necessary for the observation of stars near the zenith in
-an ordinary equatorial. The only obvious difficulty of the construction
-is the support of the very large polar axis. Being an accomplished
-mechanical engineer, Mr. Hartness worked out the details of this design
-very successfully although the moving parts weighed some 2 tons. The
-ocular is not absolutely fixed with reference to the observer but is
-always conveniently placed, and the performance of the instrument is
-reported as excellent in every respect, while the sheltering of the
-observer from the rigors of a Vermont winter is altogether admirable.
-Figure 97 shows the complete observatory as it stands. Obviously the
-higher the latitude the easier is this particular construction, which
-lends itself readily to large instruments and has the additional
-advantage of freeing the observer from the insect pests which are
-extremely troublesome in warm weather over a large part of the world.
-
-This running account of mountings makes no claim at completeness. It
-merely shows the devices in common use and some which point the way to
-further progress. The main requirements in a mount are steadiness, and
-smoothness of motion. Even an alt-azimuth mount with its need of two
-motions, if smooth working and steady, is preferable to a shaky and
-jerky equatorial.
-
-Remember that the Herschels did immortal work without equatorial
-mountings, and used high powers at that. A clock driven equatorial is
-a great convenience and practically indispensable for the photographic
-work that makes so large a part of modern astronomy, but for eye
-observations one gets on very fairly without the clock.
-
-[Illustration: FIG. 97.—Hartness Turret Observatory from the N. E.]
-
-Circles arc a necessity in all but the small telescopes used on
-portable tripods, otherwise much time will be wasted in finding. In any
-event do not skimp on the finder, which should be of ample aperture and
-wide field, say ¼ the aperture of the main objective, and 3° to 5°
-in field. Superior definition is needless, light, and sky room enough
-to locate objects quickly being the fundamental requisites.
-
-As a final word see that all the adjustments are within easy reach from
-the eyepiece, since an object once lost from a high power ocular often
-proves troublesome to locate again.
-
-
-REFERENCES
-
-  CHAMBERS’ Astronomy, Vol. II.
-  F. L. O. WADSWORTH: _Ap. J._, =5=, 132. Ranyard’s mounts for
-    reflectors.
-  G. W. RITCHEY: _Ap. J._, =5=, 143. Supporting large specula.
-  G. E. HALE: Cont. Solar Obs. # 2. The “Snow” horizontal telescope.
-  G. E. HALE: Cont. Solar Obs. # 23. The 60 ft. tower telescope.
-  J. W. DRAPER: Smithsonian Contrib. =34=. Mounting of his large
-    reflector.
-  G. W. RITCHEY: Smithsonian Contrib. =35=. Mounting of the Mt. Wilson
-    60 inch reflector.
-  SIR H. GRUBB: Tr. Roy. Dublin Soc. Ser. 2. =3=. Polar Telescopes.
-  SIR R. S. BALL: _M. N._ =59=, 152. Photographic polar telescope.
-  A. A. COMMON: Mem. R. A. S., =46=, 173. Mounting of his 3 ft.
-    reflector.
-  R. W. PORTER: _Pop. Ast._, =24=, 308. Polar reflecting telescope.
-  JAMES HARTNESS: _Trans. A. S. M. E._, 1911, Turret Telescope.
-  SIR DAVID GILL: Enc. Brit., 11th Ed. Telescope. Admirable summary of
-    mounts.
-
-
-
-
-CHAPTER VI
-
-EYE PIECES
-
-
-The eyepiece of a telescope is merely an instrument for magnifying
-the image produced by the objective or mirror. If one looks through a
-telescope without its eyepiece, drawing the eye back from the focus to
-its ordinary distance of distinct vision, the image is clearly seen as
-if suspended in air, or it can be received on a bit of ground glass.
-
-It appears larger or smaller than the object seen by the naked eye, in
-proportion as the focal length of the objective is larger or smaller
-than the distance to which the eye has to drop back to see the image
-clearly.
-
-This real image, the quality of which depends on the exactness of
-correction of the objective or mirror, is then to be magnified so much
-as may be desirable, by the eyepiece of the instrument. In broad terms,
-then, the eyepiece is a simple microscope applied to the image of an
-object instead of the object itself.
-
-And looking at the matter in the simplest way the magnifying power of
-any simple lens depends on the focal length of that lens compared with
-the ordinary seeing distance of the eye. If this be taken at 10 inches
-as it often conventionally is, then a lens of 1 inch focus brings clear
-vision down to an inch from the object, increases the apparent angle
-covered by the object 10 times and hence gives a magnifying power of 10.
-
-But if the objective has a focal length of 100 inches the image, as we
-have just seen, is already magnified 10 times as the naked eye sees it,
-hence with an objective of 100 inches focus and a 1 inch eyepiece the
-total magnification is 100 diameters. And this expresses the general
-law, for if we took the normal seeing distance of the naked eye at some
-other value than 10 inches, say 12½ inches then we should have to
-reckon the image as magnified by 8 times so far as the objective inches
-is concerned, but 12½ times due to the 1 inch eyepiece, and so
-forth. Thus the magnifying power of any eyepiece is F/f where F is the
-focal length of the objective or mirror and f that of the eyepiece.
-The focal distance of the eye quite drops out of the reckoning.
-
-All these facts appear very quickly if one explores the image from an
-objective with a slip of ground glass and a pocket lens. An ordinary
-camera tells the same story. A distant object which covers 1° will
-cover on the ground glass 1° reckoned on a radius equal to the focal
-length of the lens. If this is equal to the ordinary distance of clear
-vision, an eye at the same distance will see the image (or the distant
-object) covering the same 1°.
-
-The geometry of the situation is as follows: Let _o_ Fig. 5, Chap.
-1, be the objective. This lens, as in an ordinary camera, forms an
-inverted image of an object A B at its focus, as at _a b_, and for
-any point, as _a_, of the image there is a corresponding point of the
-object lying on the straight line from A to that point through the
-center, _c_, of the objective.
-
-A pair of rays 1, 2, diverging from the object point A pass through
-rim and center of _o_ respectively and meet in A. After crossing at
-this point they fall on the eye lens _e_, and if _a_ is nearly in the
-principal focus of _e_, the rays 1 and 2 will emerge substantially
-parallel so that the eye will unite them to form a clear image.
-
-Now if F is the focal length of _o_, and f that of _a_, the object
-forming the image subtends at the center of the objective, o, an angle
-_A c B_, and for a distant object this will be sensibly the angle under
-which the eye sees the same object.
-
-If L is the half linear dimension of the image, the eye sees half the
-object covering the angle whose tangent is L/F. Similarly half the
-image _ab_ is seen through the eye lens _e_ as covering a half angle
-whose tangent is L/f. Since the magnifying power of the combination,
-m, is directly as the ratio of increase in this tangent of the visual
-angle, which measures the image dimension
-
-  m = F/f, as before
-
-Further, as all the light which comes in parallel through the whole
-opening of the objective forms a single conical beam concentrating into
-a focus and then diverging to enter the eye lens, the diameter of the
-cone coming through the eye lens must bear the same relation to the
-diameter of _o_, that f does to F.
-
-Any less diameter of _e_ will cut off part of the emerging light; any
-more will show an emergent beam smaller than the eye lens, which is
-generally the case. Hence if we call p the diameter of the bright
-pencil of light which we see coming through the eye lens then for that
-particular eye lens,
-
-m = _o_/p
-
-That is, f = pF/_o_ which is quite the easiest way of measuring the
-focal length of an eyepiece.
-
-Point the telescope toward the clear sky, focusing for a distant object
-so that the emergent pencil is sharply defined at the ocular, and then
-measure its diameter by the help of a fine scale and a pocket lens,
-taking care that scale and emergent pencil are simultaneously in sharp
-focus and show no parallax as the eye is shifted a bit. This bright
-circle of the emerging beam is actually the projection by the eye lens
-of the focal image of the objective aperture.
-
-This method of measuring power is easy and rather accurate. But it
-leads to trouble if the measured diameter of the objective is in
-fact contracted by a stop anywhere along the path of the beam, as
-occasionally happens. Examine the telescope carefully with reference to
-this point before thus testing the power.[17]
-
- [17] A more precise method, depending on an actual measurement of the
- angle subtended by the diameter of the eyepiece diaphragm as seen
- through the eye end of the ocular and its comparison with the same
- angular diameter reckoned from the objective, is given by Schaeberle.
- M. N. =43=, 297.
-
-The eye lens of Fig. 5 is a simple double convex one, such as was used
-by Christopher Scheiner and his contemporaries. With a first class
-objective or mirror the simple eye lens such as is shown in Fig. 98a
-is by no means to be despised even now. Sir William Herschel always
-preferred it for high powers, and speaks with evident contempt of
-observers who sacrificed its advantages to gain a bigger field of view.
-Let us try to fathom the reason for his vigorously expressed opinion,
-strongly backed up by experienced observers like the late T. W. Webb
-and Mr. W. F. Denning.
-
-First of all a single lens saves about 10% of the light. Each surface
-of glass through which light passes transmits 95 to 96% of that light,
-so that a single lens transmits approximately 90%, two lenses 81%
-and so on. This loss may be enough to determine the visibility of an
-object. Sir Wm. Herschel found that faint objects invisible with the
-ordinary two lens eyepiece came to view with the single lens.
-
-Probably the actual loss is less serious than its effect on seeing
-conditions. The loss is due substantially to reflection at the
-surfaces, and the light thus reflected is scattered close to, or
-into, the eye and produces stray light in the field which injures the
-contrast by which faint objects become visible.
-
-In some eyepieces the form of the surfaces is such that reflected light
-is strongly concentrated where the eye sees it, forming a “ghost”
-quite bright enough greatly to interfere with the vision of delicate
-contrasts.
-
-The single lens has a very small sharp field, hardly 10° in angular
-extent, the image falling off rapidly in quality as it departs from the
-axis. If plano-convex, as is the eye lens of common two-lens oculars,
-it works best with the curved side to the eye, i.e., reversed from
-its usual position, the spherical aberration being much less in this
-position.
-
-[Illustration: FIG. 98.—Simple Oculars.]
-
-Herschel’s report of better definition with a single lens than with an
-ordinary two lens ocular speaks ill for the quality of the latter then
-available. Of course the single lens gives some chromatic aberration,
-generally of small account with the narrow pencils of light used in
-high powers.
-
-A somewhat better form of eye lens occasionally used is the so-called
-Coddington lens, really devised by Sir David Brewster. This, Fig. 98b,
-is derived from a glass sphere with a thick equatorial belt removed
-and a groove cut down centrally leaving a diameter of less than half
-the radius of the sphere. The focus is, for ordinary crown glass, 3/2
-the radius of the sphere, and the field is a little improved over the
-simple lens, but it falls off rather rapidly, with considerable color
-toward the edge.
-
-The obvious step toward fuller correction of the aberrations while
-retaining the advantages of the simple lens is to make the ocular
-achromatic, like a minute objective, thus correcting at once the
-chromatic and spherical aberrations over a reasonably large field. As
-the components are cemented the loss of light at their common surface
-is negligible. Figure 98c shows such a lens. If correctly designed it
-gives an admirably sharp field of 15° to 20°, colorless and with very
-little distortion, and is well adapted for high powers.
-
-[Illustration: _a_   _b_
-FIG. 99.—Triple Cemented Oculars.]
-
-Still better results in field and orthoscopy can be attained by
-going to a triple cemented lens, similar to the objective of Fig.
-57. Triplets thus constituted are made abroad by Zeiss, Steinheil
-and others, while in this country an admirable triplet designed by
-Professor Hastings is made by Bausch & Lomb.
-
-[Illustration: FIG. 100.—Path of Rays Through Huygenian Ocular.]
-
-Such lenses give a beautifully flat and sharp field over an angle of
-20° to 30°, quite colorless and orthoscopic. Fig. 99_a_, a form used
-by Steinheil, is an excellent example of the construction and a most
-useful ocular. The late R. B. Tolles made such triplets, even down to
-⅛ inch focus, which gave admirable results.
-
-A highly specialized form of triplet is the so-called monocentric of
-Steinheil Fig. 99_b_. Its peculiarity is less in the fact that all the
-curves are struck from the same center than in the great thickness
-of the front flint and the crown, which, as in some photographic
-lenses, give added facilities for flattening the field and eliminating
-distortion.
-
-The monocentric eyepiece has a high reputation for keen definition
-and is admirably achromatic and orthoscopic. The sharp field is about
-32°, rather the largest given by any of the cemented combinations.
-All these optically single lenses are quite free of ghosts, reduce
-scattered light to a minimum, and leave little to be desired in precise
-definition. The weak point of the whole tribe is the small field,
-which, despite Herschel’s opinion, is a real disadvantage for certain
-kinds of work and wastes the observer’s time unless his facilities for
-close setting are more than usually good.
-
-Hence the general use of oculars of the two lens types, all of
-them giving relatively wide fields, some of them faultless also in
-definition and orthoscopy. The earliest form, Fig. 100, is the very
-useful and common one used by Huygens and bearing his name, though
-perhaps independently devised by Campani of Rome. Probably four out of
-five astronomical eyepieces belong to this class.
-
-The Huygenian ocular accomplishes two useful results—first, it gives a
-wider sharp field than any single lens, and second it compensates the
-chromatic aberration, which otherwise must be removed by a composite
-lens. It usually consists of a plano-convex lens, convex side toward
-the objective, which is brought inside the objective focus and forms
-an image in the plane of a rear diaphragm, and a similar eye lens of
-shorter focus by which this image is examined.
-
-Fig. 100 shows the course of the rays—_A_ being the field lens, _B_
-the diaphragm and _C_ the eye lens. Let _1_, _2_, be rays which are
-incident near the margin of _A_. Each, in passing through the lens, is
-dispersed, the blue being more refracted than the red. Both rays come
-to a general focus at _B_, and, crossing, diverge slightly towards _C_.
-
-But, on reaching _C_, ray _1_, that was nearer the margin and the more
-refracted because in a zone of greater pitch, now falls on _C_ the
-nearer its center, and is less refracted than ray _2_ which strikes _C_
-nearer the rim. If the curvatures of _A_ and _C_ are properly related
-_1_ and _2_ emerge from _C_ parallel to each other and thus unite in
-forming a distinct image.
-
-Now follow through the two branches of _l_ marked _l_r_, and _l_v_, the
-red and violet components. Ray _l_v_, the more refrangible, strikes
-_C_ nearer the center, and is the less refracted, emerging from _C_
-substantially parallel with its mate _l_r_, hence blending the red and
-violet images, if, being of the same glass, _A_ and _C_ have suitably
-related focal lengths and separation.
-
-As a matter of fact the condition for this chromatic compensation is
-
- d = (f + f′)/2
-
-where d is the distance between the lenses and f, f′, their respective
-focal lengths. If this condition of achromatism be combined with
-that of equal refraction at _A_ and _C_, favorable to minimizing
-the spherical aberration, we find f = 3f′ and d = 2f′. This is the
-conventional Huygenian ocular with an eye lens ⅓ the focus of the
-field lens, spaced at double the focus of the eye lens, with the
-diaphragm midway.
-
-In practice the ratio of foci varies from 1:3 to 1:2 or even 1:1.5, the
-exact figure varying with the amount of overcorrection in the objective
-and under-correction in the eye that has to be dealt with, while the
-value of d should be adjusted by actual trial on the telescope to
-obtain the best color correction practicable. One cannot use any chance
-ocular and expect the finest results.
-
-[Illustration: FIG. 101_a_.—Airy and Mittenzuey Oculars.]
-
-The Huygenian eyepieces are often referred to as “negative” inasmuch
-as they cannot be used directly as magnifiers, although dealing
-effectively with an image rather than an object. The statement is
-also often made that they cannot be used with cross wires. This is
-incorrect, for while there is noticeable distortion toward the edge of
-the wide field, to say nothing of astigmatism, in and near the center
-of the field the situation is a good deal better.
-
-Central cross wires in the plane of the diaphragm are entirely suitable
-for alignment of the instrument, and over a moderate extent of field
-the distortion is so small that a micrometer scale in the plane of
-the diaphragm gives very good approximate measurements, and indeed is
-widely used in microscopy.
-
-It should be noted that the achromatism of this type of eyepiece is
-compensatory rather than real. One cannot at the same time bring the
-images of various colors to the same size, and also to the same plane.
-As failure in the latter respect is comparatively unimportant, the
-Huygenian eyepiece is adjusted so far to compensate the paths of the
-various rays as to bring the colored images to the same size, and in
-point of fact the result is very good.
-
-The field of the conventional form of Huygenian ocular is fully 40°,
-and the definition, particularly centrally, is very excellent. There
-are no perceptible ghosts produced, and while some 10% of light is lost
-by reflection in the extra lens it is diffused in the general field
-and is damaging only as it injures the contrast of faint objects. The
-theory of the Huygenian eyepiece was elaborately given by Littrow,
-(Memoirs R. A. S. Vol. 4, p. 599), wherein the somewhat intricate
-geometry of the situation is fully discussed.
-
-Various modifications of the Huygenian type have been devised and used.
-Figure 101_a_ is the Airy form devised as a result of a somewhat full
-mathematical investigation by Sir George Airy, later Astronomer Royal.
-Its peculiarity lies in the form of the lenses which preserve the usual
-3:1 ratio of focal lengths. The field lens is a positive meniscus with
-a noticeable amount of concavity in the rear face while the eye lens
-is a “crossed” lens, the outer curvature being about ⅙ of the inner
-curvature. The marginal field in this ocular is a little better than in
-the conventional Huygenian.
-
-[Illustration: FIG. 101_b_.—Airy and Mittenzwey Oculars.]
-
-A commoner modification now-a-days is the Mittenzwey form, Fig. 101_b_.
-This is usually made with 2:1 ratio of focal lengths, and the field
-lens still a meniscus, but less conspicuously concave than in the
-Airy form. The eye lens is the usual plano-convex. It is widely used,
-especially abroad, and gives perhaps as large available field as any
-ocular yet devised, approximately 50°, with pretty good definition out
-to the margin.
-
-Finally, we come to the solid eyepiece Fig. 102_a_, devised by the late
-R. B. Tolies nearly three quarters of a century ago, and and often
-made by him both for telescopes and microscopes. It is practically
-a Huygenian eyepiece made out of a single cylinder of glass with a
-curvature ratio of 1½:1 between the eye and the field lens. A groove
-is cut around the long lens at about ⅓ its length from the vertex of
-the field end. This serves as a stop, reducing the diameter of the
-lens to about one-half its focal length.
-
-It is in fact a Huygenian eyepiece free from the loss of light in the
-usual construction. It gives a wide field, more extensive than in the
-ordinary form, with exquisite definition. It is really a most admirable
-form of eyepiece which should be used far more than is now the case.
-The late Dr. Brashear is on record as believing that all negative
-eyepieces less than ¾ inch focus should be made in this form.
-
-[Illustration: _a_   _b_
-FIG. 102.—Tolles’ Solid and Compensated Oculars.]
-
-So far as the writer can ascertain the only reason that it is not
-more used is that it is somewhat more difficult to construct than the
-two lens form, for its curvatures and length must be very accurately
-adjusted. It is consequently unpopular with the constructing optician
-in spite of its conspicuous merits. It gives no ghosts, and the faint
-reflection at the eye end is widely spread so that if the exterior of
-the cylinder is well blackened, as it should be, it gives exceptional
-freedom from stray light. Still another variety of the Huygenian
-ocular sometimes useful is analogous to the compensating eyepiece used
-in microscopy. If, as commonly is the case, a telescope objective is
-over-corrected for color to correct for the chromatism of the eye in
-low powers, the high powers show strong over correction, the blue focus
-being longer than the red, and the blue image therefore the larger.
-
-If now the field lens of the ocular be made of heavy flint glass and
-the separation of the lenses suitably adjusted, the stronger refraction
-of the field lens for the blue pulls up the blue focus and brings its
-image to substantially the dimensions of the red, so that the eye lens
-performs as if there were no overcorrection of the objective.
-
-The writer has experimented with an ocular of this sort as shown
-in Fig. 102_b_ and finds that the color correction is, as might be
-expected, greatly improved over a Mittenzwey ocular of the same focus
-(⅕ inch). There would be material advantage in thus varying the
-ocular color correction to suit the power.
-
-In the Huyghenian eyepiece the equivalent focal length F is given by,
-
- F = 2ff′/(f + f′)
-
-where f and f′ are the focal lengths of the field and eye lenses
-respectively. This assumes the normal spacing, d, of half the sum of
-the focal lengths, not always adhered to by constructors. The perfectly
-general case, as for any two combined lenses is,
-
- F = ff_{1}/(f + f_{1}-d)
-
-[Illustration: FIG. 103.—Path of Rays Through Ramsden Ocular.]
-
-To obtain a flatter field, and particularly one free from distortion
-the construction devised by Ramsden is commonly used. This consists,
-Fig. 103, of two plano convex lenses of equal focal length, placed with
-their plane faces outward, at a distance equal to, or somewhat less
-than, their common focal length. The former spacing is the one which
-gives the best achromatic compensation since as before the condition
-for achromatism is
-
- d = ½(f + f′)
-
-When thus spaced the plane surface of the field lens is exactly in the
-focus of the eye lens, the combined focus F is the same as that of
-either lens, since as just shown in any additive combination of two
-lenses
-
- F = ff′/(f + f′-d)
-
-and while the field is flat and colorless, every speck of dust on the
-field lens is offensively in view.
-
-It is therefore usual to make this ocular in the form suggested by
-Airy, in which something of the achromatic correction is sacrificed to
-obviate this difficulty, and to obtain a better balance of the residual
-aberrations. The path of the rays is shown in Fig. 103. The lenses _A_
-and _B_ are of the same focal length but are now spaced at ⅔ of this
-length apart.
-
-The two neighboring rays _1_, _2_, coming through the objective from
-the distant object meet at the objective focus in a point, _a_, of the
-image plane _a b_. Thence, diverging, they are so refracted by _A_
-and _B_ as to leave the latter substantially parallel so that both
-appear to proceed from the point c, of the image plane _c_, _d_, in the
-principal focus of _B_.
-
-From the ordinary equation for the combination, F = ¾ f. The
-combination focusses ¼ f back of the principal focus of the
-objective, and the position of the eye is ¼ F back of the eye lens,
-which is another reason for shortening the lens spacing. At longer
-spacing the eye distance is inconveniently reduced.
-
-Thus constituted, the Ramsden ocular, known as “positive” from its
-capability for use as a magnifier of actual objects, gives a good flat
-field free from distortion over a field of nearly 35° and at some loss
-of definition a little more. It is the form most commonly used for
-micrometer work.
-
-In all optical instruments the aberrations increase as one departs from
-the axis, so that angular field is rather a loose term depending on the
-maximum aberrations that can be tolerated.[18]
-
- [18] The angular field a is defined by
-
- tan ½a = γ/F
-
- where γ is, numerically, the radius of the field sharp enough for the
- purpose in hand, and F the effective focal length of the ocular.
-
-Of the Ramsden ocular there are many modifications. Sometimes f and f′
-are made unequal or there is departure from the simple plano-convex
-form. More often the lenses are made achromatic, thus getting rid
-of the very perceptible color in the simpler form and materially
-helping the definition. Figure 104_a_ shows such an achromatic ocular
-as made by Steinheil. The general arrangement is as in the ordinary
-Ramsden, but the sharp field is slightly enlarged, a good 36°, and the
-definition is improved quite noticeably.
-
-A somewhat analogous form, but considerably modified in detail, is
-the Kellner ocular, Fig. 104_b_. It was devised by an optician of that
-name, of Wetzlar, who exploited it some three quarters of a century
-since in a little brochure entitled “Das orthoskopische Okular,” as
-notable a blast of “hot air” as ever came from a modern publicity agent.
-
-As made today the Kellner ocular consists of a field lens which is
-commonly plano-convex, plano side out, but sometimes crossed or even
-equiconvex, combined with a considerably smaller eye lens which is
-an over-corrected achromatic. The focal length of the field lens is
-approximately 7/4 F, that of the eye lens 4/3 F, separated by about ¾
-F.
-
-This ocular has its front focal plane very near the field lens,
-sometimes even within its substance, and a rather short eye distance,
-but it gives admirable definition and a usable field of very great
-extent, colorless and orthoscopic to the edge. The writer has one of
-2⅝″ focus, with an achromatic triplet as eye lens, which gives an
-admirable field of quite 50°.
-
-[Illustration: FIG. 104.—Achromatic and Kellner Oculars.]
-
-The Kellner is decidedly valuable as a wide field positive ocular, but
-it has in common with the two just previously described a sometimes
-unpleasant ghost of bright objects. This arises from light reflected
-from the inner surface of the field lens, and back again by the front
-surface to a focus. This focus commonly lies not far back of the field
-lens and quite too near to the focus of the eye lens for comfort. It
-should be watched for in going after faint objects with oculars of the
-types noted.
-
-A decidedly better form of positive ocular is the modern orthoscopic
-as made by Steinheil and Zeiss, Fig. 105_a_. It consists of a triple
-achromatic field lens, a dense flint between two crowns, with a
-plano-convex eye lens of much shorter focus (⅓ to ½) almost in
-contact on its convex side.
-
-The field triplet is heavily over-corrected for color, the front focal
-plane is nearly ½ F ahead of the front vertex of the field lens, and
-the eye distance is notably greater than in the Kellner. The field
-is above 40°, beautifully flat, sharp, and orthoscopic, free of
-troublesome ghosts. On the whole the writer is inclined to rate it as
-the best of two-lens oculars.
-
-There should also here be mentioned a very useful long relief ocular,
-often used for artillery sights, and shown in Fig. 105_b_. It consists
-like Fig. 104_a_, of a pair of achromatic lenses, but they are placed
-with the crowns almost in contact and are frequently used with a simple
-plano convex field lens of much longer focus, to render the combination
-more fully orthoscopic.
-
-The field, especially with the field lens, is wide, quite 40° as
-apparent angle for the whole instrument, and the eye distance is
-roughly equal to the focal length. It is a form of ocular that might
-be very advantageously used in finders, where one often has to assume
-uncomfortable angles of view, and long relief is valuable.
-
-[Illustration: _a_   _b_
-FIG. 105.—Orthoscopic and Long Relief Oculars.]
-
-Whatever the apparent angular field of an ocular may be, the real
-angular field of view is obtained by dividing the apparent field by the
-magnifying power. Thus the author’s big Kellner, just mentioned, gives
-a power of 20 with the objective for which it was designed, hence a
-real field of 2½°, while a second, power 65, gives a real field of
-hardly 0°40′, the apparent field in this case being a trifle over 40°.
-There is no escaping this relation, so that high power always implies
-small field.
-
-The limit of apparent field is due to increasing errors away from the
-axis, strong curvature of the field, and particularly astigmatism in
-the outer zones. The eye itself can take in only about 40° so that more
-than this, while attainable, can only be utilized by peering around the
-marginal field.
-
-For low powers the usable field is helped out by the accommodation of
-the eye, but in oculars of short focus the curvature of field is the
-limiting factor. The radius of curvature of the image is, in a single
-lens approximately 3/2 F, and in the common two lens forms about ¾ F.
-
-In considering this matter Conrady has shown (M. N. _78_ 445) that for
-a total field of 40° the sharpness of field fails at a focal length
-of about 1 inch for normal power of accommodation. The best achromatic
-combinations reduce this limit to about ½ inch.
-
-At focal lengths below this the sharpest field is obtainable only with
-reduced aperture. There is an interesting possibility of building an
-anastigmatic ocular on the lines of the modern photographic lens, which
-Conrady suggests, but the need of wide field in high powers is hardly
-pressing enough to stimulate research.
-
-[Illustration: FIG. 106.—Ordinary Terrestrial Ocular.]
-
-Finally we may pass to the very simple adjunct of most small
-telescopes, the terrestrial ocular which inverts the image and shows
-the landscape right side up. Whatever its exact form it consists of
-an inverting system which erects the inverted image produced by the
-objective alone, and an eyepiece for viewing this erected image. In its
-common form it is composed of four plano-convex lenses arranged as in
-Fig. 106. Here A and B for the inverting pair and C and D a modified
-Huygenian ocular. The image from the objective is formed in the front
-focus of AB which is practically an inverted ocular, and the erected
-image is formed in the usual way between C and D.
-
-The apparent field is fairly good, about 35°, and while slightly
-better corrections can be gained by using lenses of specially adjusted
-curvatures, as Airy has shown, these are seldom applied. The chief
-objection to this erecting system is its length, some ten times its
-equivalent focus. Now and then to save light and gain field, the
-erector is a single cemented combination and the ocular like Fig. 99_a_
-or Fig. 102_a_. Fig. 107 shows a terrestrial eyepiece so arranged,
-from an example by the late R. B. Tolles. When carefully designed an
-apparent field of 40° or more can be secured, with great brilliancy,
-and the length of the erecting system is moderate.
-
-Very much akin in principle is the eyepiece microscope, such as is made
-by Zeiss to give variable power and a convenient position of the eye
-in connection with filar micrometers, Fig. 108. It is provided with
-a focussing collar and its draw tube allows varying power just as in
-case of an ordinary microscope. In fact eyepiece microscopes have long
-been now and then used to advantage for high powers. They are easier on
-the eye, and give greater eye distance than the exceedingly small eye
-lenses of short focus oculars, and using a solid eyepiece and single
-lens objective lose no more light than an ordinary Huygenian ocular.
-The erect resultant image is occasionally a convenience in astronomical
-use.
-
-[Illustration: FIG. 107.—Tolles Triplet Inverting System.]
-
-[Illustration: FIG. 108.—Microscope as Ocular.]
-
-[Illustration: FIG. 109.—“Davon” Instrument.]
-
-Quite analogous to the eyepiece microscope is the so-called “Davon”
-micro-telescope. Originally developed as an attachment for the substage
-of a microscope to give large images of objects at a little distance
-it has grown also into a separate hand telescope, monocular or
-binocular, for general purposes. The attachment thus developed is shown
-complete in Fig. 109. D is merely a well corrected objective set in a
-mount provided with ample stops. The image is viewed by an ordinary
-microscope or special eyepiece microscope A, as the case may be,
-furnished with rack focussing at A′ and assembled with the objective by
-means of the carefully centered coupling C.
-
-It furnishes a compact and powerful instrument, very suitable for
-terrestrial or minor astronomical uses, like the Tolles’ short-focus
-hand telescopes already mentioned. When properly designed telescopes
-of this sort give nearly the field of prism glasses, weigh much less
-and lose far less light for the same effective power and aperture. They
-also have under fairly high powers rather the advantage in the matter
-of definition, other things being equal.
-
-
-
-
-CHAPTER VII
-
-HAND TELESCOPES AND BINOCULARS
-
-
-The hand telescope finds comparatively little use in observing
-celestial bodies. It is usually quite too small for any except very
-limited applications, and cannot be given sufficient power without
-being difficult to keep steady except by the aid of a fixed mounting.
-Still, for certain work, especially the observation of variable
-stars, it finds useful purpose if sufficiently compact and of good
-light-gathering power.
-
-There is most decidedly a limit to the magnifying power which can be
-given to an instrument held in the hand without making the outfit too
-unsteady to be serviceable. Anything beyond 8 to 10 diameters is highly
-troublesome, and requires a rudimentary mount or at least steadying the
-hand against something in order to observe with comfort.
-
-The longer the instrument the more difficult it is to manage, and
-the best results with hand telescopes are to be obtained with short
-instruments of relatively large diameter and low power. The ordinary
-field glass of Galilean type comes immediately to mind and in fact the
-field glass is and has been much used. As ordinarily constructed it is
-optically rather crude for astronomical purposes. The objectives are
-rarely well figured or accurately centered and a bright star usually
-appears as a wobbly flare rather than a point.
-
-Furthermore the field is generally small, and of quite uneven
-illumination from centre to periphery, so that great caution has to
-be exercised in judging the brightness of a star, according to its
-position in the field. The lens diameter possible with a field glass
-of ordinary construction is limited by the limited distance between
-the eyes, which must be well centered on the eyepieces to obtain clear
-vision.
-
-The inter-pupillary distance is generally a scant 2½ inches so that
-the clear aperture of one of the objectives of a field glass is rarely
-carried up to 2 inches. The best field glasses have each objective
-a triple cemented lens, and the concave lenses also triplets, the
-arrangement of parts being that shown in Fig. 110. Glasses of this sort
-rarely have a magnifying power above 5.
-
-In selecting a field glass with the idea of using it on the sky try it
-on a bright star, real or artificial, and if the image with careful
-focussing does not pull down to a pretty small and uniform point take
-no further interest in the instrument.
-
-[Illustration: FIG. 110.—Optical Parts of Field Glass.]
-
-The advantage of a binocular instrument is popularly much exaggerated.
-It gives a somewhat delusive appearance of brilliancy and clearness
-which is psychological rather than physical. During the late war a
-very careful research was made at the instance of the United States
-Government to determine the actual value of a binocular field glass
-against a monocular one of exactly the same type, the latter being
-cheaper, lighter, and in many respects much handier.
-
-The difference found in point of actual seeing all sorts of objects
-under varying conditions of illumination was so small as to be
-practically negligible. An increase of less than 5 per cent in
-magnifying power enabled one to see with the monocular instrument
-everything that could be seen with the binocular, equally well, and it
-is altogether probable that in the matter of seeing fine detail the
-difference would be even less than in general use, since it is not
-altogether easy to get the two sides of a binocular working together
-efficiently or to keep them so afterwards.
-
-There has been, therefore, a definite field for monocular hand
-telescopes of good quality and moderate power and such are manufactured
-by some of the best Continental makers. Such instruments have
-sometimes been shortened by building them on the exact principle of
-the telephoto lens, which gives a relatively large image with a short
-camera extension.
-
-[Illustration: FIG. 111.—Steinheil Shortened Telescope.]
-
-A much shortened telescope, as made by Steinheil for solar photographic
-purposes, is shown in Fig. 111. This instrument with a total length
-of about 2 feet and a clear aperture of 2⅜ inches gives a solar
-image of ½ inch diameter, corresponding to an ordinary glass of
-more than double that total length. Quite the same principle has been
-applied to terrestrial telescopes by the same maker, giving again an
-equivalent focus of about double the length of the whole instrument.
-This identical principle has often been used in the so-called Barlow
-lens, a negative lens placed between objective and eyepiece and
-giving increased magnification with small increase of length; also
-photographic enlargers of substantially similar function have found
-considerable use.
-
-A highly efficient hand telescope for astronomical purposes might be
-constructed along this line, the great shortening of the instrument
-making it possible to use somewhat higher powers than the ordinary
-without too much loss of steadiness. There is also constructed a
-binocular for strictly astronomical use consisting of a pair of small
-hand comet-seekers.
-
-One of these little instruments is shown in Fig. 112. It has a
-clear diameter of objectives of 1⅜ inch, magnification of 5, and
-a brilliant and even field of 7½° aperture. The objectives are
-triplets like Fig. 57, already referred to, the oculars achromatic
-doublets of the type of Fig. 104_a_.
-
-With the exception of these specialized astronomical field glasses
-the most useful and generally available hand instrument is the prism
-glass now in very general use. It is based on reversal of the image
-by internal total reflection in two prisms having their reflecting
-surfaces perpendicular each to the other. The rudiments of the process
-lie in the simple reversion prism shown in diagram in Fig. 113.
-
-[Illustration: FIG. 112.—Astronomical Binocular.]
-
-This is nothing more nor less than a right angled glass prism set with
-its hypothenuse face parallel and with its sides at 45° to the optical
-axis of the instrument. Rays falling upon one of its refracting faces
-at an angle of 45° are refracted upon the hypothenuse face, are there
-totally reflected and emerge from the second face of the prism parallel
-to their original course.
-
-Inspection of Fig. 113 shows that an element like A B perpendicular to
-the plane of the hypothenuse face is inverted by the total reflection
-so that it takes the position A′ B′. It is equally clear that an
-element exactly perpendicular to A B will be reflected from the
-hypothenuse face flatwise as it were, and will emerge without its ends
-being reversed so that the net effect of this single reflection is to
-invert the image without reversing it laterally at the same time.
-
-On the other hand if a second prism be placed behind the first, flat
-upon its side, with its hypothenuse face occupying a plane exactly
-perpendicular to that of the first prism, the line A′B′ will be
-refracted, totally reflected and refracted again out of the prism
-without a second inversion, while a line perpendicular to A′B′ will be
-refracted endwise on the hypothenuse face of the second prism and will
-be inverted as was the line A B at the start.
-
-[Illustration: FIG. 113.—Reversion Prism.]
-
-Consequently two prisms thus placed will completely invert the image,
-producing exactly the same effect as the ordinary inverting system Fig.
-106. The simple reversion prism is useful as furnishing a means, when
-placed over an eye lens, and rotated, of revolving the image on itself,
-a procedure occasionally convenient, especially in stellar photometry.
-The two prisms together constitute a true inverting system and have
-been utilized in that function, but they give a rather small angular
-field and have never come into a material amount of use. The exact
-effect of this combination, known historically as Dove’s prisms, is
-shown plainly in Fig. 114.
-
-The first actual prismatic inverting system was due to M. Porro, who
-invented it about the middle of the last century, and later brought it
-out commercially under the name of “Lunette à Napoleon Troisiéme,” as a
-glass for military purposes.
-
-[Illustration: FIG. 114.—Dove’s Prisms.]
-
-[Illustration: FIG. 115.—Porro’s Prism System.]
-
-The prism system of this striking form of instrument is shown in Fig.
-115. It was composed of three right angle prisms _A_, _B_, and _C_. _A_
-presented a cathetus face to the objective and _B_ a cathetus face to
-the ocular. Obviously a vertical element brought in along _a_ from the
-objective would be reflected at the hypothenuse face _b_, to a position
-at right angles to the original one, would enter the hypothenuse face
-of _C_ and thence after two reflections at _c_ and _d_ flatwise and
-without change of direction would emerge, enter the lower cathetus face
-of _B_ and by reflection at the hypothenuse face _e_ of _B_ would be
-turned another 90° making a complete reversion as regards up and down
-at the eye placed at _f_. An element initially at right angles to the
-one just considered would enter _A_, be reflected flatwise, in the
-faces of _C_ be twice reflected endwise, thereby completely inverting
-it, and would again be reflected flatwise from the hypothenuse face
-of _C_, thereby effecting, as the path of the rays indicated plainly
-shows, a complete inversion of the image. Focussing was very simply
-attained by a screw motion affecting the prism _C_ and the whole affair
-was in a small flat case, the external appearance and size of which is
-indicated in Fig. 116.
-
-[Illustration: FIG. 116.—Lunette à Napoleon Troisiéme.]
-
-[Illustration: FIG. 117.—Porro’s First Form of Prisms.]
-
-From ocular to objective the length was about an inch and a half. It
-was of 10 power and took in a field of 45 yards at a distance of 1000
-yards. Here for the first time we find a prismatic inverting system of
-strictly modern type. And it is interesting to note that if one had
-wished to make a binocular “Lunette à Napoleon Troisiéme” he would
-inevitably have produced an instrument with enhanced stereoscopic
-effect like the modern prism field glass by the mere effort to dodge
-the observer’s nose. Somewhat earlier M. Porro had arranged his prisms
-in the present conventional form of Fig. 117, where two right angle
-prisms have their faces positioned in parallel planes, but turned
-around by 90° as in Fig. 114. The ray traced through this conventional
-system shows that exactly the same inversion occurs here as in the
-original Porro construction, and this form is the one which has been
-most commonly used for prismatic inversion and is conveniently known as
-Porro’s first form, it actually having been antecedent in principle and
-practice to the “Lunette à Napoleon Troisiéme.” The original published
-description of Porro’s work, translated from “Cosmos” Vol. 2, p. 222
-(1852) et seq. is here annexed as it sets forth the origin of the
-modern prism glass in unmistakable terms.
-
-_Cosmos, Vol. 2_, p. 222.—“We have wished for some time to make known
-to our readers the precious advantages of the “longue-vue cornet” or
-télémetre of M. Porro. Ordinary spyglasses or terrestrial telescopes
-of small dimensions are at least 30 or 40 cm. long when extended to
-give distinct vision of distant objects. The length is considerably
-reduced by substituting for a fixed tube multiple tubes sliding into
-each other. But the drawing out which this substitution necessitates is
-a somewhat grave inconvenience; one cannot point the telescope without
-arranging it and losing time.
-
-For a long time we have wished it were possible to have the power
-of viewing distant objects, with telescopes very short and without
-draw. M. Porro’s “longue-vue cornet” seems to us to solve completely
-this difficult and important problem. Its construction rests upon an
-exceedingly ingenious artifice which literally folds triply the axis
-of the telescope and the luminous ray so that by this fact alone the
-length of the instrument is reduced by two-thirds.
-
-Let us try to give an idea of this construction: Behind the telescope
-objective M. Porro places a rectangular isosceles prism of which the
-hypothenuse is perpendicular to the optic axis. The luminous rays
-from the object fall upon the rectangular faces of this prism, are
-twice totally reflected, and return upon themselves parallel to their
-original direction: half way to the point where they would form the
-image of the object, they are arrested by a second prism entirely
-similar to the first, which returns them to their original direction
-and sends them to the eyepiece through which we observe the real image.
-If the rectangular faces of the second prism were parallel to the
-faces of the first, this real image would be inverted—the telescope
-would be an astronomical and not a terrestrial telescope. But M. Porro
-being an optician eminently dextrous, well divined that to effect the
-reinversion it sufficed to place the rectangular faces of the second
-prism perpendicular to the corresponding faces of the first by turning
-them a quarter revolution upon themselves.
-
-In effect, a quarter revolution of a reflecting surface is a half
-revolution for the image, and a half revolution of the image evidently
-carries the bottom to the top and the right to the left, effecting a
-complete inversion. As the image is thus _redressed_ independently of
-the eyepiece one can evidently view it with a simple two-lens ocular
-which decreases still further the length of the telescope so that it
-is finally reduced to about a quarter of that of a telescope of equal
-magnifying power, field and clearness.
-
-The new telescope is then a true pocket telescope even with a
-magnifying power of 10 or 15. Its dimensions in length and bulk are
-those of a field glass usually magnifying only 4 to 6 times. The more
-draws, the more bother,—it here suffices to turn a little thumbscrew to
-find in an instant the point of sharpest vision.
-
-In brilliancy necessarily cut down a little, not by the double total
-reflection, which as is well known does not lose light, but by the
-quadruple passage across the substance of the two prisms, the cornet
-in sharpness and amplification of the images can compare with the
-best hunting telescopes of the celebrated optician Ploessl of Vienna.
-M. Porro has constructed upon the same principles a marine telescope
-only 15 c.m. long with an objective of 40 m.m. aperture which replaces
-an ordinary marine glass 70 c.m. long. He has done still better,—a
-telescope only 30 c.m. long carries a 60 m.m. objective and can be made
-by turns a day and a night glass, by substituting by a simple movement
-of the hand and without dismounting anything, one ocular for the other.
-Its brilliancy and magnification of a dozen times with the night
-ocular, of twenty-five times with the day ocular, permits observing
-without difficulty the eclipses of the satellites of Jupiter.
-
-This is evidently immense progress. One of the most illustrious
-of German physicists, M. Dove of Berlin, gave in 1851 the name of
-reversion prism to the combination of two prisms placed normally one
-behind the other so that their corresponding faces were perpendicular.
-He presented this disposition as an important new discovery made by
-himself. He doubtless did not know that M. Porro, who deserves all the
-honor of this charming application, had realized it long before him.”
-
-A little later M. Porro produced what is commonly referred to as
-Porro’s second form, which is derived directly from annexing _A_ Fig.
-115 to the corresponding half of _C_ as a single prism, the other half
-of _B_ being similarly annexed to the prism _C_, thus forming two
-sphenoid prisms, such as are shown in Fig. 118 which may be mounted
-separately or may have their faces cemented together to save loss of
-light by reflections. The sphenoid prisms have had the reputation of
-being much more difficult to construct than the plain right angled
-prisms of the other forms shown. In point of fact they are not
-particularly difficult to make and the best inverting eye pieces for
-telescopes are now constructed with sphenoid prisms like those just
-described.
-
-[Illustration: FIG. 118.—Porro’s Second Form.]
-
-[Illustration: FIG. 119.—Clark Prismatic Eyepiece.]
-
-This particular arrangement lends itself very readily to a fairly
-compact and symmetrical mounting, as is well shown in Fig. 119 which
-is the terrestrial prismatic eyepiece as constructed by the Alvan
-Clark corporation for application to various astronomical telescopes
-of their manufacture. A glance at the cut shows the compactness of
-the arrangement, which actually shortens the linear distance between
-objective and ocular by the amount of the path of the ray through the
-prisms instead of lengthening the distance as in the common terrestrial
-eyepiece.
-
-The field moreover is much larger than that attainable by a
-construction like Fig. 110, extending to something over 40°, and there
-is no strong tendency for the illumination or definition to fall off
-near the edge of the field.
-
-In the practical construction of prism field glasses the two right
-angled prisms are usually separated by a moderate space as in Porro’s
-original instruments so as to shorten the actual length of the prism
-telescope by folding the ray upon itself as in Fig. 120, which is a
-typical modern binocular of this class.
-
-[Illustration: FIG. 120.—Section of Prism Binocular.]
-
-The path of the rays is plainly shown and the manner in which the
-prisms fold up the total focal length of the objective is quite
-obvious. The added stereoscopic effect obtained by the arrangement of
-the two sides of the instrument is practically a very material gain.
-It gives admirable modelling of the visible field, a perception of
-distance which is at least very noticeable and a certain power of
-penetration, as through a mass of underbrush, which results from the
-objectives to a certain extent seeing around small objects so that
-one or the other of them gives an image of something beyond. For near
-objects there is some exaggeration of stereoscopic effect but on the
-whole for terrestrial use the net gain is decidedly in evidence.
-
-A well made prism binocular is an extremely useful instrument for
-observation of the heavens, provided the objectives are of fair size,
-and the prisms big enough to receive the whole beam from the objective,
-and well executed enough to give a thoroughly good image with a flat
-field.
-
-The weak points of the prism glass are great loss of light through
-reflection at the usual 10 air-glass surfaces and the general presence
-of annoying ghosts of bright objects in the field. Most such binoculars
-have Kellner eyepieces which are peculiarly bad, as we have seen, with
-respect to reflected images, and present the plane surface of the last
-prism to the plane front of the field lens. Recently some constructors
-have utilized the orthoscopic eyepiece, Figure 105_a_, as a substitute
-with great advantage in the matter of reflections.
-
-The loss of light in the prism glass is really a serious matter,
-between reflection at the surfaces and absorption in the thick masses
-of glass necessary in the prisms. If of any size the transmitted light
-is not much over one-half of that received, very seldom above 60%.
-If the instrument is properly designed the apparent field is in the
-neighborhood of 45°, substantially flat and fairly evenly illuminated.
-Warning should here be given however that many binoculars are on the
-market in which the field is far from flat and equally far from being
-uniform.
-
-In many instances the prisms are too small to take the whole bundle of
-rays from the objective back to the image plane without cutting down
-the marginal light considerably. Even when the field is apparently
-quite flat this fault of uneven illumination may exist, and in a glass
-for astronomical uses it is highly objectionable.
-
-Before picking out a binocular for a study of the sky make very careful
-trial of the field with respect to flatness and clean definition of
-objects up to the very edge. Then judge as accurately as you may of the
-uniformity of illumination, if possible by observation on two stars
-about the radius of the field apart. It should be possible to observe
-them in any part of the field without detectable change in their
-apparent brilliancy.
-
-If the objectives are easily removable unscrew one of them to obtain a
-clear idea as to the actual size of the prisms.[19] Look out, too, for
-ghosts of bright stars.
-
- [19] There are binoculars on the market which are to outward
- appearance prism glasses, but which are really ordinary opera glasses
- mounted with intent to deceive, sometimes bearing a slight variation
- on the name of some well known maker.
-
-The objectives of prism glasses usually run from ¾ inch to 1½ inch
-in diameter, and the powers from 6 to 12. The bigger the objectives the
-better, provided the prisms are of ample size, while higher power than
-6 or 8 is generally unnecessary and disadvantageous. Occasional glasses
-of magnifying power 12 to 20 or more are to be found but such powers
-are inconveniently great for an instrument used without support. Do not
-forget that a first class monocular prism glass is extremely convenient
-and satisfactory in use, to say nothing of being considerably less in
-price than the instrument for two eyes. A monocular prism glass, by
-the way, makes an admirable finder when fitted with coarse cross lines
-in the eyepiece. It is particularly well suited to small telescopes
-without circles.
-
-[Illustration: FIG. 121.—Binocular with Extreme Stereoscopic Effect.]
-
-Numerous modifications of Porro’s inverting prisms have been made
-adapting them to different specific purposes. Of these a single
-familiar example will suffice as showing the way in which the Porro
-prism system can be treated by mere rearrangement of the prismatic
-elements. In Fig. 121 is shown a special Zeiss binocular capable of
-extreme stereoscopic effect. It is formed of two Porro prism telescopes
-with the rays brought into the objectives at right angles to the axis
-of the instrument by a right angled prism external to the objective.
-
-The apertures of these prisms appear pointing forward in the cut. As
-shown they are in a position of maximum stereoscopic effect.
-
-Being hinged the tubes can be swung up from the horizontal position,
-in which latter the objectives are separated by something like eight
-times the interocular distance. The stereoscopic effect with the tubes
-horizontal is of course greatly exaggerated so that it enables one to
-form a fair judgment as to the relative position of somewhat distant
-objects, a feature useful in locating shell bursts.
-
-The optical structure of one of the pair of telescopes is shown in Fig.
-122 in which the course of the entering ray can be traced through the
-exterior prism of the objective and the remainder of the reversing
-train and thence through the eyepiece. This prism erecting system is
-obviously derived from the “Lunette à Napoleon Troisiéme” by bringing
-down the prism _B_ upon the corresponding half _A_ and cementing it
-thereto, meanwhile placing the objective immediately under _A_.
-
-One occasionally meets prismatic inverting systems differing
-considerably from the Porro forms. Perhaps the best known of these is
-the so called roof prism due to Prof. Abbé, Fig. 123, and occasionally
-useful in that the entering and emerging rays lie in the same straight
-line, thus forming a direct vision system. Looking at it as we did at
-the Porro system a vertical element in front of the prism is reversed
-in reflection from the two surfaces a and b, while a corresponding
-horizontal element is reflected flatwise so far as these are concerned,
-but is turned end for end by reflection at the roof surfaces c and d,
-thus giving complete inversion.
-
-In practice the prism is made as shown, in three parts, two of them
-right angled prisms, the third containing the roof surfaces. The
-extreme precision required in figuring the roof forms a considerable
-obstacle to the production of such prisms in quantity and while
-they have found convenient use in certain special instruments like
-gunsights, where direct vision is useful, they are not extensively
-employed for general purposes, although both monocular and binocular
-instruments have been constructed by their aid.
-
-[Illustration: FIG. 122.—Path of Ray in Fig. 121.]
-
-[Illustration: FIG. 123.—Abbé Roof Prism.]
-
-One other variety of prism involving the roof principle has found some
-application in field glasses manufactured by the firm of Hensoldt. The
-prism form used is shown in Fig. 124. This like other forms of roof
-prism is less easy to make than the conventional Porro type. Numerous
-inverting and laterally reflecting prisms are in use for specific
-purposes. Some of them are highly ingenious and remarkably well adapted
-for their use, but hardly can be said to form a material portion of
-telescope practice. They belong rather to the technique of special
-instruments like gunsights and periscopes, while some of them have been
-devised chiefly as ingenious substitutes for the simpler Porro forms.
-
-Most prism telescopes both monocular and binocular are generally made
-on one or the other of the Porro forms. This is particularly true
-of the large binoculars which are occasionally constructed. Porro’s
-second form with the sphenoid prisms seems to be best adapted to cases
-where shortening of the instrument is not a paramount consideration.
-For example, some Zeiss short focus telescopes are regularly made in
-binocular form, and supplied with inverting systems composed of two
-sphenoid prisms, and with oculars constructed on the exact principle
-of the triple nose-piece of a microscope, so that three powers are
-immediately available to the observer.
-
-[Illustration: FIG. 124.—Hensoldt Prism.]
-
-Still less commonly binocular telescopes of considerable aperture
-are constructed, primarily for astronomical use, being provided with
-prismatic inversion for terrestrial employment, but more particularly
-in order to gain by the lateral displacement of a Porro system the
-space necessary for two objectives of considerable size. As we have
-already seen, the practical diameter of objectives in a binocular
-is limited to a trifle over 2 inches unless space is so gained. The
-largest prismatic binocular as yet constructed is one made years ago
-by the Clarks, of 6¼ inches objective aperture and 92¼ inches
-focal length. So big and powerful an instrument obviously would give
-admirable binocular views of the heavens and so accurately was it
-constructed that the reports of its performance were exceedingly good.
-The same firm has made a good many similar binoculars of 3 inch and
-above, of which a typical example of 4 inch aperture and 60 inch focal
-length is shown in Fig. 125. In this case the erecting systems were
-of Porro’s first form, and were provided with Kellner oculars of very
-wide field. These binoculars constructions in instruments of such size,
-however well made and agreeable for terrestrial observation, hardly
-justify the expense for purely astronomical use.
-
-[Illustration: FIG. 125.—Clark 4″ Binocular Telescope.]
-
-
-
-
-CHAPTER VIII
-
-ACCESSORIES
-
-
-Aside from the ordinary equipment of oculars various accessories
-form an important part of the observer’s equipment, their number and
-character depending on the instrument in use and the purposes to which
-it is devoted.
-
-[Illustration: FIG. 126.—Star Diagonal.]
-
-First in general usefulness are several special forms of eyepiece
-equipment supplementary to the usual oculars. At the head of the list
-is the ordinary star diagonal for the easier viewing of objects near
-the zenith here shown in Fig. 126. It is merely a tube, _A_, fitting
-the draw tube of the telescope, with a slotted side tube _B_, at a
-right angle, into which the ordinary ocular fits, and a right angled
-prism _C_ with its two faces perpendicular respectively to the axes of
-the main and side tubes, and the hypothenuse face at 45° to each. The
-beam coming down the tube is totally reflected at this face and brought
-to focus at the ocular. The lower end of the tube is closed by a cap to
-exclude dust.
-
-One looks, by help of this, horizontally at zenith stars, or, if
-observing objects at rather high altitude, views them at a comfortable
-angle downward. The prism must be very accurately made to avoid injury
-to the definition, but loses only about 10% of the light, and adds
-greatly to the comfort of observing.
-
-Of almost equal importance is the solar diagonal devised by Sir John
-Herschel, Fig. 127. Here the tube structure _A_, _B_, is quite the
-same as in Fig. 126 but the right angled prism is replaced by a simple
-elliptical prism _C_ of small angle, 10° or less, with its upper face
-accurately plane and at 45° to the axes of the tubes, resting on a
-lining tube _D_ cut off as shown. In viewing the sun only about 5% of
-the light (and heat) is reflected at this upper surface to form the
-image at the eye piece.
-
-[Illustration: FIG. 127.—Solar Diagonal.]
-
-Any reflection from the lower polished surface is turned aside out
-of the field, while the remainder of the radiation passes through
-the prism _C_ and is concentrated below it. To prevent scorching the
-observer the lower end of the tube is capped at _E_, but the cap has
-side perforations to provide circulation for the heated air. Using such
-a prism, the remnant of light reflected can be readily toned down by a
-neutral tinted glass over the ocular.
-
-In the telescopes of 3 inches and less aperture, and ordinary focal
-ratio, a plane parallel disc of very dark glass over the ocular gives
-sufficient protection to the eye. This glass is preferably of neutral
-tint, and commonly is a scant 1/16 inch thick. Some observers prefer
-other tints than neutral. A green and a red glass superimposed give
-good results and so does a disc of the deepest shade of the so-called
-Noviweld glass, which is similar in effect.
-
-With an aperture as large as 3 inches a pair of superimposed dark
-glasses is worth while, for the two will not break simultaneously from
-the heat and there will be time to get the eye away in safety. A broken
-sunshade is likely to cost the observer a permanent scotoma, blindness
-in a small area of the retina which will neither get better nor worse
-as time goes on.
-
-Above 3 inches aperture the solar prism should be used or, if one cares
-to go to fully double the cost, there is nothing more comfortable to
-employ in solar observation than the polarizing eye piece, Fig. 128.
-This shows schematically the arrangement of the device. It depends on
-the fact that a ray of light falling on a surface of common glass at an
-angle of incidence of approximately 57° is polarized by the reflection
-so that while it is freely reflected if it falls again on a surface
-parallel to the first, it is absorbed if it falls at the same incidence
-on a surface at right angles to the first.
-
-[Illustration: FIG. 128.—Diagram of Polarizing Eyepiece.]
-
-Thus in Fig. 128 the incident beam from the telescope falls on the
-black glass surface _a_ at 57° incidence, is again reflected from the
-parallel mirror _b_, and then passed on, parallel to its original
-path, to the lower pair of mirrors _c_, _d_. The purpose of the
-second reflection is to polarize the residual light which through the
-convergence of the rays was incompletely polarized at the first.
-
-The lower pair of mirrors _c_, _d_, again twice reflect the light at
-the polarizing angle, and, in the position shown, pass it on to the
-ocular diminished only by the four reflections. But if the second pair
-of mirrors be rotated together about a line parallel to _b c_ as an
-axis the transmitted light begins to fade out, and when they have been
-turned 90°, so that their planes are inclined 90° to _a_ and _b_ (= 33°
-to the plane of the paper), the light is substantially extinguished.
-
-Thus by merely turning the second pair of mirrors the solar image can
-be reduced in brilliancy to any extent whatever, without modifying its
-color in any way. The typical form given to the polarizing eyepiece is
-similar to Fig. 129. Here _t__2 is the box containing the polarizing
-mirrors, _a b_, fitted to the draw tube, but for obvious reasons
-eccentric with it, _t__1 is the rotating box containing the “analysing”
-mirrors _c_, _d_, and _a_ is the ocular turning with it.
-
-Sometimes the polarizing mirrors are actually a pair of Herschel prisms
-as in Fig. 126, facing each other, thus getting rid of much of the
-heat. Otherwise the whole set of mirrors is of black glass to avoid
-back reflections. In simpler constructions single mirrors are used as
-polarizer and analyser, and in fact there are many variations on the
-polarizing solar eyepiece involving about the same principles.
-
-[Illustration: FIG. 129.—Polarizing Solar Eyepiece.]
-
-In any solar eyepiece a set of small diaphragms with holes from perhaps
-1/64 inch up are useful in cutting down the general glare from the
-surface outside of that under scrutiny. These may be dropped upon the
-regular diaphragm of the ocular or conveniently arranged in a revolving
-diaphragm like that used with the older photographic lenses.
-
-The measurement of celestial objects has developed a large group of
-important auxiliaries in the micrometers of very varied forms. The
-simplest needs little description, since it consists merely of a plane
-parallel disc of glass fitting in the focus of a positive ocular,
-and etched with a network of uniform squares, forming a reticulated
-micrometer by which the distance of one object from another can be
-estimated.
-
-It can be readily calibrated by measuring a known distance or noting
-the time required for an equatorial star to drift across the squares
-parallel to one set of lines. It gives merely a useful approximation,
-and accurate measures must be turned over to more precise instruments.
-
-[Illustration: FIG. 130.—Diagram of Ring Micrometer.]
-
-The ring micrometer due, like so much other valuable apparatus, to
-Fraunhofer, is convenient and widely used for determining positions.
-It consists, as shown in Fig. 130, of an accurately turned opaque
-ring, generally of thin steel, cemented to a plane parallel glass or
-otherwise suspended in the center of the eyepiece field. The whole
-ring is generally half to two thirds the width of the field and has a
-moderate radial width so that both the ingress and the egress of a star
-can be conveniently timed.
-
-It depends wholly on the measurement of time as the stars to be
-compared drift across the ring while the telescope is fixed, and while
-a clock or chronometer operating a sounder is a desirable adjunct
-one can do pretty well with a couple of stop watches since only
-differential times are required.
-
-For full directions as to its use consult Loomis’ Practical Astronomy,
-a book which should be in the library of every one who has the least
-interest in celestial observations. Suffice it to say here that
-the ring micrometer is very simple in use, and the computation of
-the results is quite easy. In Fig. 130 F is the edge of the field,
-R the ring, and _a b_, _a′b′_, the paths of the stars _s_ and _s′_,
-the former well into the field, the latter just within the ring. The
-necessary data comprise the time taken by each star to transverse
-the ring, and the radius of the ring in angular measure, whence the
-difference in R. A. or Dec, can be obtained.[20]
-
- [20] r the radius of the ring, is given by, r = (15/2)(t′-t) cos Dec.,
- t′-t being the seconds taken for transit.
-
-Difference of R. A. = ½ (t′-t)½ (T′-T) where (T′-T) is the time
-taken for transit of second star. To obtain differences of declination
-one declination should be known at least approximately, and the second
-estimated from its relative position in the ring or otherwise. Then
-with these tentative values proceed as follows.
-
-Put x = angle _aob_ and _x_′ = angle _a′o′b′_
-
-Also let d  = approximate declination of _s_ and
-         d′ = approximate declination of _s′_
-
-Then sin x = (15/2r) cos d (T′-T)
-
-     sin x′ = (15/2r) cos d′ (t′-t) and finally
-
-Difference of Dec. = r (cos x′-cos x), when both arcs are on the same
-side of center of ring. If on opposite sides, Diff. = r (cos x′ + cos
-x).
-
-[Illustration: _Chamber’s “Astronomy”_ (_Clarendon Press_).
-FIG. 131.—Double Image Micrometer. (_Courtesy of The Clarendon Press._)]
-
-There is also now and then used a square bar micrometer, consisting of
-an opaque square set with a diagonal in the line of diurnal motion.
-It is used in much the same way as the ring, and the reductions are
-substantially the same. It has some points of convenience but is
-little used, probably on account of the great difficulty of accurate
-construction and the requirement, for advantageous use, that the
-telescope should be on a well adjusted equatorial stand.[21] The ring
-micrometer works reasonably well on any kind of steady mount, requires
-no illumination of the field and is in permanent working adjustment.
-
- [21] (For full discussion of this instrument see Chandler, Mem. Amer.
- Acad. Arts & Sci. 1885, p. 158).
-
-Still another type of micrometer capable of use without a clock-drive
-is the double image instrument. In its usual form it is based on the
-principle that if a lens is cut in two along a diameter and the halves
-are slightly displaced along the cut all objects will be seen double,
-each half of the lens forming its own set of images.
-
-Conversely, if one choses two objects in the united field these can be
-brought together by sliding the halves of the lens as before, and the
-extent of the movement needed measures the distance between them. Any
-lens in the optical system can be thus used, from the objective to the
-eyepiece. Fig. 131 shows a very simple double image micrometer devised
-by Browning many years ago. Here the lens divided is a so-called Barlow
-lens, a weak achromatic negative lens sometimes used like a telephoto
-lens to lengthen the focus and hence vary the power of a telescope.
-
-This lens is shown at A with the halves widely separated by the double
-threaded micrometer screw B, which carries them apart symmetrically.
-The ocular proper is shown at C.
-
-Double image micrometers are now mainly of historical interest, and
-the principle survives chiefly in the heliometer, a telescope with the
-objective divided, and provided with sliding mechanism of the highest
-refinement. The special function of the heliometer is the direct
-micrometric measurement of stellar distances too great to be within the
-practicable range of a filar micrometer—distances for example up to
-1½° or even more.
-
-The observations with the heliometer are somewhat laborious and demand
-rather intricate corrections, but are capable of great precision. (See
-Sir David Gill’s article “Heliometer” in the Enc. Brit. 11th Ed.). At
-the present day celestial photography, with micrometric measurement
-of the resulting plates, has gone far in rendering needless visual
-measurements of distances above a very few minutes of arc, so that
-it is somewhat doubtful whether a large heliometer would again be
-constructed.
-
-[Illustration: FIG. 132.—Filar Micrometer. (_Courtesy of J. B.
-Lippincott Co._)]
-
-The astronomer’s real arm of precision is the filar micrometer. This
-is shown in outline in Fig. 132, the ocular and the plate that carries
-it being removed so as to display the working parts. It consists of a
-main frame aa, carrying a slide bb, which is moved by the screws and
-milled head B. The slide bb carries the vertical spider line mm, and
-usually one or more horizontal spider lines, line mm is the so-called
-fixed thread of the micrometer, movable only as a convenience to avoid
-shifting the telescope.
-
-On bb moves the micrometer slide cc, carrying the movable spider line
-nn and the comb which records, with mm as reference line, the whole
-revolutions of the micrometer screw C. The ocular sometimes has a
-sliding motion of its own on cc, to get it positioned to the best
-advantage. In use one star is set upon mm by the screw B and then C is
-turned until nn bisects the other star.
-
-Then the exact turns and fraction of a turn can be read off on the comb
-and divided head of C, and reduced to angular measure by the known
-constant of the micrometer, usually determined by the time of passage
-of a nearly equatorial star along the horizontal thread when mm, nn,
-are at a definite setting
-
-apart. (Then r = (15(t′-t) cos d)/N where r is the value of a
-revolution in seconds of arc, N the revolutions apart of mm, nn, and t
-and d as heretofore.)
-
-Very generally the whole system of slides is fitted to a graduated
-circle, to which the fixed horizontal thread is diametral. Then by
-turning the micrometer until the horizontal threads cut the two objects
-under comparison, their position angle with reference to a graduated
-circle can be read off. This angle is conventionally counted from 0° to
-360° from north around through east.
-
-[Illustration: FIG. 133.—Filar Position Micrometer.]
-
-Figure 133 shows the micrometer constructed by the Clarks for their
-24 inch equatorial of the Lowell Observatory. Here A is the head of
-the main micrometer screw of which the whole turns are reckoned on the
-counter H in lieu of the comb of Fig. 132. B is the traversing screw
-for the fixed wire system, C the clamping screw of the position circle,
-D its setting pinion, E the rack motion for shifting the ocular, F
-the reading glass for the position circle, and G the little electric
-lamp for bright wire illumination. The parts correspond quite exactly
-with the diagram of Fig. 132 but the instrument is far more elegant in
-design than the earlier forms of micrometer and fortunately rid of the
-oil lamps that were once in general use. A small electric lamp with
-reflector throws a little light on the spider lines—just enough to show
-them distinctly. Or sometimes a faint light is thus diffused in the
-field against which the spider lines show dark.
-
-Commonly either type of illumination can be used and modified as
-occasion requires. The filar micrometer is seldom used on small
-telescopes, since to work easily with it the instrument should be
-permanently mounted and clock-driven. Good work was done by some of the
-early observers without these aids, but at the cost of infinite pains
-and much loss of time.
-
-The clock drive is in fact a most important adjunct of the telescope
-when used for other purposes than ordinary visual observations, though
-for simple seeing a smooth working slow motion in R. A. answers well.
-The driving clock from the horological view-point is rudimentary. It
-consists essentially of a weight-driven, or sometimes spring-driven,
-drum, turning by a simple gear connection a worm which engages a
-carefully cut gear wheel on the polar axis, while prevented from
-running away by gearing up to a fast running fly-ball governor, which
-applies friction to hold the clockwork down to its rate if the speed
-rises by a minute amount. There is no pendulum in the ordinary sense,
-the regularity depending on the uniformity of the total friction—that
-due to the drive plus that applied by the governor.
-
-Figure 134 shows a simple and entirely typical driving clock by Warner
-& Swasey. Here A is the main drum with its winding gear at B, C is the
-bevel gear, which is driven from another carried by A, and serves to
-turn the worm shaft D; E marks the fly balls driven by the multiplying
-gearing plainly visible. The governor acts at a predetermined rotation
-speed to lift the spinning friction disc F against its fixed mate,
-which can be adjusted by the screw G.
-
-The fly-balls can be slightly shifted in effective position to complete
-the regulation. These simple clocks, of which there are many species
-differing mainly in the details of the friction device, are capable of
-excellent precision if the work of driving the telescope is kept light.
-
-For large and heavy instruments, particularly if used for photographic
-work where great precision is required, it is difficult to keep the
-variations of the driving friction within the range of compensation
-furnished by the governor friction alone, and in such case recourse
-is often taken to constructions in which the fly balls act as relay
-to an electrically controlled brake, or in which the driving power is
-supplied by an electric motor suitably governed either continuously
-or periodically. For such work independent hand guiding mechanism is
-provided to supplement the clockwork. For equatorials of the smallest
-sizes, say 3 to 4 inches aperture, spring operated driving clocks are
-occasionally used. The general plan of operation is quite similar to
-the common weight driven forms, and where the weights to be carried are
-not excessive such clocks do good work and serve a very useful purpose.
-
-[Illustration: FIG. 134.—Typical Driving Clock. (_Courtesy of The
-Clarendon Press._)]
-
-An excellent type of the simple spring driving clock is shown in
-Fig. 136 as constructed by Zeiss. Here 1 is the winding gear, 2 the
-friction governor, and 3 the regulating gear. It will be seen that the
-friction studs are carried by the fly balls themselves, somewhat as in
-Fraunhofers’ construction a century since, and the regulation is very
-easily and quickly made by adjusting the height of the conical friction
-surface above the balls.
-
-For heavier work the same makers generally use a powerful weight driven
-train with four fly-balls and electric seconds control, sometimes with
-the addition of electric motor slow motions to adjust for R. A. in both
-directions.
-
-[Illustration: FIG. 135.—Clark Driving Clock.]
-
-Figure 135 is a rather powerful clock of analogous form by the Clarks.
-It differs a little in its mechanism and especially in the friction
-gear in which the bearing disc is picked up by a delicately set latch
-and carried just long enough to effect the regulation. It is really
-remarkable that clockworks of so simple character as these should
-perform as well as experience shows that they do. In a few instances
-clocks have depended on air-fans for their regulating force, something
-after the manner of the driving gear of a phonograph, but though rather
-successful for light work they have found little favor in the task
-of driving equatorials. An excellent type of a second genus is the
-pendulum controlled driving clock due to Sir David Gill. This has a
-powerful weight-driven train with the usual fly-ball governor. But the
-friction gear is controlled by a contact-making seconds pendulum in the
-manner shown diagrammatically in Fig. 137. Two light leather tipped
-rods each controlled by an electro magnet act upon an auxiliary brake
-disc carried by the governor spindle which is set for normal speed with
-one brake rod bearing lightly on it. Exciting the corresponding magnet
-relieves the pressure and accelerates the clock, while exciting the
-other adds braking effect and slows it.
-
-[Illustration: FIG. 136.—Spring Operated Driving Clock.]
-
-In Fig. 137 is shown from the original paper, (M. N. Nov., 1873), the
-very ingenious selective control mechanism. At P is suspended the
-contact-making seconds-pendulum making momentary contact by the pin Q
-with a mercury globule at R. Upon a spindle of the clock which turns
-once a second is fixed a vulcanite disc γ, δ, ε, σ. This has a rim of
-silver broken at the points γ, δ, ε, σ, by ivory spacers covering 3° of
-circumference. On each side of this disc is another, smaller, and with
-a complete silver rim. One, ηθ, is shown, connected with the contact
-spring V; its mate η′θ′, on the other side contacts with U, while a
-third contact K bears on the larger disc.
-
-The pair of segments σ, γ, and δ, ε, are connected to η θ, the other
-pair of segments to η′ θ′. Now suppose the discs turning with the
-arrows: If K rests on one of the insulated points when the pendulum
-throws the battery C Z into circuit nothing happens. If the disc is
-gaining on the pendulum, K, instead of resting on γ as shown will
-contact with segment γ, σ, and actuate a relay via V, exciting the
-appropriate brake magnet.
-
-[Illustration: FIG. 137.—Sir David Gill’s Electric Control.]
-
-If the disc is losing, K contacts with segment γ, δ, and current
-will pass via η′θ′ and U to a relay that operates the other brake
-magnet and lets the clock accelerate. A fourth disc (not shown) on
-the same spindle is entirely insulated on its edge except at points
-corresponding to γ and ε, and with a contact spring like K.
-
-If the disc is neither gaining nor losing when the pendulum makes
-contact, current flows via this fourth disc and sets the relay on
-the mid-point ready to act when needed. This clock is the prototype
-of divers electrically-braked driving clocks with pendulum control,
-and proved beautifully precise in action, like various kindred devices
-constructed since, though the whole genus is somewhat expensive and
-intricate.
-
-The modern tendency in driving apparatus for telescopes, particularly
-large instruments, is to utilize an electric motor for the source of
-power, using a clock mechanism merely for the purpose of accurately
-regulating the rate of the motor. We thus have the driving clock in
-its simplest form as a purely mechanical device worked by a sensitive
-fly-ball governor. The next important type is that in which the clock
-drive is precisely regulated by a pendulum clock, the necessary
-governing power being applied electrically as in Fig. 137 or sometimes
-mechanically.
-
-Finally we come to the type now under consideration where the
-instrument itself is motor driven and the function of the clock is
-that of regulating the motor. A very good example of such a drive is
-the Gerrish apparatus used for practically all the instruments at the
-various Harvard observatory stations, and which has proved extremely
-successful even for the most trying work of celestial photography.
-The schematic arrangement of the apparatus is shown in Fig. 138. Here
-an electric motor shown in diagram in 1, Fig. 138, is geared down to
-approximately the proper speed for turning the right ascension axis of
-the telescope. It is supplied with current either from a battery or
-in practice from the electric supply which may be at hand. This motor
-is operated on a 110 volt circuit which supplies current through the
-switch 2 which is controlled by the low voltage clock circuit running
-through the magnet 3. The clock circuit can be closed and opened at two
-points, one controlled by the seconds pendulum 5, the other at 7 by the
-stud on the timing wheel geared to the motor for one revolution per
-second. There is also a shunt around the pendulum break, closed by the
-magnet switch at 6. This switch is mechanically connected to the switch
-2 by the rod 4, so that the pair open and close together.
-
-The control operates as follows: Starting with the motor at rest, the
-clock circuit is switched on, switches 2, 6 being open and 7 closed.
-At the first beat of the pendulum 2, 6 closes and the current, shunted
-across the loop containing 5, holds 2 closed until the motor has
-started and broken the clock circuit at the timer. The fly-wheel
-carries on until the pendulum again closes the power circuit via 2,
-6, and current stays on the motor until the timer has completed its
-revolution.
-
-This goes on as the motor speeds up, the periodic power supply being
-shortened as the timer breaks it earlier owing to the acceleration,
-until the motor comes to its steady speed at which the power is applied
-just long enough to maintain uniformity. If the motor for any cause
-tends to overspeed the cut-off is earlier, while slowing down produces
-a longer power-period bringing the speed back to normal. The power
-period is generally ¼ to ½ second. The power supplied to the motor
-is very small even in the example here shown, only 1 ampere at 110
-volts.
-
-[Illustration: FIG. 138.—Diagram of Gerrish Electric Control.]
-
-The actual proportion of a revolution during which current is supplied
-the motor is therefore rigorously determined by the clock pendulum,
-and the motor is selected so that its revolutions are exactly timed
-to this clock pendulum which has no work to do other than the circuit
-closing, and can hence be regulated to keep accurate time. The small
-fly-wheel (9), the weight of which is carefully adjusted with respect
-to the general amount of work to be done, attached to the motor shaft,
-effectively steadies its action during the process of government.
-This Gerrish type has been variously modified in detail to suit the
-instruments to which it has been applied, always following however the
-same fundamental principles.
-
-[Illustration: FIG. 139.—Gerrish Drive on 24 inch Reflector.]
-
-An admirable example of the application of this drive is shown in Fig.
-139, the 24 inch reflector at the Harvard Observatory. The mount is
-a massive open fork, and the motor drive is seen on the right of the
-mount. There are here two motors, ordinary fan motors in size. The
-right hand motor carries the fly-wheel and runs steadily on under the
-pendulum control. The other, connected to the same differential gear as
-the driving motor, serves merely for independent regulation and can be
-run in either direction by the observer to speed or slow the motion in
-R. A. These examples of clock drive are merely typical of those which
-have proved to be successful in use for various service, light and
-heavy. There are almost innumerable variations on clocks constructed on
-one or another of the general lines here indicated, so many variations
-in fact that one almost might say there are few driving clocks which
-are not in some degree special.
-
-The tendency at present is for large instruments very distinctly toward
-a motor-driven mechanism operating on the right ascension axis, and
-governed in one of a considerable variety of ways by an actual clock
-pendulum. For smaller instruments the old mechanical clock, often
-fitted with electric brake gear and now and then pendulum regulated, is
-capable of very excellent work.
-
-The principle of the spectroscope is rudimentarily simple, in the
-familiar decomposition of white light into rainbow colors by a prism.
-One gets the phenomena neatly by holding a narrow slit in a large piece
-of cardboard at arms length and looking at it through a prism held with
-its edge parallel to the slit. If the light were not white but of a
-mixture of definite colors each color present would be represented by
-a separate image of the slit instead of the images being merged into a
-continuous colored band.
-
-With the sun as source the continuous spectrum is crossed by the dark
-lines first mapped by Fraunhofer, each representing the absorption by
-a relatively cool exterior layer of some substance that at a higher
-temperature below gives a bright line in exactly the same position.
-
-The actual construction of the astronomical spectroscope varies greatly
-according to its use. In observations on the sun the distant slit is
-brought nearer for convenience by placing it in the focus of a small
-objective pointed toward the prisms (the collimator) and the spectrum
-is viewed by a telescope of moderate magnifying power to disclose more
-of detail. Also, since there is extremely bright light available, very
-great dispersion can be used, obtained by several or many prisms, so
-that the spectrum is both fairly wide, (the length of the slit) and
-extremely long.
-
-In trying to get the spectrum of a star the source is a point,
-equivalent to an extremely minute length of a very narrow slit.
-Therefore no actual slit is necessary and the chief trouble is to get
-the spectrum wide enough and bright enough to examine.
-
-The simplest form of stellar spectroscope and the one in most common
-use with small telescopes is the ocular spectroscope arranged much like
-Fig. 140. This fits into the eye tube of a telescope and the McClean
-form made by Browning of London consists of an ordinary casing with
-screw collar _B_, a cylindrical lens _C_, a direct vision prism _c_,
-_f_, _c_, and an eye-cap _A_.
-
-The draw tube is focussed on the star image as with any other ocular,
-and the light is delivered through _C_ to the prism face nearly
-parallel, and thence goes to the eye, after dispersion by the prism.
-This consists of a central prism, _f_, of large angle, made of
-extremely dense flint, to which are cemented a pair of prisms of light
-crown _c_, _c_, with their bases turned away from that of _f_.
-
-We have already seen that the dispersions of glasses vary very much
-more than their refractions so that with proper choice of materials and
-angles the refraction of _f_ is entirely compensated for some chosen
-part of the spectrum, while its dispersion quite overpowers that of the
-crown prisms and gives a fairly long available spectrum.
-
-The cylindrical lens _C_ merely serves to stretch out the tiny round
-star image into a short line thereby giving the resulting spectrum
-width enough to examine comfortably. The weak cylindrical lens is
-sometimes slipped over the eye end of the prisms to give the needed
-width of spectrum instead of putting it ahead of the prisms.
-
-A small instrument of this kind used with a telescope of 3 inches to 5
-inches aperture gives a fairly good view of the spectra of starts above
-second or third magnitude, the qualities of tolerably bright comets and
-nebulæ and so forth. The visibility of stellar spectra varies greatly
-according to their type, those with heavy broad bands being easy to
-observe, while for the same stellar magnitude spectra with many fine
-lines may be quite beyond examination. Nevertheless a little ocular
-spectroscope enables one to see many things well worth the trouble of
-observing.
-
-[Illustration: FIG. 140.—McClean Ocular Spectroscope.]
-
-With the larger instruments, say 6 or 8 inches, one can well take
-advantage of the greater light to use a spectroscope with a slit, which
-gives somewhat sharper definition and also an opportunity to measure
-the spectrum produced.
-
-An excellent type of such an instrument is that shown in Fig. 141,
-due to Professor Abbé. The construction is analogous to Fig. 140. The
-ocular is a Huyghenian one with the slit mechanism (controlled by a
-milled head) at A in the usual place of the diaphragm. The slit is
-therefore in the focus of the eye lens, which serves as collimating
-lens. Above is the direct vision system J with the usual prisms which
-are slightly adjustable laterally by the screw P and spring Q.
-
-At N is a tiny transparent scale of wave lengths illuminated by a faint
-light reflected from the mirror O, and in the focus of the little lens
-R, which transfers it by reflection from the front face of the prism
-to the eye, alongside the edge of the spectrum. One therefore sees the
-spectrum marked off by a bright line wave-length scale.
-
-[Illustration: FIG. 141.—Abbé Ocular Spectroscope.]
-
-The pivot K and clamp L enable the whole to be swung side-wise so that
-one can look through the widened slit, locate the star, close the slit
-accurately upon it and swing on the prisms. M is the clamp in position
-angle. Sometimes a comparison prism is added, together with suitable
-means for throwing in spectra of gases or metals alongside that of
-the star, though these refinements are more generally reserved for
-instruments of higher dispersion.
-
-To win the advantage of accurate centering of the star in the field
-gained by the swing-out of the spectroscope in Fig. 141 simple
-instruments like Fig. 140 are sometimes mounted with an ordinary ocular
-in a double nose-piece like that used for microscope objectives, so
-that either can be used at will.
-
-Any ordinary pocket spectroscope, with or without scale or a comparison
-prism over part of the slit, can in fact be fitted to an adapter and
-used with the star focussed on the slit and a cylindrical lens, if
-necessary, as an eye-cap.
-
-Such slit spectroscopes readily give the characteristics of stellar
-spectra and those of the brighter nebulæ or of comets. They enable one
-to identify the more typical lines and compare them with terrestrial
-sources, and save for solar work are about all the amateur observer
-finds use for.
-
-For serious research a good deal more of an instrument is required,
-with a large telescope to collect the light, and means for
-photographing the spectra for permanent record. The cumulative effect
-of prolonged exposures makes it possible easily to record spectra
-much too faint to see with the same aperture, and exposures are often
-extended to many hours.
-
-Spectroscopes for such use commonly employ dense flint prisms of about
-60° refracting angle and refractive index of about 1.65, one, two, or
-three of these being fitted to the instrument as occasion requires.
-A fine example by Brashear is shown in Fig. 142, arranged for visual
-work on the 24 inch Lowell refractor. Here A is the slit, B the prism
-box, C the observing telescope, D the micrometer ocular with electric
-lamp for illuminating the wires, and E the link motion that keeps the
-prism faces at equal angles with collimator and observing telescope
-when the angle between these is changed to observe different parts of
-the spectrum. This precaution is necessary to maintain the best of
-definition.
-
-When photographs are to be taken the observing telescope is unscrewed
-and a photographic lens and camera put in its place. If the brightness
-of the object permits, three prisms are installed, turning the beam
-180° into a camera braced to the same frame alongside the slit.
-
-For purely photographic work, too, the objective prism used by
-Fraunhofer for the earliest observation of stellar spectra is in wide
-use. It is a prism fitted in front of the objective with its refracting
-faces making equal angles with the telescope and the region to be
-observed, respectively. Its great advantages are small loss of light
-and the ability to photograph many spectra at once, for all the stars
-in the clear field of the instrument leave their images spread out into
-spectra upon the photographic plate.
-
-Figure 143 shows such an objective prism mounted in front of an
-astrographic objective. The prism is rotatable into any azimuth about
-the axis of the objective and by the scale i and clamping screw r can
-have its refracting face adjusted with respect to that axis to the
-best position for photographing any part of the spectrum. Such an
-arrangement is typical of those used for small instruments say from 3
-inches to 6 inches aperture.
-
-[Illustration: FIG. 142.—Typical Stellar Spectroscope.]
-
-For larger objectives the prism is usually of decidedly smaller angle,
-and, if the light warrants high dispersion, several prisms in tandem
-are used. The objective prism does its best work when applied to true
-photographic objectives of the portrait lens type which yield a fairly
-large field. It is by means of big instruments of such sort that the
-spectra for the magnificent Draper Catalogue have been secured by the
-Harvard Observatory, mostly at the Arequipa station. In photographing
-with the objective prism the spectra are commonly given the necessary
-width for convenient examination by changing just a trifle the rate of
-the driving clock so that there is a slight and gradual drift in R. A.
-The refracting edge of the prism being turned parallel to the diurnal
-motion this drift very gradually and uniformly widens the spectrum to
-the extent of a few minutes of arc during the whole exposure.
-
-When one comes to solar spectroscopy one meets an entirely different
-situation. In stellar work the difficulty is to get enough light, and
-the tendency is toward large objectives of relatively short focal
-length and spectroscopes of moderate dispersion. In solar studies there
-is ample light, and the main thing is to get an image big enough to be
-scrutinized in detail with very great dispersion.
-
-[Illustration: FIG. 143.—Simple Objective Prism.]
-
-Especially is this true in the study of the chromospheric flames
-that rim the solar disc and blaze over its surface. To examine these
-effectively the spectroscope should have immense dispersion with a
-minimum amount of stray light in the field to interfere with vision of
-delicate details.
-
-In using a spectroscope like Fig. 142, if one turned the slit toward
-the landscape, the instrument being removed from the telescope and the
-slit opened wide, he could plainly see its various features, refracted
-through the prism, and appearing in such color as corresponded to
-the part of the spectrum in the line of the observing telescope. In
-other words one sees refracted images quite distinctly in spite of the
-bending of the rays. With high dispersion the image seen is practically
-monochromatic.
-
-Now if one puts the spectroscope in place, brings the solar image
-tangent to the slit and then cautiously opens the slit, he sees the
-bright continuous spectrum of the sky close to the sun, plus any light
-of the particular color for which the observing telescope is set, which
-may proceed from the edge of the solar disc. Thus, if the setting is
-for the red line of hydrogen (C), one sees the hydrogen glow that plays
-in fiery pillars of cloud about the sun’s limb quite plainly through
-the opened slit, on a background of light streaming from the adjacent
-sky. To see most clearly one must use great dispersion to spread this
-background out into insignificance, must keep other stray light out of
-the field, and limit his view to the opened slit.
-
-[Illustration: FIG. 144.—Diagram of Evershed Solar Spectroscope.]
-
-To these ends early solar spectroscopes had many prisms in tandem,
-up to a dozen or so, kept in proper relation by complicated linkages
-analogous to the simple one shown in Fig. 142. Details can be found
-in almost any astronomical work of 40 years ago. They were highly
-effective in giving dispersion but neither improved the definition nor
-cut out light reflected back and forth from their many surfaces.
-
-Of late simpler constructions have come into use of which an excellent
-type is the spectroscope designed by Mr. Evershed and shown in diagram
-in Fig. 144. Here the path of the rays is from the slit through the
-collimator objective, then through a very powerful direct vision
-system, giving a dispersion of 30° through the visible spectrum, then
-by reflection from the mirror through a second such system, and thence
-to the observing telescope. The mirror is rotated to get various parts
-of the spectrum into view, and the micrometer screw that turns it gives
-means for making accurate measurement of wave lengths.
-
-There are but five reflecting surfaces in the prism system (for the
-cemented prism surfaces do not count for much) as against more than
-20 in one of the older instruments of similar power, and as in other
-direct vision systems the spectrum lines are substantially straight
-instead of being strongly curved as with multiple single prisms. The
-result is the light, compact, and powerful spectroscope shown complete
-in Fig. 145, equally well fitted for observing the sun’s prominences
-and the detailed spectrum from his surface.
-
-[Illustration: FIG. 145.—Evershed Solar Spectroscope.]
-
-In most of the solar spectroscopes made at the present time the prisms
-are replaced by a diffraction grating. The original gratings made by
-Fraunhofer were made of wire. Two parallel screws of extremely fine
-thread formed two opposite sides of a brass frame. A very fine wire was
-then wound over these screws, made fast by solder on one side of each,
-and then cut away on the other, so as to leave a grating of parallel
-wires with clear spaces between.
-
-Today the grating is generally ruled by an automatic ruling engine
-upon a polished plate of speculum metal. The diamond point carried by
-the engine cuts very smooth and fine parallel furrows, commonly from
-10,000 to 20,000 to the inch. The spaces between the furrows reflect
-brilliantly and produce diffraction spectra.[22]
-
- [22] For the principle of diffraction spectra see Baly, Spectroscopy;
- Kayser, Handbuch d. Specktroskoie or any of the larger textbooks of
- physics.
-
-When a grating is used instead of prisms the instrument is commonly
-set up as shown in Fig. 146. Here _A_ is the collimator with slit upon
-which the solar image light falls, _B_ is the observing telescope, and
-_C_ the grating set in a rotatable mount with a fine threaded tangent
-screw to bring any line accurately upon the cross wires of the ocular.
-
-[Illustration: FIG. 146.—Diagram of Grating Spectroscope.]
-
-The grating gives a series of spectra on each side of the slit,
-violet ends toward the slit, and with deviations proportional to 1,
-2, 3, 4, etc., times the wave length of the line considered. The
-spectra therefore overlap, the ultra violet of the second order being
-superimposed on the extreme red of the first order and so on. Colored
-screens over the slit or ocular are used to get the overlying spectra
-out of the way.
-
-The grating spectroscopes are very advantageous in furnishing a wide
-range of available dispersions, and in giving less stray light than
-a prism train of equal power. The spectra moreover are very nearly
-“normal,” _i.e._, the position of each line is proportional to its
-wave length instead of the blue being disproportionately long as in
-prismatic spectra.
-
-In examining solar prominences the widened slit of a grating
-spectroscope shows them foreshortened or stretched to an amount
-depending on the angular position of the grating, but the effect is
-easily reckoned.[23]
-
- [23] The effect on the observed height of a prominence is h = h′ sin
- c/sin t, where h is the real height, h′ the apparent height, c the
- angle made by the grating face with the collimator, and t that with
- the telescope (Fig. 146).
-
-If the slit is nearly closed one sees merely a thin line, irregularly
-bright according to the shape of the prominence; a shift of the slit
-with respect to the solar image shows a new irregular section of the
-prominence in the same monochromatic light.
-
-These simple phenomena form the basis of one of the most important
-instruments of solar study—the spectro-heliograph. This was devised
-almost simultaneously by G. E. Hale and M. Deslandres about 30 years
-ago, and enables photographs of the sun to be taken in monochromatic
-light, showing not only the prominences of the limb but glowing masses
-of gas scattered all over the surface.
-
-The principle of the instrument is very simple. The collimator of a
-powerful grating spectroscope is provided with a slit the full length
-of the solar diameter, arranged to slide smoothly on a ball-bearing
-carriage clear across the solar disc. Just in front of the photographic
-plate set in the focus of the camera lens is another narrow sliding
-slit, which, like a focal plane shutter, exposes strip after strip of
-the plate.
-
-The two slits are geared together by a system of levers or otherwise
-so that they move at exactly the same uniform rate of speed. Thus
-when the front slit is letting through a monochromatic section of
-a prominence on the sun’s limb the plate-slit is at an exactly
-corresponding position. When the front slit is exactly across the sun’s
-center so is the plate slit, at each element of movement exposing a
-line of the plate to the monochromatic image from the moving front
-slit. The grating can of course be turned to put any required line
-into action but it usually is set for the K line (calcium), which is
-photographically very brilliant and shows bright masses of floating
-vapor all over the sun’s surface.
-
-Figure 147 shows an early and simple type of Professor Hale’s
-instrument. Here A is the collimator with its sliding slit, B the
-photographic telescope with its corresponding slide and C the lever
-system which connects the slides in perfectly uniform alignment.
-The source of power is a very accurately regulated water pressure
-cylinder mounted parallel with the collimator. The result is a complete
-photograph of the sun taken in monochromatic light of exactly defined
-wave length and showing the precise distribution of the glowing vapor
-of the corresponding substance.
-
-Since the spectro-heliograph of Fig. 147, which shows the principle
-remarkably well, there have been made many modifications, in particular
-for adapting the scheme to the great horizontal and vertical fixed
-telescopes now in use. (For details of these see Cont. from the Solar
-Obs. Mt. Wilson, Nos. 3, 4, 23, and others). The chief difficulty
-always is to secure entirely smooth and uniform motion of the two
-moving elements.
-
-[Illustration: FIG. 147.—Hale’s Spectro-heliograph (Early Form).]
-
-So great and interesting a branch of astronomy is the study of variable
-stars that some form of photometer should be part of the equipment of
-every telescope in serious use for celestial observation. An immense
-amount of useful work has been done by Argelander’s systematic method
-of eye observation, but it is far from being precise enough to disclose
-many of the most important features of variability.
-
-The conventional way of reckoning by stellar magnitudes is conducive to
-loose measurements, since each magnitude of difference implies a light
-ratio of which the log is 0.4, _i.e._, each magnitude is 2.512 times
-brighter than the following one. As a result of this way of reckoning
-the light of a star of mag. 9.9 differs from one of mag. 10.0 not by
-one per cent but by about nine. Hence to grasp light variations of
-small order one must be able to measure far below 0.1^_m_.
-
-[Illustration: FIG. 148.-Double Image Stellar Photometer.]
-
-The ordinary laboratory photometer enables one to compare light sources
-of anywhere near similar color to a probable error of well under 0.1
-per cent, but it allows a comparison between sharply defined juxtaposed
-fields from the two illuminants, a condition much more favorable to
-precision than the comparison of two points of light, even if fairly
-near together.
-
-Stellar photometers may in principle be divided into three classes. (1)
-Those in which two actual stars are brought into the same field and
-compared by varying the light from one or both in a known degree. (2)
-Those which bring a real star into the field alongside an artificial
-star, and again bring the two to equality by a known variation,
-usually comparing two or more stars via the same artificial star;
-(3) those which measure the light of a star by a definite method of
-extinguishing it entirely or just to the verge of disappearance in a
-known progression. Of each class there are divers varieties. The type
-of the first class may be taken as the late Professor E. C. Pickering’s
-polarizing photometer. Its optical principle is shown in Fig. 148. Here
-the brightness of two neighboring objects is compared by polarizing
-at 90° apart the light received from each and reducing the resulting
-images to equality by an analyzing Nicol prism. The photometer is
-fully described, with, several other polarizing instruments, in H. A.
-Vol. II from which Fig. 148 is taken.
-
-A is a Nicol prism inserted in the ocular _B_, which revolves carrying
-with it a divided circle _C_ read against the index _D_. In the tube
-_E_ which fits the eye end of the telescope, is placed the double
-image quartz prism _F_ capable of sliding either way without rotation
-by pulling the cord _G_. With the objects to be compared in the same
-field, two images of each appear. By turning the analyzing Nicol the
-fainter image of the brighter can always be reduced to equality with
-the brighter image of the fainter, and the amount of rotation measures
-the required ratio of brightness.[24] This instrument works well for
-objects near enough to be in the same field of view. The distance
-between the images can be adjusted by sliding the prism _F_ back and
-forth, but the available range of view is limited to a small fraction
-of a degree in ordinary telescopes.
-
- [24] If A be the brightness of one object and B that of the other, α
- the reading of the index when one image disappears and β the reading
- when the two images are equal then A/B = tan²(α-β). There are
- four positions of the Nicol, 90° apart, for which equality can be
- established, and usually all are read and the mean taken. (H. A. II,
- 1.)
-
-The meridian photometer was designed to avoid this small scope. The
-photometric device is substantially the same as in Fig. 148. The
-objects compared are brought into the field by two exactly similar
-objectives placed at a small angle so that the images, after passing
-the double image prism, are substantially in coincidence. In front of
-each of the objectives is a mirror. The instrument points in the east
-and west line and the mirrors are at 45° with its axis. One brings
-Polaris into the field, the other by a motion of rotation about the
-telescope axis can bring any object in or close to the meridian into
-the field alongside Polaris. The images are then compared precisely
-as in the preceding instance.[25] There are suitable adjustments for
-bringing the images into the positions required.
-
- [25] For full description and method see H. A. Vol. 14, also Miss
- Furness’ admirable “Introduction to the Study of Variable Stars,” p.
- 122, et seq. Some modifications are described in H. A. Vol. 23. These
- direct comparison photometers give results subject to some annoying
- small corrections, but a vast amount of valuable work has been done
- with them in the Harvard Photometry.
-
-The various forms of photometer using an artificial star as
-intermediary in the comparison of real stars differ chiefly in the
-method of varying the light in a determinate measure. Rather the best
-known is the Zöllner instrument shown in diagram in Fig. 149. Here
-_A_ is the eye end of the main telescope tube. Across it at an angle
-of 45° is thrown a piece of plane parallel glass _B_ which serves to
-reflect to the focus the beam from down the side tube, _C_, forming the
-artificial star.
-
-[Illustration: FIG. 149.—Zöllner Photometer Diagram.]
-
-At the end of this tube is a small hole or more often a diaphragm
-perforated with several very small holes any of which can be brought
-into the axis of the tube. Beyond at _D_, is the source of light,
-originally a lamp flame, now generally a small incandescent lamp, with
-a ground glass disc or surface uniformly to diffuse the light.
-
-Within the tube _C_ lie three Nicol prisms _n_, _n__{1}, _n__{2}.
-Of these _n_, is fixed with respect to the mirror B and forms the
-analyser, which _n__{1} and _n__{2} turn together forming the
-polarizing system. Between _n_1_ and _n_2_ is a quartz plate _e_ cut
-perpendicular to the crystal axis. The color of the light transmitted
-by such a plate in polarized light varies through a wide range.
-By turning the Nicol _n_2_ therefore, the color of the beam which
-forms the artificial star can be made to match the real star under
-examination, and then by turning the whole system _n_2_, _E_, _n_1_,
-reading the rotation on the divided circle at _F_, the real star can be
-matched in intensity by the artificial one.
-
-[Illustration: FIG. 150.—Wedge Photometer.]
-
-This is viewed via the lens _G_ and two tiny points of light appear
-in the field of the ocular due respectively to reflection from the
-front and back of the mirror _B_, the latter slightly fainter than
-the former. Alongside or between these the real star image can be
-brought for a comparison, and by turning the polarizer through an angle
-α the images can be equalized with the real image. Then a similar
-comparison is made with a reference star. If A be the brightness of the
-former and B of the latter then
-
-A/B = sin²α/sin²ββ
-
-The Zöllner photometer was at first set up as an alt-azimuth instrument
-with a small objective and rotation in altitude about the axis _C_.
-Since the general use of electric lamps instead of the inconvenient
-flame it is often fitted to the eye end of an equatorial.
-
-Another very useful instrument is the modern wedge photometer, closely
-resembling the Zöllner in some respects but with a very different
-method of varying the light; devised by the late Professor E. C.
-Pickering. It is shown somewhat in diagram in Fig. 150. Here as before
-O is the eye end of the tube, B the plane parallel reflector, C the
-side tube, L the source of light D the diaphragm and A the lens forming
-the artificial star by projecting the hole in the diaphragm. In actual
-practice the diameter of such hole is 1/100 inch or less.
-
-[Illustration: FIG. 151.—Simple Polarizing Photometer.]
-
-The light varying device W is a “photographic wedge” set in a frame
-which is graduated on the edge and moved in front of the aperture by a
-rack and pinion at R. There are beside colored and shade glasses for
-use as occasion requires. The “photographic wedge” is merely a strip
-of fine grained photographic plate given an evenly graduated exposure
-from end to end, developed, and sealed under a cover glass. Its
-absorption is permanent, non-selective as to color, and it can be made
-to shade off from a barely perceptible density to any required opacity.
-Sometimes a wedge of neutral tinted glass is used in its stead.
-
-Before using such a “wedge photometer” the wedge must be accurately
-calibrated by observation of real or artificial stars of known
-difference in brightness. This is a task demanding much care and is
-well described, together with the whole instrument by Parkhurst (Ap.
-J. 13, 249). The great difficulty with all instruments of this general
-type is the formation of an artificial star the image of which shall
-very closely resemble the image of the real star in appearance and
-color.
-
-Obviously either the real or artificial star, or both, may be varied
-in intensity by wedge or Nicols, and a very serviceable modification
-of the Zöllner instrument, with this in mind was recently described by
-Shook (Pop. Ast. 27, 595) and is shown in diagram in Fig. 151. Here A
-is the tube which fits the ordinary eyepiece sleeve. E is a side tube
-into which is fitted the extension D with a fitting H at its outer
-end into which sets the lamp tube G. This carries on a base plug F a
-small flash light bulb run by a couple of dry cells. At O is placed
-a little brass diaphragm perforated with a minute hole. Between this
-and the lamp is a disc of diffusing glass or paper. A Nicol prism is
-set a little ahead of O, and a lens L focusses the perforation at the
-principal focus of the telescope after reflection from the diagonal
-glass M, as in the preceding examples. I is an ordinary eyepiece over
-which is a rotatable Nicol N with a position circle K. At P is a third
-Nicol in the path of the rays from the real star, thereby increasing
-the convenient range of the instrument. The original paper gives the
-details of construction as well as the methods of working. Obviously
-the same general arrangement could be used for a wedge photometer using
-the wedge on either real or artificial star or both.
-
-The third type of visual photometer depends on reducing the light of
-the star observed until it just disappears. This plan was extensively
-employed by Professor Pritchard of Oxford some 40 years ago. He used
-a sliding wedge of dark glass, carefully calibrated, and compared two
-stars by noting the point on the wedge at which each was extinguished.
-A photographic wedge may be used in exactly the same way.
-
-Another device to the same end depends on reducing the aperture of the
-telescope by a “cat’s eye,” an iris diaphragm, or similar means until
-the star is no longer visible or just disappearing. The great objection
-to such methods is the extremely variable sensitivity of the eye under
-varying stimulus of light.
-
-The most that can be said for the extinction photometer is that in
-skillful and experienced hands like Pritchard’s it has sometimes given
-much more consistent readings than would be expected. It is now and
-then very convenient for quick approximation but by no courtesy can
-it be considered an instrument of precision either in astronomical or
-other photometry.[26]
-
- [26] The general order of precision attained by astronomical
- photometers is shown in the discovery, photographically, by
- Hertzsprung in 1911, that Polaris, used as a standard magnitude for
- many years, is actually a variable. Its period is very near to four
- days, its photographic amplitude 0.17 and its visual amplitude about
- 0.1, _i.e._, a variation of ± 5 per cent in the light was submerged in
- the observational uncertainties, although once known it was traced out
- in the accumulated data without great difficulty.
-
-The photometer question should not be closed without referring the
-reader to the methods of physical photometry as developed by Stebbins,
-Guthnick and others. The first of these depends on the use of the
-selenium cell in which the electrical resistance falls on exposure
-of the selenium to light. The device is not one adapted to casual
-use, and requires very careful nursing to give the best results, but
-these are of an order of precision beyond anything yet reached with an
-astronomical visual photometer. Settings come down to variations of
-something like 2 per cent, and variations in stellar light entirely
-escaping previous methods become obvious.
-
-The photoelectric cell depends on the lowering of the apparent electric
-resistance of a layer of rarified inert gas between a platinum grid and
-an electrode of metallic potassium or other alkali metal when light
-falls on that electrode. The rate of transmission of electricity is
-very exactly proportional to the illumination, and can be best measured
-by a very sensitive electrometer. The results are extraordinarily
-consistent, and the theoretical “probable error” is very small, though
-here, as elsewhere, “probable error” is a rather meaningless term
-apt to lead to a false presumption of exactness. Again the apparatus
-is somewhat intricate and delicate, but gives a precision of working
-if anything a little better than that of the selenium cell, quite
-certainly below 1 per cent.
-
-Neither instrument constitutes an attachment to the ordinary
-telescope of modest size which can be successfully used for ordinary
-photometry, and both require reduction of results to the basis
-of visual effect.[27] But both offer great promise in detecting
-minute variations of light and have done admirable work. For a good
-fundamental description of the selenium cell photometer see Stebbins,
-Ap. J. =32=, 185 and for the photoelectric method see Guthnick A. N.
-=196=, 357 also A. F. and F. A. Lindemann, M. N. =39=, 343. The volume
-by Miss Furness already referred to gives some interesting details of
-both.
-
- [27] Such apparatus is essentially appurtenant to large instruments
- only, say of not less than 12″ aperture and preferably much more. The
- eye is enormously more sensitive as a detector of radiant energy than
- any device of human contrivance, and thus small telescopes can be well
- used for visual photometry, the bigger instruments having then merely
- the advantage of reaching fainter stars.
-
-
-
-
-CHAPTER IX
-
-THE CARE AND TESTING OF TELESCOPES
-
-
-A word at the start concerning the choice and purchase of telescopes.
-The question of refractors vs. reflectors has been already considered.
-The outcome of the case depends on how much and how often you are
-likely to use the instrument, and just what you want it for. For casual
-observations and occasional use—all that most busy buyers of telescopes
-can expect—the refractor has a decided advantage in convenience. If
-one has leisure for frequent observations, and particularly if he can
-give his telescope a permanent mount, and is going in for serious work,
-he will do well not to dismiss the idea of a reflector without due
-deliberation.
-
-In any case it is good policy to procure an instrument from one of
-the best makers. And if you do not buy directly of the actual maker
-it is best to deal with his accredited agents. In other words avoid
-telescopes casually picked up in the optical trade unless you chance to
-have facilities for thorough testing under competent guidance before
-purchase. No better telescopes are made than can be had from the best
-American makers. A few British and German makers are quite in the same
-class. So few high grade French telescopes reach this country as to
-cause a rather common, but actually unjust,[28] belief that there are
-none.
-
- [28] E. g., the beautiful astrographic and other objectives turned out
- by the brothers Henry.
-
-If economy must be enforced it is much wiser to try to pick up a used
-instrument of first class manufacture than to chance a new one at a
-low price. Now and then a maker of very ordinary repute may turn out
-a good instrument, but the fact is one to be proved—not assumed. Age
-and use do not seriously deteriorate a telescope if it has been given
-proper care. Some of Fraunhofer’s are still doing good service after a
-century, and occasionally an instrument from one of the great makers
-comes into the market at a real bargain. It may drift back to the maker
-for resale, or turn up at any optician’s shop, and in any case is
-better worth looking at than an equally cheap new telescope.
-
-The condition of the tube and stand cuts little figure if they are
-mechanically in good shape. Most of the older high grade instruments
-were of brass, beautifully finished and lacquered, and nothing looks
-worse after hard usage. It is essential that the fitting of the parts
-should be accurate and that the focussing rack should work with the
-utmost smoothness. A fault just here, however, can be remedied at
-small cost. The mount, whatever its character, should be likewise
-smooth working and without a trace of shakiness, unless one figures on
-throwing it away.
-
-As to the objective, it demands very careful examination before a
-real test of its optical qualities. The objective with its cell
-should be taken out and closely scrutinized in a strong light after
-the superficial dust has been removed with a camel’s hair brush or
-by wiping very gently with the soft Japanese “lens paper” used by
-opticians.
-
-One is likely to find plenty to look at; spots, finger marks, obvious
-scratches, and what is worse a network of superficial scratches, or a
-surface with patches looking like very fine pitting. These last two
-defects imply the need of repolishing the affected surface, which means
-also more or less refiguring. Ordinary brownish spots and finger marks
-can usually be removed with little trouble.
-
-The layman, so to speak, is often warned never to remove the cell from
-a telescope but he might as well learn the simpler adjustments first as
-last. In taking off a cell the main thing is to see what one is about
-and to proceed in an orderly manner. If the whole cell unscrews, as
-often is the case in small instruments, the only precaution required is
-to put a pencil mark on the cell and its seat so that it can be screwed
-back to where it started.
-
-If as is more usual the cell fits on with three pairs of screws, one of
-each pair will form an abutment against which its mate pulls the cell.
-A pencil mark locating the position of the head of each of the pulling
-screws enables one to back them out and replace them without shifting
-the cell.
-
-The first inspection will generally tell whether the objective is
-worth further trouble or not. If all surfaces save the front are in
-good condition it may pay to send the objective to the maker for
-repolishing. If more than one surface is in bad shape reworking hardly
-pays unless the lens can be had for a nominal figure. In buying a used
-instrument from its original source these precautions are needless
-as the maker can be trusted to stand back of his own and to put it in
-first class condition.
-
-However, granted that the objective stands well the inspection for
-superficial defects, it should then be given a real test for figure
-and color correction, bearing in mind that objectives, even from first
-class makers, may now and then show slightly faulty corrections, while
-those from comparatively unknown sources may now and then turn out
-well. In this matter of necessary testing old and new glasses are quite
-on all fours save that one may safely trust the maker with a well
-earned reputation to make right any imperfections. Cleansing other than
-dusting off and cautiously wiping with damp and then dry lens paper
-requires removal of the lenses from their cell which demands real care.
-
-With a promising looking objective, old or new, the first test to be
-applied is the artificial star—artificial rather than natural since
-the former stays put and can be used by day or by night. For day use
-the “star” is merely the bright reflection of the sun from a sharply
-curved surface—the shoulder of a small round bottle, a spherical flask
-silvered on the inside, a small silvered ball such as is used for
-Christmas tree decoration, a bicycle ball, or a glass “alley” dear to
-the heart of the small boy.
-
-The object, whatever it is, should be set up in the sun against a dark
-background distant say 40 or 50 times the focal length of the objective
-to be tested. The writer rather likes a silvered ball cemented to a
-big sheet of black cardboard. At night a pin hole say 1/32 inch or
-less in diameter through cardboard or better, tinfoil, with a flame,
-or better a gas filled incandescent lamp behind it, answers well. The
-latter requires rather careful adjustment that the projected area of
-the closely coiled little filament may properly fill the pinhole just
-in front of it.
-
-Now if one sets up the telescope and focusses it approximately with a
-low power the star can be accurately centered in the field. Then if
-the eyepiece is removed, the tube racked in a bit, and the eye brought
-into the focus of the objective, one can inspect the objective for
-striæ. If these are absent the field will be uniformly bright all
-over. Not infrequently however one will see a field like Fig. 152 or
-Fig. 153. The former is the appearance of a 4 inch objective that the
-author recently got his eye upon. The latter shows typical striæ of
-the ordinary sort. An objective of glass as bad as shown in Fig. 152
-gives no hope of astronomical usefulness, and should be relegated to
-the porch of a seashore cottage. Figure 153 may represent a condition
-practically harmless though undesirable.
-
-The next step is a really critical examination of the focal image.
-Using a moderately high power ocular, magnifying say 50 to the inch of
-aperture, the star should be brought to the sharpest focus possible
-and the image closely examined. If the objective is good and in
-adjustment this image should be a very small spot of light, perfectly
-round, softening very slightly in its brilliancy toward the edge,
-and surrounded by two or three thin, sharp, rings of light, exactly
-circular and with well defined dark spaces separating them.
-
-[Illustration: FIG. 152.—A Bad Case of Striæ.]
-
-[Illustration: FIG. 153.—Ordinary Striæ.]
-
-Often from the trembling of the air the rings will seem shaky and
-broken, but still well centered on the star-disc. The general
-appearance is that shown in Fig. 154.[29]
-
- [29] This and several of the subsequent figures are taken from quite
- the best account of testing objectives: “On the Adjustment and Testing
- of Telescope Objectives.” T. Cooke & Sons, York, 1891, a little
- brochure unhappily long since out of print. A new edition is just now,
- 1922, announced.
-
-[Illustration: FIG. 154.—A First Class Star Image.]
-
-Instead, several very different appearances may turn up. First, the
-bright diffraction rings may be visible only on one side of the central
-disc, which may itself be drawn out in the same direction. Second, the
-best image obtainable may be fairly sharp but angular or irregular
-instead of round or oval and perhaps with a hazy flare on one side.
-Third, it may be impossible to get a really sharp focus anywhere, the
-image being a mere blob of light with nothing definite about it.
-
-One should be very sure that the eyepiece is clean and without fault
-before proceeding further. As to the first point a bit of lens paper
-made into a tiny swab on a sliver of soft wood will be of service, and
-the surfaces should be inspected with a pocket lens in a good light to
-make sure that the cleaning has been thorough. Turning the ocular round
-will show whether any apparent defects of the image turn with it.
-
-In the first case mentioned the next step is to rack the ocular gently
-out when the star image will expand into a more or less concentric
-series of bright interference rings separated by dark spaces, half a
-dozen or so resulting from a rather small movement out of focus. If
-these rings are out of round and eccentric like Fig. 155 one has a
-clear case of failure of the objective to be square with the tube, so
-that the ocular looks at the image askew.
-
-[Illustration: FIG. 155.—Effect of Objective Askew.]
-
-In the ordinary forms of objective this means that the side of the
-objective toward the brighter and less expanded part of the ring system
-is too near the ocular. This can be remedied by pushing that side
-of the objective outwards a trifle. Easing off the pulling screw on
-that side and slightly tightening the abutment screw makes the needed
-correction, which can be lessened if over done at the first trial,
-until the ring system is accurately centered. It is a rather fussy job
-but not at all difficult if one remembers to proceed cautiously and to
-use the screw driver gently.
-
-[Illustration: FIG. 156.—Effect of Flaws in Objective.]
-
-In the second case, racking out the ocular a little gives a ring
-system which exaggerates just the defects of the image. The faults may
-be due to mechanical strain of the objective in its cell, which is
-easily cured, or to strains or flaws in the glass itself, which are
-irremediable. Therefore one should, with the plane of the objective
-horizontal, loosen the retaining ring that holds the lenses, without
-disturbing them, and then set it back in gentle contact and try the out
-of focus rings once more. If there is no marked improvement the fault
-lies in the glass and no more time should be wasted on that particular
-objective. Fig. 156 is a typical example of this fault.
-
-In dealing with case three it is well to give the lens a chance by
-relieving it of any such mechanical strains, for now and then they will
-apparently utterly ruin the definition, but the prognosis is very bad
-unless the objective has been most brutally mishandled.
-
-In any case failure to give a sharply defined focus in a very definite
-plane is a warning that the lens (or mirror) is rather bad. In testing
-a reflector some pains must be taken at the start with both the main
-and the secondary mirror. Using an artificial star as before, one
-should focus and look sharply to the symmetry of the image, taking
-care to leave the instrument in observing position and screened from
-the sun for an hour or two before testing. Reflectors are much more
-sensitive to temperature than refractors and take longer to settle
-down to stability of figure. With a well mounted telescope of either
-sort a star at fair altitude on a fine night gives even better testing
-conditions than an artificial star, (Polaris is good in northern
-latitudes) but one may have a long wait.
-
-If the reflector is of good figure and well adjusted, the star image,
-in focus or out, has quite the same appearance as in a refractor except
-that with a bright star in focus one sees a thin sharp cross of light
-centered on the image, rather faint but perfectly distinct. This is
-due to the diffraction effect of the four thin strips that support the
-small mirror, and fades as the star is put out of focus.
-
-The rings then appear as usual, but also a black disc due to the
-shadowing of the small mirror. Fig. 157 shows the extra-focal image of
-a real or artificial star when the mirror is well centered, and the
-star in the middle of the field. There only are the rings round and
-concentric with the mirror spot. The rings go out of round and the spot
-out of center for very small departure from the middle of the field
-when the mirror is of large relative aperture—F/5 or F/6.
-
-[Illustration: FIG. 157.—Extra-focal Image from Reflector.]
-
-If the star image shows flare or oval out-of-focus rings when central
-of the field, one or both mirrors probably need adjustment. Before
-laying the trouble to imperfect figure, the mirrors should be adjusted,
-the small one first as the most likely source of trouble. The side of
-the mirror toward which the flare or the expanded side of the ring
-system projects should be slightly pushed away from the ocular. (Note
-that owing to the reflection this movement is the reverse of that
-required with a refractor.)
-
-If the lack of symmetry persists one may as well get down to first
-principles and center the mirrors at once. Perhaps the easiest plan is
-to prepare a disc of white cardboard exactly the size of the mirror
-with concentric circles laid out upon it and an eighth inch hole in the
-center. Taking out the ocular and putting a half inch stop in its place
-one can stand back, lining up the stop with the draw tube, and see
-whether the small mirror looks perfectly round and is concentric with
-the reflected circles. If not, a touch of the adjusting screws will be
-needed.
-
-Then with a fine pointed brush dot the center of the mirror itself
-through the hole, with white paint. Then, removing the card, one will
-see this dot accurately centered in the small mirror if the large one
-is in adjustment, and it remains as a permanent reference point. If
-the dot be eccentric it can be treated as before, but by the adjusting
-screws of the large mirror.
-
-The final adjustment can then be made by getting a slightly extra-focal
-star image fairly in the center of the field with a rather high power
-and making the system concentric as before described. This sounds a
-bit complicated but it really is not. If the large mirror is not in
-place, its counter cell may well be centered and levelled by help of a
-plumb line from the center of the small mirror and a steel square, as a
-starting point, the small mirror having been centered as nearly as may
-be by measurement.[30]
-
- [30] Sometimes with ever so careful centering the ring system in the
- middle of the field is still eccentric with respect to the small
- mirror, showing that the axis of the parabola is not perpendicular to
- the general face of the mirror. This can usually be remedied by the
- adjusting screws of the main mirror as described, but now and then
- it is necessary actually to move over the small mirror into the real
- optical axis. Draper (loc. cit.) gives some experiences of this sort.
-
-So much for the general adjustment of the objective or mirror. Its
-actual quality is shown only on careful examination.
-
-As a starting point one may take the extra-focal system of rings given
-by an objective or mirror after proper centering. If the spherical
-aberration has thoroughly removed the appearance of the rings when
-expanded so that six or eight are visible should be like Fig. 158. The
-center should be a sharply defined bright point and surrounding it, and
-exactly concentric, should be the interference rings, truly circular
-and gradually increasing in intensity outwards, the last being very
-noticeably the strongest.
-
-One can best make the test when looking through a yellow glass screen
-which removes the somewhat confusing flare due to imperfect achromatism
-and makes the appearances inside and outside focus closely similar.
-Just inside or outside of focus the appearance should be that of Fig.
-159 for a perfectly corrected objective or mirror.
-
-[Illustration: FIG. 158.—Correct Extra-focal Image.]
-
-Sometimes an objective will be found in which one edge of the focussed
-star image is notably red and the opposite one tinted with greenish or
-bluish, showing unsymmetrical coloring, still more obvious when the
-image is put a little out of focus. This means that the optical centers
-of crown and flint are out of line from careless edging of the lenses
-or very bad fitting. The case is bad enough to justify trying the only
-remedy available outside the optician’s workshop—rotating one lens upon
-the other and thus trying the pair in different relative azimuths.
-
-The initial positions of the pair must be marked plainly, care must be
-taken not to displace the spacers 120° apart often found at the edges
-of the lenses, and the various positions must be tried in an orderly
-manner. One not infrequently finds a position in which the fault is
-negligible or disappears altogether, which point should be at once
-marked for reference.
-
-[Illustration: FIG. 159.—Correct Image Just Out of Focus.]
-
-In case there is uncorrected spherical aberration there is departure
-from regular gradation of brightness in the rings. If there is a “short
-edge,” _i.e._, + spherical aberration, so that rays from the outer
-zone come to a focus too short, the edge ring will look too strong
-within focus, and the inner rings relatively weak; with this appearance
-reversed outside focus. A “long edge” _i.e._, - spherical aberration,
-shows the opposite condition, edge rings too strong outside focus and
-too weak within. Both are rather common faults. The “long edge” effect
-is shown in Figs. 160 and 161, as taken quite close to focus.
-
-It takes a rather sharp eye and considerable experience to detect small
-amounts of spherical aberration; perhaps the best way of judging is
-in quickly passing from just inside to just outside focus and back
-again, using a yellow screen and watching very closely for variations
-in brightness. Truth to tell a small amount of residual aberration,
-like that of Fig. 160, is not a serious matter as regards actual
-performance—it hurts the telescopist’s feelings much more than the
-quality of his images.
-
-[Illustration: FIG. 160.—Spherical Aberration Just Inside Focus.]
-
-[Illustration: FIG. 161.—Spherical Aberration Just Outside Focus.]
-
-A much graver fault is zonal aberration, where some intermediate
-zone of objective or mirror comes to a focus too long or too short,
-generally damaging the definition rather seriously, depending on the
-amount of variation in focus of the faulty zone. A typical case is
-shown in Fig. 162 taken within focus. Here two zones are abnormally
-strong showing, just as in the case of simple spherical aberration,
-too short focus. Outside of focus the intensities would change places,
-the outer and midway zones and center being heavy, and the strong
-zones of Fig. 162 weak. These zonal aberrations are easily detected
-and are rather common both in objectives and mirrors, though rarely as
-conspicuous as in Fig. 162.
-
-Another failing is the appearance of astigmatism, which, broadly, is
-due to a refracting or reflecting surface which is not a surface of
-revolution and therefore behaves differently for rays incident in
-different planes around its optical axis. In its commonest form the
-surface reflects or refracts more strongly along one plane than along
-another at right angles to it. Hence the two have different foci and
-there is no point focus at all, but two line foci at right angles.
-Figs. 163 and 164 illustrate this fault, the former being taken inside
-and the latter outside focus, under fairly high power. If a star image
-is oval and the major axis of this oval has turned through 90° when one
-passes to the other side of focus, astigmatism is somewhere present.
-
-As more than half of humanity is astigmatic, through fault of the eye,
-one should twist the axis of the eyes some 90° around the axis of the
-telescope and look again. If the axis of the oval has turned with the
-eyes a visit to the oculist is in order. If not, it is worth while
-rotating the ocular. If the oval does not turn with it that particular
-telescope requires reworking before it can be of much use.
-
-This astigmatism due to fault of figure must not be confused with the
-astigmatic difference of the image surfaces referred to in Chapter IV
-which is zero on the axis and not of material importance in ordinary
-telescopes. Astigmatism of figure on the contrary is bad everywhere and
-always. It should be especially looked out for in reflecting surfaces,
-curved or plane, since it is a common result of flexure.
-
-Passing on now from these simple tests for figure, chromatic aberration
-has to be examined. Nothing is better than an artificial star formed
-by the sun in daylight, for the preliminary investigation. At night
-Polaris is advantageous for this as for other tests.
-
-[Illustration: FIG. 162.—A Case of Zonal Aberration.]
-
-[Illustration: FIG. 163.—Astigmatism Inside Focus.]
-
-[Illustration: FIG. 164.—Astigmatism Outside Focus.]
-
-The achromatization curves, Fig. 163, really tell the whole story
-of what is to be seen. When the telescope is carefully focussed for
-the bright part of the spectrum, getting the sharpest star image
-attainable, the central disc, small and clean, should be yellowish
-white, seen under a power of 60 or 70 per inch of aperture.
-
-But the red and blue rays have a longer focus and hence rim the image
-with a narrow purplish circle varying slightly in hue according to the
-character of the achromatization. Pushing the ocular a little inside,
-focus, the red somewhat overbalances the blue and the purple shades
-toward the red. Pulling out the ocular very slightly one brings the
-deep red into focus as a minute central red point, just as the image
-begins to expand a little. Further outside focus a bluish or purplish
-flare fills the center of the field, while around it lies a greenish
-circle due to the rays from the middle of the secondary spectrum
-expanding from their shorter focus.
-
-In an under-corrected objective this red point is brighter and the
-fringe about the image, focussed or within focus, is conspicuously
-reddish. Heavy overcorrection gives a strong bluish fringe and the red
-point is dull or absent. With a low power ocular, unless it be given a
-color correction of its own, any properly corrected objective will seem
-under-corrected as already explained.
-
-The color correction can also be well examined by using an ocular
-spectroscope like Fig. 140, with the cylindrical lens removed.
-Examining the focussed star image thus, the spectrum is a narrow line
-for the middle color of the secondary spectrum, widening equally
-at F and B, and expanding into a sort of brush at the violet end.
-Conversely, when moved outside focus until the width is reduced to a
-narrow line at F and B, the widening toward the yellow and green shows
-very clearly the nature and extent of the secondary spectrum. In this
-way too, the actual foci for the several colors can easily be measured.
-
-The exact nature of the color correction is somewhat a matter of taste
-and of the uses for which the telescope is designed, but most observers
-agree in the desirability of the B-F correction commonly used as best
-balancing the errors of eye and ocular. With reflectors, achromatic or
-even over-corrected oculars are desirable. The phenomena in testing a
-telescope for color vary with the class of star observed—the solar type
-is a good average. Trying a telescope on α Lyræ emphasizes unduly
-the blue phases, while α Orionis would overdo the red.
-
-The simple tests on star discs in and out of focus here described are
-ample for all ordinary purposes, and a glass which passes them well is
-beyond question an admirably figured one. The tests are not however
-quantitative, and it takes an experienced eye to pick out quickly minor
-errors, which are somewhat irregular. One sometimes finds the ring
-system excellent but a sort of haze in the field, making the contrasts
-poor—bad polish or dirt, but figure good.
-
-A test found very useful by constructors or those with laboratory
-facilities is the knife edge test, worked out chiefly by Foucault and
-widely used in examining specula. It consists in principle of setting
-up the mirror so as to bring the rays to the sharpest possible focus.
-For instance in a spherical mirror a lamp shining through a pin hole is
-placed in the centre of curvature, and the reflected image is brought
-just alongside it where it can be inspected by eye or eyepiece. In
-Fig. 165 all the rays which emanate from the pinhole _b_ and fall on
-the mirror a are brought quite exactly to focus at _c_. The eye placed
-close to _c_ will see, if the mirror surface is perfect, a uniform disc
-of light from the mirror.
-
-[Illustration: FIG. 165.—The Principle of the Foucault Test.]
-
-If now a knife edge like _d_, say a safety razor blade, be very
-gradually pushed through the focus the light will be cut off in a
-perfectly uniform manner—no zone or local spot going first. If some
-error in the surface at any point causes the reflected ray to miss the
-focus and cross ahead of or behind it as in the ray _bef_, then the
-knife edge will catch it first or last as the case may be, and the spot
-_e_ will be first darkened or remain bright after the light elsewhere
-is extinguished.
-
-[Illustration: FIG. 166.—Foucault Test of Parabolic Mirror.]
-
-One may thus explore the surface piecemeal and detect not only zones
-but slight variations in the same zone with great precision. In case of
-a parabolic mirror as in Fig. 166 the test is made at the focus by aid
-of the auxiliary plane mirror, and a diagonal as shown, the pinhole and
-knife edge being arranged quite as before. A very good description of
-the practical use of the knife edge test may be found in the papers of
-Dr. Draper and Mr. Ritchey already cited.
-
-It is also applied to refractors, in which case monochromatic light had
-better be used, and enables the experimenter to detect even the almost
-infinitesimal markings sometimes left by the polishing tool, to say
-nothing of slight variations in local figure which are continually lost
-in the general illumination about the field when one uses the star test
-in the ordinary manner.
-
-The set-up for the knife edge experiments should be very steady and
-smooth working to secure precise results, and it therefore is not
-generally used save in the technique of figuring mirrors, where it is
-invaluable. With micrometer motions on the knife edge, crosswise and
-longitudinally, one can make a very exact diagnosis of errors of figure
-or flexure.
-
-A still more delicate method of examining the perfection of figuring
-is found in the Hartmann test. (Zeit. fur Instk., 1904, 1909). This is
-essentially a photographic test, comparing the effect of the individual
-zones of the objective inside and outside of focus. Not only are the
-effects of the zones compared but also the effects of different parts
-of the same zone, so that any lack of symmetry in performance can be at
-once found and measured.
-
-The Hartmann test is shown diagrammatically in Fig. 167. The objective
-is set up for observing a natural or artificial star. Just in front
-of it is placed an opaque screen perforated with holes, as shown in
-section by Fig. 167, where A is the perforated screen. The diameters
-of the holes are about 1/20 the diameter of the objective as the test
-is generally applied, and there are usually four holes 90° apart for
-each zone. And such holes are not all in one line, but are distributed
-symmetrically about the screen, care being taken that each zone shall
-be represented by holes separated radially and also tangentially,
-corresponding to the pairs of elements in the two astigmatic image
-surfaces, an arrangement which enables the astigmatism as well as
-figure to be investigated.
-
-[Illustration: FIG. 167.—The Principle of the Hartmann Test.]
-
-The arrangement of holes actually found useful is shown in Hartmann’s
-original papers, and also in a very important paper by Plaskett (Ap.
-J. _25_ 195) which contains the best account in English of Hartmann’s
-methods and their application. Now each hole in the screen transmits
-a pencil of light through the objective at the corresponding point,
-and each pencil comes to a focus and then diverges, the foci being
-distributed somewhere in the vicinity of what one may regard as the
-principal focus, _B_. For instance in Fig. 167 are shown five pairs
-of apertures _a_, _a′_, _b_, _b′_, etc., in five different zones.
-Now if a photographic plate be exposed a few inches inside focus as
-at C each pencil from an aperture in the screen will be represented
-by a dot on the photograph, at such distance from the axis and from
-the corresponding dot on the other side of the axis as the respective
-inclinations of the pencils of light may determine.
-
-Similarly a plate exposed at approximately equal distance on the other
-side of the general focus, as at _D_, will show a pattern of dots due
-to the distribution of the several rays at a point beyond focus. Now
-if all the pencils from the several apertures met at a common focus in
-_B_, the two patterns on the plates _C_ and _D_ would be exactly alike
-and for equal distance away from focus of exactly the same size. In
-general the patterns will not exactly correspond, and the differences
-measured with the micrometer show just how much any ray in question has
-departed from meeting at an exact common focus with its fellows.
-
-For instance in the cut it will be observed that the rays _e_ and _a′_
-focus barely beyond _C_ and by the time they reach _D_ are well spread
-apart. The relative distance of the dots upon these corresponding
-plates, with the distance between the plates, shows exactly at what
-point between _C_ and _D_ these particular rays actually did cross and
-come to a focus.
-
-Determining this is merely a matter of measuring up similar triangles,
-for the path of the rays is straight. Similarly inspection will show
-that the rays _d_ and _d′_ meet a little short of _B_, and measurement
-of their respective records on the plates _C_ and _D_ would show the
-existence of a zone intermediate in focus between the focus of _e,e′_
-and the general focus at _B_. The exact departure of this zone from
-correct focus can therefore be at once measured.
-
-A little further examination discloses the fact that the outer zone
-represented by the rays _a,b_, and _a′,b′_ has not quite the same focus
-at the two extremities of the same diameter of the objective. In other
-words the lens is a little bit flatter at one end of this diameter
-than it is at the other, so that the rays here have considerably
-longer focus than they should, a fault by no means unknown although
-fortunately not very common.
-
-It will be seen that the variations between the two screen patterns on
-_C_ and _D_, together with the difference between them, give accurately
-the performance of each point of the objective represented by an
-aperture in the screen. And similar investigations by substantially
-the same method may be extended to the astigmatic variations, to the
-general color correction, and to the difference in the aberrations for
-the several colors. The original papers cited should be consulted for
-the details of applying this very precise and interesting test.
-
-It gives an invaluable record of the detailed corrections of an
-objective, and while it is one with which the ordinary observer has
-little concern there are times when nothing else can give with equal
-precision the necessary record of performance. There are divers other
-tests used for one purpose or another in examining objectives and
-mirrors, but those here described are ample for nearly all practical
-purposes, and indeed the first two commonly disclose all that it is
-necessary to know.
-
-Now and then one has to deal with an objective which is unmitigatedly
-dirty. It can be given a casual preliminary cleaning in the way already
-mentioned, but sometimes even this will not leave it in condition for
-testing. Then one must get down to the bottom of things and make a
-thorough job of it.
-
-The chief point to remember in undertaking this is that the thing which
-one is cleaning is glass, and very easy to scratch if one rubs dust
-into it, but quite easy to clean if one is careful. The second thing to
-be remembered is that once cleaned it must be replaced as it was before
-and not in some other manner.
-
-The possessor of a dirty objective is generally advised to take it
-to the maker or some reliable optician. If the maker is handy, or an
-optician of large experience in dealing with telescope objectives is
-available, the advice is good, but there is no difficulty whatever in
-cleaning an objective with the exercise of that ordinary care which the
-user of a telescope may be reasonably expected to possess.
-
-It is a fussy job, but not difficult, and the best advice as to how to
-clean a telescope objective is to “tub” it, literally, if beyond the
-stage where the superficial wiping described is sufficient.
-
-To go about the task one first sets down the objective in its cell on
-a horizontal surface and removes the screws that hold in the retaining
-ring, or unscrews the ring itself as the case may be. This leaves the
-cell and objective with the latter uppermost and free to be taken
-out. Prepare on a table a pad of anything soft, a little smaller than
-the objective, topping the pad with soft and clean old cloth; then,
-raising up the cell at an edge, slip the two thumbs under it and lay
-the fingers lightly on the outer lens of the objective, then invert the
-whole affair upon the pad and lift off the cell, leaving the objective
-on its soft bed.
-
-Before anything else is done the edge of the objective should be marked
-with a hard lead pencil on the edge of both the component lenses,
-making two well defined v’s with their points touching. Also, if, as
-usual, there are three small separators between the edges of the flint
-and crown lenses, mark the position of each of these 1, 2, 3, with the
-same pencil.
-
-Forming another convenient pad of something soft, lift off the upper
-lens, take out the three separators and lay them in order on a sheet of
-paper without turning them upside down. Mark alongside each, the serial
-number denoting its position. Then when these spacers, if in good
-condition, are put back, they will go back in the same place rightside
-up, and the objective itself will go back into place unchanged.
-
-Now have at hand a wooden or fibre tub or basin which has been
-thoroughly washed out with soap and water and wiped dry. Half fill it
-with water slightly lukewarm and with a good mild toilet soap, shaving
-soap for example, with clean hands and very soft clean cloth, go at
-one of the lenses and give it a thorough washing. After this it should
-be rinsed very thoroughly and wiped dry. As to material for wiping,
-the main thing is that it must be soft and free from dust that will
-scratch. Old handkerchiefs serve a good turn.
-
-Dr. Brashear years ago in describing this process recommended cheese
-cloth. The present day material that goes under this name is far from
-being as soft at the start as it ought to be, and only the best quality
-of it should be used, and then only after very thorough soaking,
-rinsing and drying. The very soft towels used for cleaning cut glass,
-if washed thoroughly clean and kept free from dust, answer perfectly
-well. The cheese cloth has the advantage of being comparatively cheap
-so that it can be thrown away after use. Whatever the cloth, it should
-be kept, after thorough washing and drying, in a closed jar.
-
-Rinsing the lens thoroughly and wiping it clean and dry is the main
-second stage of cleansing. It sometimes will be found to be badly
-spotted in a way which this washing will not remove. Sometimes the
-spotting will yield to alcohol carefully rubbed on with soft absorbent
-cotton or a bunch of lens paper.
-
-If alcohol fails the condition of the surface is such as to justify
-trying more strenuous means. Nitric acid of moderate strength rubbed on
-with a swab of absorbent cotton will sometimes clear up the spotting.
-If this treatment be used it should be followed up with a 10 per cent
-solution of pure caustic potash or moderately strong c.p. ammonia and
-then by very thorough rinsing. Glass will stand without risk cautious
-application of both acid and alkali, but the former better than the
-latter.
-
-Then a final rinsing and drying is in order. Many operators use a final
-washing with alcohol of at least 90 per cent strength which is allowed
-to evaporate with little or no wiping. Alcohol denatured with methyl
-alcohol serves well if strong enough but beware denatured alcohol of
-unknown composition. Others have used petroleum naphtha and things of
-that sort. At the present time these commercial petroleum products are
-extremely uncertain in quality, like gasoline, being obtained, Heaven
-knows how, from the breaking down of heavier petroleum products.
-
-If pure petroleum ether can be obtained it answers quite as well as
-alcohol, but unless the volatile fluid is pure it may leave streaks.
-Ordinarily neither has to be used, as after the proper wiping the glass
-comes perfectly clean. This done the glass can be replaced on the pad
-whence it came and its mate put through the same process.
-
-Flint glass is more liable to spot than the crown, but the crown is
-by no means immune against the deterioration of the surface, perhaps
-incipient devitrification, and during the war many objectives “went
-blind” from unexplained action of this character. As a rule the soap
-and water treatment applied with care leaves even a pretty hard looking
-specimen of objective in fairly good condition except for the scratches
-which previous users have put upon it.
-
-Then if the spacing pieces, usually of tinfoil, are not torn or
-corroded they can be put back into place, the one lens superimposed
-upon the other, and the pair put back into the cell by dropping it
-gently over them and re-inverting the whole, taking care this time to
-have soft cloth or lens paper under the fingers. Then the retaining
-ring can be put into place again and the objective is ready for testing
-or use as the case may be.
-
-If the spacers are corroded or damaged it may be necessary to replace
-them with very thin tinfoil cut the same size and shape, leaving
-however a little extra length to turn down over the edge of the lower
-lens. They are fastened in place on the extreme edge only by the merest
-touch of mucilage, shellac or Canada balsam, whichever comes to hand.
-The one important thing is that the spacers should be entirely free of
-the sticky material where they lap over the edge of the lens to perform
-the separation. This lap is generally not over 1/16 of an inch, not
-enough to show at the outside of the objective when it is in its cell.
-When the upper lens is lightly pressed down into place, after the gum
-or shellac is dry, all the projecting portion can be trimmed away with
-a sharp pen-knife leaving simply the spacers in the appointed places
-from which the original ones were removed.
-
-Some little space has been given to this matter of cleaning objectives,
-as in many situations objectives accumulate dirt rather rapidly and it
-is highly desirable for the user to learn how to perform the simple but
-careful task of cleansing them.
-
-In ordinary use, when dirt beyond the reach of mere dusting with a
-camel’s hair brush has stuck itself to the exterior of an objective, a
-succession of tufts of absorbent cotton or wads of lens paper at first
-dampened with pure water or alcohol and then followed lightly, after
-the visible dirt has been gently mopped up, by careful wiping with the
-same materials, will keep the exterior surface in good condition, the
-process being just that suggested in the beginning of this chapter as
-the ordinary cleaning up preparatory to a thorough examination.
-
-The main thing to be avoided in the care of a telescope, aside from
-rough usage generally, is getting the objective wet and then letting
-it take its chances of drying. In many climates dew is a very serious
-enemy and the customary dew cap three or four diameters long, bright
-on the outside and blackened within, is of very great service in
-lessening the deposit of dew upon the glass. Also the dew cap keeps out
-much stray light that might otherwise do mischief by brightening the
-general field. In fact its function as a light-trap is very important
-especially if it is materially larger in diameter than the objective
-and provided with stops.
-
-The finder should be similarly protected, otherwise it will
-mysteriously go blind in the middle of an evening’s work due to a heavy
-deposit of moisture on the objective. The effect is an onset of dimness
-and bad definition which is altogether obnoxious.
-
-As regards the metal parts of a telescope they should be treated like
-the metal parts of any other machine, while the moving parts require
-from time to time a little touch of sperm or similar oil like every
-other surface where friction may occur.
-
-The old fashioned highly polished and lacquered brass tube was
-practically impossible to keep looking respectably well provided it
-was really used to any considerable extent. About the most that could
-be done to it was dusting when dusty, and cautiously and promptly
-wiping off any condensed moisture. The more modern lacquered tubes
-require very little care and if they get in really bad condition can be
-relacquered without much expense or difficulty.
-
-Wooden tubes, occasionally found in old instruments, demand the
-treatment which is accorded to other highly finished wooden things,
-occasional rubbing with oil or furniture polish according to the
-character of the original surface. Painted tubes may occasionally
-require a fresh coat, which it does not require great skill to
-administer. If the surface of wooden tripods comes to be in bad shape
-it needs the oil or polish which would be accorded to other well
-finished wooden articles.
-
-Mountings are usually painted or lacquered and either surface can be
-renewed eventually at no great trouble. Bright parts may be lightly
-touched with oil as an ordinary rust preventive.
-
-Reflecting telescopes are considerably more troublesome to keep in
-order than refractors owing to the tender nature of the silvered
-surface. It may remain in good condition with fairly steady use for
-several years or it may go bad in a few months or a few weeks. The
-latter is not an unusual figure in telescopes used about a city where
-smoke is plentiful. The main thing is to prevent the deposit of dew on
-the mirror, or getting it wet in any other way, for in drying off the
-drops almost invariably leave spots.
-
-Many schemes have been proposed for the prevention of injury to the
-mirror surface. A close fitting metal cover, employed whenever the
-mirror is not in use, has given good results in many places. Where
-conditions are extreme this is sometimes lined with a layer of dry
-absorbent cotton coming fairly down upon the mirror surface, and if
-this muffler is dry, clean, and a little warmer than the mirror when
-put on, it seems to be fairly effective. Preferably the mirror should
-be kept, when not in use, at a little higher temperature than the
-surrounding air so that dew will not tend to deposit upon it.
-
-As to actual protective measures the only thing that seems to be
-really efficient is a very thin coating of lacquer, first tried by
-Perot at the Paris Observatory. The author some ten years since took
-up the problem in protecting some laboratory mirrors against fumes
-and moisture and found that the highest grade of white lacquer, such
-as is used for the coating of fine silverware in the trade, answered
-admirably if diluted with six or eight volumes of the thinner sold
-with such commercial lacquers. It is best to thin the lacquer to the
-requisite amount and then filter.
-
-If now a liberal amount of the mixture is poured upon the mirror
-surface after careful dusting, swished quickly around, and the mirror
-is then immediately turned up on edge to drain and dry, a very thin
-layer of lacquer will be left upon it, only a fraction of a wave length
-thick, so that it shows broad areas of interference colors.
-
-Treated in this way and kept dry the coating will protect the
-brilliancy of the silver for a good many months even under rather
-unfavorable circumstances. After trying out the scheme rather
-thoroughly the treatment was applied to the 24 inch reflector of the
-Harvard Observatory and has been in use ever since. The author applied
-the first coating in the spring of 1913, and since that time it has
-only been necessary to resilver perhaps once in six months as against
-about as many weeks previously.
-
-The lacquer used in this case was the so-called “Lastina” lacquer made
-by the Egyptian Lacquer Company of New York, but there are doubtless
-others of similar grade in the market. It is a collodion lacquer and
-in recent years it has proved desirable to use as a thinner straight
-commercial amylacetate rather than the thinner usually provided with
-the lacquer, perhaps owing to the fact that difficulty of obtaining
-materials during the war may have caused, as in so many other cases,
-substitutions which, while perfectly good for the original purpose did
-not answer so well under the extreme conditions required in preserving
-telescope mirrors.
-
-The lacquer coating when thinned to the extent here recommended does
-not apparently in any way deteriorate the definition as some years of
-regular work at Harvard have shown. Some experimenters have, however,
-found difficulty, quite certainly owing to using too thick a lacquer.
-The endurance of a lacquer coating where the mirror is kept free from
-moisture, and its power to hold the original brilliancy of the surface
-is very extraordinary.
-
-The writer took out and tested one laboratory mirror coated seven years
-before, and kept in a dry place, and found the reflecting power still
-a little above .70, despite the fact that the coating was so dry as
-to be almost powdery when touched with a tuft of cotton. At the start
-the mirror had seen some little use unprotected and its reflection
-coefficient was probably around .80. If the silver coating is thick
-as it can be conveniently made, on a well coated mirror, the coat of
-lacquer, when tarnish has begun, can be washed off with amylacetate and
-tufts of cotton until the surface is practically clear of it, and the
-silver itself repolished by the ordinary method and relacquered.
-
-There are many silvering processes in use and which one should be
-chosen for re-silvering a mirror, big or little, is quite largely a
-matter of individual taste, and more particularly experience. The two
-most used in this country are those of Dr. Brashear and Mr. Lundin,
-head of the Alvan Clark Corporation, and both have been thoroughly
-tried out by these experienced makers of big mirrors.
-
-The two processes differ in several important particulars but both
-seem to work very successfully. The fundamental thing in using either
-of them is that the glass surface to be silvered should be chemically
-clean. The old silver, if a mirror is being resilvered, is removed with
-strong nitric acid which is very thoroughly rinsed off after every
-trace of silver has been removed. Sometimes a second treatment with
-nitric acid may advantageously follow the first with more rinsing.
-The acid should be followed by a 10 per cent solution of c.p. caustic
-potash (some operators use c.p. ammonia as easier to clear away) rinsed
-off with the utmost thoroughness.
-
-On general principles the last rinsing should be with distilled water
-and the glass surface should not be allowed to dry between this rinsing
-and starting the silvering process, but the whole mirror should be kept
-under water until the time for silvering. In Dr. Brashear’s process the
-following two solutions are made up; first the reducing solution as
-follows:
-
-Rock candy, 20 parts by weight.
-
-Strong nitric acid (spec. gr. 1.22), 1 part.
-
-Alcohol, 20 parts.
-
-Distilled water, 200 parts.
-
-This improves by keeping and if this preparation has to be hurried the
-acid, sugar and distilled water should be boiled together and then the
-alcohol added after the solution is cooled.
-
-Second, make up the silvering solution in three distinct portions;
-first the silver solution proper as follows:
-
-  1. 2 parts silver nitrate. 20 parts distilled water.
-  Second, the alkali solution as follows:
-  2. 1⅓ parts c.p. caustic potash. 20 parts distilled water.
-  Third, the reserve silver solution as follows:
-  3. ¼ part silver nitrate. 16 parts distilled water.
-
-The working solution of silver is then prepared thus: Gradually add
-to the silver solution No. 1 the strongest ammonia, slowly and with
-constant stirring. At first the solution will turn dark brown and then
-it will gradually clear up. Ammonia should be added only just to the
-point necessary to clear the solution.
-
-Then add No. 2, the alkali solution. Again the mixture will turn dark
-brown and must be cautiously cleared once more with ammonia until it is
-straw colored but clear of precipitate. Finally add No. 3, the reserve
-solution, very cautiously with stirring until the solution grows
-darker and begins to show traces of suspended matter which will not
-stir out. Then filter the whole through absorbent cotton to free it of
-precipitate and it is ready for use. One is then ready for the actual
-silvering.
-
-Now there are two ways of working the process, with the mirror face
-up, or face down. The former is advantageous in allowing better
-inspection of the surface as it forms, and also it permits the mirror
-of a telescope to be silvered without removing it from the cell, as was
-in fact done habitually in case of the big reflector of the Alleghany
-Observatory where the conditions were such as to demand re-silvering
-once a month. The solution was kept in motion during the process by
-rocking the telescope as a whole.
-
-When silvering face up the mirror is made to form the bottom of the
-silvering vessel, being fitted with a wrapping of strong paraffined
-or waxed paper or cloth, wound several times around the rim of the
-mirror and carried up perhaps half the thickness of the mirror to
-form a retainer for the silvering solution. This band is firmly tied
-around the edge of the mirror making a water tight joint. Ritchey uses
-a copper band fitted to the edge of the mirror and drawn tight by
-screws, and finishes making tight with paraffin and a warm iron.
-
-In silvering face down the mirror is suspended a little distance above
-the bottom of a shallow dish, preferably of earthen ware, containing
-the solution. Various means are used for supporting it. Thus cleats
-across the back cemented on with hard optician’s pitch answer well for
-small mirrors, and sometimes special provision is made for holding the
-mirror by the extreme edge in clamps.
-
-Silvering face down is in some respects less convenient but does free
-the operator from the very serious trouble of the heavy sediment which
-is deposited from the rather strong silver solution. This is the
-essential difficulty of the Brashear process in silvering face up. The
-trouble may be remedied by very gentle swabbing of the surface under
-the liquid with absorbent cotton, from the time when the silver coating
-begins fairly to form until it is completed.
-
-The Brashear process is most successfully worked at a temperature
-between 65° and 70° F. and some experience is required to determine the
-exact proportion of the reducing solution to be added to the silvering
-solution. Ritchey advises such quantity of the reducing solution as
-contains of sugar one-half the total weight of the silver nitrate used.
-The total amount of solution after mixing should cover the mirror about
-an inch deep. Too much increases the trouble from sediment and fails to
-give a clean coating. The requisite quantity of reducing solution is
-poured into the silvering solution and then immediately, if the mirror
-is face up, fairly upon it, without draining it of the water under
-which it has been standing.
-
-If silvering face down the face will have been immersed in a thin
-layer of distilled water and the mixed solutions are poured into the
-dish. In either case the solution is rocked and kept moving pretty
-thoroughly until the process is completed which will take about five
-minutes. If silvering is continued too long there is likelihood of an
-inferior whitish outer surface which will not polish well, but short of
-this point the thicker the coat the better, since a thick coat stands
-reburnishing where a thin one does not and moreover the thin one may be
-thin enough to transmit some valuable light.
-
-When the silvering is done the solution should be rapidly poured off,
-the edging removed or the mirror lifted out of the solution, rinsed
-off first with tap water and then with distilled, and swabbed gently
-to clear the remaining sediment. Then the mirror can be set up on edge
-to dry. A final flowing with alcohol and the use of a fan hastens the
-process.
-
-In Lundin’s method the initial cleaning process is the same but after
-the nitric acid has been thoroughly rinsed off the surface is gently
-but thoroughly rubbed with a saturated solution of tin chloride,
-applied with a wad of absorbent cotton. After the careful rubbing the
-tin chloride solution must be washed off with the utmost thoroughness,
-preferably with moderately warm water. It is just as important to get
-off the tin chloride completely, as it is to clean completely the
-mirror surface by its use. Otherwise streaks may be left where the
-silvering will not take well.
-
-When the job has been properly done one can wet the whole surface with
-a film of water and it will stay wet even when the surface is slightly
-tilted. As in the Brashear process the mirror must be kept covered with
-water. Mr. Lundin always silvers large mirrors face up, and forms the
-dish by wrapping around the edge of the mirror a strip of bandage cloth
-soaked in melted beeswax and smoothed off by pulling it while still hot
-between metal rods to secure even distribution of the wax so as to make
-a water tight joint. This rim of cloth is tied firmly around the edge
-of the mirror and the strings then wet to draw them still tighter.
-
-Meanwhile the water should cover the mirror by ¾ of an inch or more.
-It is to be noted that in the Lundin process ordinary water is usually
-found just as efficient as distilled water, but it is hardly safe to
-assume that such is the case, without trying it out on a sample of
-glass.
-
-There are then prepared two solutions, a silver solution,
-
-2.16 parts silver nitrate (see King, Pop. Ast =30=, 93)
-
-100 parts water.
-
-and a reducing solution,
-
-4 parts Merck’s formaldehyde
-
-20 parts water.
-
-This latter quantity is used for each 100 parts of the above silver
-solution, and the whole quantity made up is determined by the amount of
-liquid necessary to cover the mirror as just described.
-
-The silver solution is cautiously and completely cleared up by strong
-ammonia as in the Brashear process. The silver and reducing solutions
-are then mixed, the water covering the mirror poured quickly off, and
-the silvering solution immediately poured on. The mirror should then be
-gently rocked and the silver coating carefully watched as it forms.
-
-As the operation is completed somewhat coarse black grains of sediment
-will form and when these begin to be in evidence the solution should
-be poured off, the mirror rinsed in running water, the edging removed
-while the mirror is still rinsing and finally the sediment very gently
-swabbed off with wet absorbent cotton. Then the mirror can be set up to
-dry.
-
-The Lundin process uses a considerably weaker silver solution than the
-Brashear process, is a good deal more cleanly while in action, and
-is by experienced workers said to perform best at a materially lower
-temperature than the Brashear process, with the mirror, however, always
-slightly warmer than the solution. Some workers have had good results
-by omitting the tin chloride solution and cleaning up the surface
-by the more ordinary methods. In the Lundin process the solution is
-sufficiently clear for the density acquired by the silver coating to be
-roughly judged by holding an incandescent lamp under the mirror. A good
-coating should show at most only the faintest possible outline of the
-filament, even of a gas filled lamp.
-
-Whichever process of silvering is employed, and both work well, the
-final burnishing of the mirror after it is thoroughly dry is performed
-in the same way, starting by tying up a very soft ball of absorbent
-cotton in the softest of chamois skin.
-
-This burnisher is used at first without any addition, simply to smooth
-and condense the film by going over it with quick, short, and gentle
-circular strokes until the entire surface has been thoroughly cleaned
-and begins to show a tendency to take polish. Then a very little of the
-finest optical rouge should be put on to the same, or better another,
-rubber, and the mirror gone steadily over in a similar way until it
-comes to a brilliant polish.
-
-A good deal of care should be taken in performing this operation to
-avoid the settling of dust upon the surface since scratches will
-inevitably result. Great pains should also be taken not to take any
-chance of breathing on the mirror or in any other way getting the
-surface in the slightest degree damp. Otherwise it will not come to a
-decent polish.
-
-Numerous other directions for silvering will be found in the
-literature, and all of them have been successfully worked at one time
-or another. The fundamental basis of the whole process is less in the
-particular formula used than in the most scrupulous care in cleaning
-the mirror and keeping it clean until the silvering is completed. Also
-a good bit of experience is required to enable one to perform the
-operation so as to obtain a uniform and dense deposit.
-
-
-
-
-CHAPTER X
-
-SETTING UP AND HOUSING THE TELESCOPE
-
-
-In regard to getting a telescope into action and giving it suitable
-protection, two entirely different situations present themselves. The
-first relates to portable instruments or those on temporary mounts,
-the second to instruments of position. As respects the two, the
-former ordinarily implies general use for observational purposes, the
-latter at least the possibility of measurements of precision, and a
-mount usually fitted with circles and with a driving clock. Portable
-telescopes may have either alt-azimuth or equatorial mounting, while
-those permanently set up are now quite universally equatorials.
-
-Portable telescopes are commonly small, ranging from about 2½ inches
-to about 5 inches in aperture. The former is the smallest that can
-fairly be considered for celestial observations. If thoroughly good and
-well mounted even this is capable of real usefulness, while the five
-inch telescope if built and equipped in the usual way, is quite the
-heaviest that can be rated as portable, and deserves a fixed mount.
-
-Setting up an alt-azimuth is the simplest possible matter. If on a
-regular tripod it is merely taken out and the tripod roughly levelled
-so that the axis in azimuth is approximately vertical. Now and then one
-sets it deliberately askew so that it may be possible to pass quickly
-between two objects at somewhat different altitudes by swinging on the
-azimuth axis.
-
-If one is dealing with a table tripod like Fig. 69 it should merely be
-set on any level and solid support that may be at hand, the main thing
-being to get it placed so that one may look through it conveniently.
-This is a grave problem in the case of all small refractors, which
-present their oculars in every sort of unreachable and uncomfortable
-position.
-
-Of course a diagonal eyepiece promises a way out of the difficulty,
-but with small apertures one hesitates to lose the light, and often
-something of definition, and the observer must pretty nearly stand
-on his head to use the finder. With well adjusted circles, such
-are commonly found on a fixed mount, location of objects is easy.
-On a portable set-up perhaps the easiest remedy is a pair of well
-aligned coarse sights near the objective end of the tube and therefore
-within reach when it is pointed zenith-ward. The writer has found a
-low, armless, cheap splint rocker, such as is sold for piazza use,
-invaluable under these painful circumstances, and can cordially
-recommend it.
-
-Even better is an observing box and a flat cushion. The box is merely a
-coverless affair of any smooth ⅞ inch stuff firmly nailed or screwed
-together, and of three unequal dimensions, giving three available
-heights on which to sit or stand. The dimensions originally suggested
-by Chambers (_Handbook of Astronomy_, II, 215) were 21 × 12 × 15
-inches, but the writer finds 18 × 10 × 14 inches a better combination.
-
-The fact is that the ordinary stock telescope tripod is rather too high
-for sitting, and too low for standing, comfortably. A somewhat stubby
-tripod is advantageous both in point of steadiness and in accessibility
-of the eyepiece when one is observing within 30° of the zenith, where
-the seeing is at its best; and a sitting position gives a much greater
-range of convenient upward vision than a standing one.
-
-When an equatorial mount is in use one faces the question of adjustment
-in its broadest aspect. Again two totally different situations arise in
-using the telescope. First is the ordinary course of visual observation
-for all general purposes, in which no precise measurements of position
-or dimensions are involved.
-
-Here exact following is not necessary, a clock drive is convenient
-rather than at all indispensable, and even circles one may get along
-without at the cost of a little time. Such is the usual situation with
-portable equatorials. One does not then need to adjust them to the
-pole with extreme precision, but merely well enough to insure easy
-following; otherwise one is hardly better off than with an alt-azimuth.
-
-In a totally different class falls the instrument with which one
-undertakes regular micrometric work, or enters upon an extended
-spectroscopic program or the use of precise photometric apparatus, to
-say nothing of photography. In such cases a permanent mount is almost
-imperative, the adjustments must be made with all the exactitude
-practicable, one finds great need of circles, and the lack of a clock
-drive is a serious handicap or worse.
-
-Moreover in this latter case one usually has, and needs, some sort of
-timepiece regulated to sidereal time, without which a right ascension
-circle is of very little use.
-
-In broad terms, then, one has to deal, first; with a telescope on a
-portable mount, with or without position circles, generally lacking
-both sidereal clock and driving clock, and located where convenience
-dictates; second, with a telescope on a fixed mount in a permanent
-location, commonly with circles and clock, and with some sort of
-permanent housing.
-
-Let us suppose then that one is equipped with a 5 inch instrument like
-Fig. 168, having either the tripod mount, or the fixed pillar mount
-shown alongside it; how shall it be set up, and, if on the fixed mount,
-how sheltered?
-
-In getting an equatorial into action the fundamental thing is to place
-the optical axis of the telescope exactly parallel to the polar axis
-of the mount and to point the latter as nearly as possible at the
-celestial pole.
-
-The conventional adjustments of an equatorial telescope are as follows:
-
-1. Adjust polar axis to altitude of pole.
-
-2. Adjust index of declination circle.
-
-3. Adjust polar axis to the meridian.
-
-4. Adjust optical axis perpendicular to declination axis.
-
-5. Adjust declination axis perpendicular to polar axis.
-
-6. Adjust index of right ascension circle, and
-
-7. Adjust optical axis of finder parallel to that of telescope.
-
-Now let us take the simplest and commonest case, the adjustment of
-a portable equatorial on a tripod mount, when the instrument has a
-finder but neither circles nor driving clock. Adjustments 2 and 6
-automatically drop out of sight, 5 vanishes for lack of any means to
-make the adjustment, and on a mount made with high precision, like the
-one before us, 4 is negligible for any purpose to which our instrument
-is applicable.
-
-Adjustments 1, 3 and 7 are left and these should be performed in the
-order 7, 1, 3, for sake of simplicity. To begin with the finder has
-cross-wires in the focus of its eyepiece, and the next step is to
-provide the telescope itself with similar cross-wires.
-
-These can readily be made, if not provided, by cutting out a disc of
-cardboard to fit snugly either the spring collar just in front of
-a positive eyepiece or the eyepiece itself at the diaphragm, if an
-ordinary Huygenian. Rule two diametral lines on the circle struck for
-cutting the cardboard, crossing at the center, cut out the central
-aperture, and then very carefully stretch over it, guided by the
-diametral lines, two very fine threads or wires made fast with wax or
-shellac.
-
-[Illustration: FIG. 168.—Clark 5-inch with Tripod and Pier.]
-
-Now pointing the telescope at the most distant well defined object in
-view, rotate the spring collar or ocular, when, if the crossing of the
-threads is central, their intersection should stay on the object. If
-not shift a thread cautiously until the error is corrected.
-
-Keeping the intersection set on the object by clamping the tube, one
-turns attention to the finder. Either the whole tube is adjustable
-in its supports or the cross-wires are capable of adjustment by
-screws just in front of the eyepiece. In either case finder tube or
-cross-wires should be shifted until the latter bear squarely upon the
-object which is in line with the cross threads of the main telescope.
-Then the adjusting screws should be tightened, and the finder is in
-correct alignment.
-
-As to adjustments 1 and 3, in default of circles the ordinary
-astronomical methods are not available, but a pretty close
-approximation can be made by levelling. A good machinist’s level is
-quite sensitive and reliable. The writer has one picked out of stock at
-a hardware shop that is plainly sensitive to 2′ of arc, although the
-whole affair is but four inches long.
-
-Most mounts like the one of Fig. 168 have a mark ruled on the support
-of the polar axis and a latitude scale on one of the cheek pieces.
-Adjustment of the polar axis to the correct altitude is then made by
-placing the level on the declination axis, or any other convenient
-place, bringing it to a level, and then adjusting the tripod until the
-equatorial head can be revolved without disturbing this level. Then
-set the polar axis to the correct latitude and adjustment number 1 is
-complete for the purpose in hand.
-
-Lacking a latitude scale, it is good judgment to mark out the latitude
-by the help of the level and a paper protractor. To do this level the
-polar axis to the horizontal, level the telescope tube also, and clamp
-it in declination to maintain it parallel. Then fix the protractor to
-a bit of wood tied or screwed to the telescope support, drop a thin
-thread plumb line from a pin driven into the wood, the declination axis
-being still clamped, note the protractor reading, and then raise the
-polar axis by the amount of the latitude.
-
-Next, with a knife blade scratch a conspicuous reference line on the
-sleeve of the polar axis and its support so that when the equatorial
-head is again levelled carefully you can set approximately to the
-latitude at once.
-
-Now comes adjustment 3, the alignment of the polar axis to the
-meridian. One can get it approximately by setting the telescope tube
-roughly parallel with the polar axis and, sighting along it, shifting
-the equatorial head in azimuth until the tube points to the pole star.
-Then several methods of bettering the adjustment are available.
-
-At the present date Polaris is quite nearly 1° 07′ from the true pole
-and describes a circle of that radius about it every 24 hours. To get
-the correct place of the pole with reference to Polaris one must have
-at least an approximate knowledge of the place of that star in its
-little orbit, technically its hour-angle. With a little knowledge of
-the stars this can be told off in the skies almost as easily as one
-reckons time on a clock. Fig. 169 is, in fact, the face of the cosmic
-clock, with a huge sweeping hour hand that he who runs may read.
-
-[Illustration: FIG. 169.—The Cosmic Clock.]
-
-It is a clock in some respects curious; it has a twenty-four hour face
-like some clocks and watches designed for Continental railway time; the
-hour hand revolves backward, (“counter-clockwise”) and it stands in the
-vertical not at noon, but at 1.20 Star Time. The two stars which mark
-the tip and the reverse end of the hour hand are delta Cassiopeæ and
-zeta Ursæ Majoris respectively. The first is the star that marks the
-bend in the back of the great “chair,” the second (Mizar), the star
-which is next to the end of the “dipper” handle.
-
-One or the other is above the horizon anywhere in the northern
-hemisphere. Further, the line joining these two stars passes almost
-exactly through the celestial pole, and also very nearly through
-Polaris, which lies between the pole and δ Cassiopeæ. Consequently if
-you want to know the hour-angle of Polaris just glance at the clock and
-note where on the face δ Cassiopeæ stands, between the vertical which
-is XXIV o’clock, and the horizontal, which is VI (east) or XVIII (west)
-o’clock.
-
-You can readily estimate its position to the nearest half hour, and
-knowing that the great hour hand is vertical (δ Cassiopeæ up) at I^h
-20^m or (ζ Ursæ Majoris up) at XIII^h 20^m, you can make a fairly close
-estimate of the sidereal time.
-
-A little experience enables one to make excellent use of the clock
-in locating celestial objects, and knowledge of the approximate hour
-angle of Polaris thus observed can be turned to immediate use in making
-adjustment 3. To this end slip into the plane of the finder cross wires
-a circular stop of metal or paper having a radius of approximately 1°
-15′ which means a diameter of 0.52 inch per foot of focal length.
-
-Then, leaving the telescope clamped in declination as it was after
-adjustment 1, turn it in azimuth across the pole until the pole star
-enters the field which, if the finder inverts it will do on the other
-side of the center; i.e. if it stands at IV to the naked eye it will
-enter the field apparently from the XVI o’clock quarter. When just
-comfortably inside the field, the axis of the telescope is pointing
-substantially at the pole.
-
-It is better to get Polaris in view before slipping in the stop and if
-it is clearly coming in too high or too low shift the altitude of the
-polar axis a trifle to correct the error. This approximate setting can
-be made even with the smallest finder and on any night worth an attempt
-at observation.
-
-With a finder of an inch or more aperture a very quick and quite
-accurate setting to the meridian can be made by the use of Fig. 170,
-which is a chart of all stars of 8 mag. or brighter within 1° 30′ of
-the pole. There are only three stars besides Polaris at all conspicuous
-in this region, one quite close to Polaris, the other two forming with
-it the triangle marked on the chart. These two are, to the left, a
-star of magnitude 6.4 designated B. D. 88 112, and to the right one of
-magnitude 7.0, B. D. 89 13.
-
-The position of the pole for the rest of the century is marked on the
-vertical arrow and with the stars in the field of the finder one can
-set the cross wires on the pole, the instrument remaining clamped in
-declination, within a very few minutes of arc, quite closely enough
-for any ordinary use of a portable mount. All this could be done even
-better with the telescope itself, but it is very rare to find an
-eyepiece with sufficient field.
-
-[Illustration: FIG. 170.—The Pole among the Stars.]
-
-At all events the effect of any error likely to be made in these
-adjustments is not serious for the purpose in hand, since if one makes
-an error of a minute of arc in the setting the resulting displacement
-of a star in the field will even in the most unfavorable case reach
-this full amount only after 6 hours following. I.e. with any given
-eyepiece an error of adjustment equal to the radius of the field will
-still permit following a star for an hour or two before it drifts
-inconveniently wide of the center.
-
-Considerable space has been devoted to these easy approximations in
-setting up, since the directions commonly given require circles and
-often a clock drive.
-
-In some cases one has to set up a portable equatorial where from
-necessity for clear sky space, Polaris is not visible. The best plan
-then is to set up with great care where Polaris can be seen, paying
-especial attention to the levelling. Then establish two meridian marks
-on stakes at a convenient distance by turning the telescope 180° on its
-declination axis and sighting through it in both directions. Now with
-a surveyor’s tape transfer the meridian line East or West as the case
-may be until it can be used where there is clear sky room.
-
-Few observers near a city can get good sky room, from the interference
-of houses, trees or blazing street lamps, and the telescope must often
-be moved from one site to another to reach different fields. In such
-case it is wise to take the very first step toward giving the telescope
-a local habitation by establishing a definite placement for the tripod.
-
-To this end the three legs should be firmly linked together by chains
-that will not stretch—leg directly to leg, and not to a common
-junction. Then see to it that each leg has a strong and moderately
-sharp metal point, and, the three points of support being thus
-definitely fixed, establish the old reliable point-slot-plane bearing
-as follows:
-
-Lay out at the site (or sites) giving the desired clear view, a circle
-scratched on the ground of such size that the three legs of your tripod
-may rest approximately on its periphery. Then lay out on the circle
-three points 120° apart. At each point sink a short post 12 to 18
-inches long and of any convenient diameter, well tarred, and firmly set
-with the top levelled off quite closely horizontal.
-
-To the top of each bolt a square or round of brass or iron about half
-an inch thick. The whole arrangement is indicated in diagram in Fig.
-171. In _a_ sink a conical depression such as is made by drilling
-nearly through with a 1 inch twist drill. The angle here should be a
-little broader than the point on the tripod leg. In _b_ have planed a V
-shaped groove of equally broad angle set with its axis pointing to the
-conical hole in _a_. Leave the surface of _c_ a horizontal plane.
-
-Now if you set a tripod leg in _a_, another in the slot at _b_ and
-the third on _c_, the tripod will come in every instance to the same
-level and orientation. So, if you set up your equatorial carefully in
-the first place and leave the head clamped in azimuth, you can take it
-in and replace it at any time still in adjustment as exact as at the
-start. And if it is necessary to shift from one location to another you
-can do it without delay still holding accurate adjustment of the polar
-axis to the pole, and avoiding the need of readjustment.
-
-In case the instrument has a declination circle the original set-up
-becomes even simpler. One has only to level the tripod, either with
-or without the equatorial head in place, and then to set the polar
-axis either vertical or horizontal, levelling the tube with it either
-by placing the level across the objective cell perpendicular to the
-declination axis, or laying it along the tube when horizontal.
-
-[Illustration: FIG. 171.—A Permanent Foothold for the Tripod.]
-
-Then, reading the declination circle, one can set off the co-atitude
-or latitude as the case may be and, leaving the telescope clamped in
-declination, lower or raise the polar axis until the tube levels to
-the horizontal. When the mount does not permit wide adjustment and has
-no latitude scale one is driven to laying out a latitude templet and,
-placing a straight edge under the equatorial head, or suspending a
-plumb line from the axis itself, setting it mechanically to latitude.
-
-Now suppose we are dealing with the same instrument, but are planning
-to plant it permanently in position on its pillar mount. It is now
-worth while to make the adjustments quite exactly, and to spend some
-time about it. The pillar is commonly assembled by well set bolts on a
-brick or concrete pier. The preliminary steps are as already described.
-
-The pillar is levelled across the top, the equatorial head, which turns
-upon it in azimuth, is levelled as before, the adjustment being made
-by metal wedges under the pillar or by levelling screws in the mount
-if there are any. Then the latitude is set off by the scale, or by
-the declination circle, and the polar axis turned to the approximate
-meridian as already described.
-
-There is likely to be an outstanding error of a few minutes of arc
-which should in a permanent mount be reduced as far as practicable. At
-the start adjust the declination of the optical axis of the telescope
-to that of the polar axis. This is done in the manner suggested by Fig.
-172.
-
-Here _p_ is the polar axis and _d_ the declination axis. Now if one
-sights, using the cross wires, through the telescope a star near the
-meridian, i.e., one that is changing in declination quite slowly,
-starting from the position _A_ with the telescope _E_. of the polar
-axes, and turns it over 180° into the position _B_, _W_. of the polar
-axis, the prolongation of the line of sight, _b_, will fall below _a_,
-when as here the telescope points too high in the _A_ position.
-
-[Illustration: FIG. 172.—Aligning the Optical Axis.]
-
-In other words the apparent altitude of the star will change by twice
-the angle between _A_ and _p_. Read both altitudes on the declination
-circle and split the difference with the slow motion as precisely as
-the graduation of the declination circle permits.
-
-The telescope will probably not now point exactly at the star, but as
-the tube is swung from the _A_ to the _B_ position and back the visible
-stars will describe arcs of circles which should be nearly concentric
-with the field as defined by the stop in the eyepiece. If not, a very
-slight touch on the declination slow motion one way or the other will
-make them do so to a sufficient exactness, especially if a rather high
-power eyepiece is used.
-
-The optical axis of the telescope is now parallel to the polar axis,
-but the latter may be slightly out of position in spite of the
-preliminary adjustment. Now reverting to the polar field of Fig. 170,
-swing from position _A_ to _B_ and back again, correcting any remaining
-eccentricity of the star arcs around the pole by cautious shifting
-of the polar axis, leaving the telescope clamped in declination. The
-first centering is around the pole of the instrument, the second around
-the celestial pole by help of a half dozen small stars within a half
-degree on both sides of it, magnitudes 9 and 10, easily visible in a 3”
-or 4” telescope, using the larger field of the finder for the coarse
-adjustment.
-
-If the divided circles read to single minutes or closer, which they
-generally do not on instruments of moderate size, one can use the
-readings to set the polar axis and the declination circle, and to make
-the other adjustments as well.
-
-In default of this help, the declination circle adjustment may be set
-to read 90° when the optical axis is brought parallel to the polar
-axis, and after the adjustment of the latter is complete, the R. A.
-circle can be set by swinging up the telescope in the meridian and
-watching for the transit of any star of known R. A. over the central
-cross wire, at which moment the circle should be clamped to the R. A.
-thus defined.
-
-Two possible adjustments are left, the perpendicularity of the polar
-and declination axes, and that of the optical axis to the declination
-axis. As a rule there is no provision for either of these, which are
-supposed to have been carried out by the maker. The latter adjustment
-if of any moment will disclose itself as a lateral wobble in trying
-to complete the adjustment of optical axis to polar axis. It can be
-remedied by a liner of tinfoil or even paper under one end of the
-tube’s bearing on its cradle. Adjustment of the former is strictly a
-job for the maker.
-
-For details of the rigorous adjustments on the larger instruments the
-reader will do well to consult Loomis’ _Practical Astronomy_ page 28
-and following.[31] The adjustments here considered are those which can
-be effectively made without driving clock, finely divided circles,
-or exact knowledge of sidereal time. The first and last of these
-auxiliaries, however, properly belong with an instrument as large as
-Fig. 168, on a fixed mount.
-
- [31] See also two valuable papers by Sir Howard Grubb, _The
- Observatory_, Vol. VII, pp. 9, 43. Also in Jour. Roy. Ast. Soc.
- Canada, Dec., 1921, Jan. 1922.
-
-There are several rather elegant methods of adjusting the polar axis
-to the pole which depend on the use of special graticules in the
-eyepiece, or on auxiliary devices applied to the telescope, the general
-principle being automatically to provide for setting off the distance
-between Polaris and the pole at the proper hour angle. A beautifully
-simple one is that of Gerrish (_Pop. Ast._ =29=, 283).
-
-The simple plan here outlined will generally, however, prove sufficient
-for ordinary purposes and where high precision is necessary one has to
-turn to the more conventional astronomical methods.
-
-If one gives his telescope a permanent footing such as is shown in Fig.
-171 adjustment has rarely to be repeated. With a pillar mount such as
-we have just now been considering the instrument itself can be taken in
-doors and replaced with very slight risk of disturbing its setting, but
-some provision must be made for sheltering the mount.
-
-A tarpaulin is sometimes recommended and indeed answers well,
-particularly if a bag of rubber sheeting is drawn loosely over the
-mount first. Better still is a box cover of copper or galvanized iron
-set over the mount and closely fitting well down over a base clamped to
-the pillar with a gasket to close the joint.
-
-But the fact is when one is dealing with a fine instrument like Fig.
-168 of as much as 5 inches aperture, the question of a permanent
-housing (call it observatory if you like) at once comes up and will not
-down.
-
-It is of course always more convenient to have the telescope
-permanently in place and ready for action. Some observers feel that
-working conditions are better with the telescope in the open, but most
-prefer a shelter from the wind, even if but partial, and the protection
-of a covering, however slight, in severe weather.
-
-In the last resort the question is mainly one of climate. Where nights,
-otherwise of the best seeing quality, are generally windless or with
-breezes so slight that the tube does not quiver a telescope in the
-open, however protected between times, works perfectly well.
-
-In other regions the clearest nights are apt to be those of a steady
-gentle wind producing great uniformity of conditions at the expense
-of occasional vibration of the instrument and of discomfort to the
-observer. Hence one finds all sorts of practice, varied too, by the
-inevitable question of expense.
-
-The simplest possible housing is to provide for the fixed instrument
-a moveable cover which can be lifted or slid quite out of the way
-leaving the telescope in the open air, exposed to wind, but free from
-the disturbing air currents that play around the opening of a dome.
-Shelters of this cheap and simple sort have been long in use both for
-small and large instruments.
-
-[Illustration: FIG. 173.—The Simplest of Telescope Housings.]
-
-For example several small astrographic instruments in the Harvard
-equipment are mounted as shown in Fig. 173. Here are two fork mounts,
-each on a short pier, and covered in by galvanized iron hoods made in
-two parts, a vertical door which swings down, as in the camera of the
-foreground, and the hood proper, hinged to the base plate and free to
-swing down when the rear door is unlocked and opened. A little to the
-rear is a similar astrographic camera with the hood closed. It is all
-very simple, cheap, and effective for an instrument not exceeding say
-two or three feet in focal length.
-
-A very similar scheme has been successfully tried on reflectors as
-shown in Fig. 174. The instrument shown is a Browning equatorial of
-8½ inches aperture. The cover is arranged to open after the manner
-of Fig. 173 and the plan proved very effective, preserving much greater
-uniformity of conditions and hence permitting better definition than in
-case of a similar instrument peering through the open shutter of a dome.
-
-Such a contrivance gets unwieldly in case of a refractor on account of
-the more considerable height of the pier and the length of the tube
-itself. But a modification of it may be made to serve exceedingly well
-in climates where working in the open is advantageous. A good example
-is the equatorial of the Harvard Observatory station at Mandeville,
-Jamaica, which has been thus housed for some twenty years, as shown in
-Fig. 175.
-
-This 11 inch refractor, used mainly on planetary detail, is located
-alongside the polar telescope of 12 inches aperture and 135 feet 4
-inches focal length used for making a photographic atlas of the moon
-and on other special problems. The housing, just big enough to take in
-the equatorial with the tube turned low, opens on the south side and
-then can be rolled northward on its track, into the position shown,
-where it is well clear of the instrument, which is then ready for use.
-
-[Illustration: FIG. 174.—Cover for Small Reflector.]
-
-The climate of Jamaica, albeit extremely damp, affords remarkably
-good seeing during a large part of the year, and permits use of the
-telescope quite in the open without inconvenience to the observer. The
-success of this and all similar housing plans depends on the local
-climate more than on anything else—chiefly on wind during the hours
-of good seeing. An instrument quite uncovered suffers from gusts far
-more than one housed under a dome, which is really the sum of the whole
-matter, save that a dome to a slight extent does shelter the observer
-in extremely cold weather.
-
-Even very large reflectors can be housed in similar fashion if suitably
-mounted. For example in Fig. 176 is shown the 36 inch aperture
-reflector of the late Dr. Common, which was fitted with an open fork
-equatorial mounting. Here the telescope itself, with its short pier and
-forked polar axis, is shown in dotted lines.
-
-[Illustration: FIG. 175.—Sliding Housing for 11-inch Refractor.]
-
-Built about it is a combined housing and observing stand rotatable on
-wheels _T_ about a circular track _R_. The housing consists of low
-corrugated metal sides and ends, here shown partly broken away, of
-dimensions just comfortably sufficient to take in the telescope when
-the housing is rotated to the north and south position, and the tube
-turned down nearly flat southward. A well braced track _WW_ extends
-back along the top of the side housing and well to the rear. On this
-track rolls the roof of the housing _X,X,X_, with a shelter door at the
-front end.
-
-[Illustration: FIG. 176.—Sliding Housing for a Big Reflector.]
-
-The members _U_ constitute a framing which supports at once the housing
-and the observing platform, to which access is had by a ladder, _Z_,
-provided with a counterbalanced observing seat. The instrument is
-put into action by clearing the door at the end of the roof, running
-the roof back to the position shown in the dotted lines, raising the
-tube, and then revolving the whole housing into whatever position is
-necessary to permit the proper setting of the tube.
-
-[Illustration: FIG. 177.—Sliding Roof Observatory.]
-
-This arrangement worked well but was found a bit troublesome owing to
-wind and weather. With a skeleton tube and in a favorable climate the
-plan would succeed admirably providing an excellent shelter for a large
-telescope at very low cost.
-
-Since a fork mount allows the tube to lie flat, such an instrument, up
-to say 8 or 10 inches aperture can be excellently protected by covers
-fitting snugly upon a base and light enough to lift off as a whole.
-
-The successful use of all these shelters however depends on climatic
-conditions. They require circumstances allowing observation in the
-open, as with tripod mounts, and afford no protection from wind or
-cold. Complete protection for the observer cannot be had, except by
-some of the devices shown in Chapter V, but conditions can be improved
-by permanent placement in an observatory, simple or elaborate, as the
-builder may wish.
-
-The word observatory may sound formidable, but a modest one can be
-provided at less expense than a garage for the humblest motor car.
-The chief difference in the economic situation is that not even the
-most derided car can be picked up and carried into the back hall for
-shelter, and it really ought not to be left out in the weather.
-
-The next stage of evolution is the telescope house with a sliding roof
-in one or more sections—ordinarily two. In this case the building
-itself is a simple square structure large enough to accommodate the
-instrument with maneuvering room around it. The side walls are carried
-merely high enough to give clearance to the tube when turned nearly
-flat and to give head room to the observer. The roof laps with a close
-joint in the middle and each half rolls on a track supported beyond the
-ends of the building by an out-rigger arranged in any convenient manner.
-
-When the telescope is in use the roof sections are displaced enough
-to give an ample clear space for observing, often wide open as shown
-in Fig. 177, which is the house of the 16 inch Metcalf photographic
-doublet at the Harvard Observatory. This instrument is in an open fork
-mount like that shown in Fig. 139.
-
-The sliding roof type is on the whole the simplest structure that can
-be regarded as an observatory in the sense of giving some shelter to
-the observer as well as the instrument. It gives ample sky room for
-practical purposes even to an instrument with a fork mount, since in
-most localities the seeing within 30° or so of the horizon is decidedly
-bad. If view nearer the horizon is needed it can readily be secured by
-building up the pier a bit.
-
-Numberless modifications of the sliding roof type will suggest
-themselves on a little study. One rather interesting one is used in
-the housing of the 24 inch reflector of the Harvard Observatory, 11
-feet 3 inches in focal length, the same of which the drive in its
-original dome is shown in Fig. 139. As now arranged the lower part
-of the observatory remains while the upper works are quite similar
-in principle to the housing of Dr. Common’s 3 foot reflector of Fig.
-176. The cover open is shown in Fig. 178. It will be seen that on the
-north side of the observatory there is an out-rigger on which the top
-housing slides clear of the low revolving turret which gives access to
-the ocular fitting used generally to carry the plate holder, and the
-eyepiece for following when required.
-
-The tube cannot be brought to the horizontal, but it easily commands
-all the sky-space that can advantageously be used in this situation,
-and the protection given the telescope when not in use is very
-complete. To close the observatory the tube is brought north and south
-and turned low and the sliding roof is then run back into its fixed
-position. The turret is very easily turned by hand.
-
-[Illustration: FIG. 178.—Turret Housing of the 24-inch Harvard
-Reflector.]
-
-Of course for steady work with the maximum shelter for observer
-obtainable without turning to highly special types of housing, the
-familiar dome is the astronomer’s main reliance. It is in the larger
-sizes usually framed in steel and covered with wood, externally
-sheathed in copper or steel. Sometimes in smaller domes felt covered
-with rubberoid serves a good purpose, and painted canvas is now and
-then used, with wooden framing.
-
-But even the smallest dome of conventional construction is heavy
-and rather expensive, and for home talent offers many difficulties,
-especially with respect to the shutter and shutter opening. A
-hemisphere is neither easy to frame nor to cover, and the curved
-sliding shutter is especially troublesome.
-
-[Illustration: FIG. 179.—The Original “Romsey” Observatory.]
-
-Hence for small observatories other forms of revolving roof are
-desirable, and quite the easiest and cheapest contrivance is that
-embodied in the “Romsey” type of observatory, devised half a century
-ago by that accomplished amateur the Rev. E. L. Berthon, vicar of
-Romsey. The feature of his construction is an unsymmetrical peak in the
-revolving roof which permits the ordinary shutter to be replaced by a
-hinged shutter like the skylight in a roof, exposing the sky beyond the
-zenith when open, and closing down over a coaming to form a water tight
-joint.
-
-Berthon’s original description of his observatory, which accommodated a
-9¼ inch reflector, may be found in Vol. 14 of the _English Mechanic
-and World of Science_ whence Fig. 179 is taken. In this plate Fig. 1
-shows the complete elevation and Fig. 2 the ground plan, each to a
-scale of a eighth of an inch to the foot. In the plan, _A,A_, are the
-main joists, _P_ the pier for the telescope, T that for the transit,
-and _C_ the clock. Figs. 3, 4, and 5 are of details. In the last named
-_A_ is a rafter, _b_ the base ring, _c_ the plate, _d_ one of the sash
-rollers carrying the roof, and _e_ a lateral guide roller holding the
-roof in place.
-
-The structure can readily be built without the transit shelter, and in
-fact now-a-days most observers find it easier to pick up their time by
-wireless. The main bearing ring is cut out of ordinary ⅞ inch board,
-in ten or a dozen, or more, sections according to convenience, done in
-duplicate, joints lapping, and put very firmly together with screws set
-up hard. Sometimes 3 layers are thus used.
-
-The roof in the original “Romsey” observatory was of painted canvas,
-but rubberoid or galvanized iron lined with roofing paper answers well.
-The shutter can be made single or double in width, and counterbalanced
-if necessary. The framing may be of posts set in the ground as here
-shown, or with sills resting on a foundation, and the walls of any
-construction—matched boards of any kind, cement on wire lath, hollow
-tile, or concrete blocks.
-
-Chambers’ _Handbook of Astronomy_ Vol. II contains quite complete
-details of the “Romsey” type of observatory and is easier to get at
-than the original description.
-
-A very neat adaptation of the plan is shown in Fig. 180, of which
-a description may be found in _Popular Astronomy_ =28=, 183. This
-observatory was about 9 feet in diameter, to house a 4 inch telescope,
-and was provided with a rough concrete foundation on which was built a
-circular wall 6 feet high of hollow glazed tile, well levelled on top.
-To this was secured a ring plate built up in two layers, carrying two
-circles of wooden strips with a couple of inches space between them for
-a runway. In this ran 6 two-inch truck castors secured to a similar
-ring plate on which was built up the frame of the “dome” arranged as
-shown. Altogether a very neat and workmanlike affair, in this case
-built largely by the owner but permitting construction at very small
-expense almost anywhere. Another interesting modification of the same
-general plan in the same volume just cited is shown in Fig. 181. This
-is also for a 4 inch refractor and the dome proper is but 8 feet 4
-inches in diameter. Like the preceding structure the foundation is of
-concrete but the walls are framed in spruce and sheathed in matched
-boards with a “beaver-board” lining.
-
-[Illustration: FIG. 180.—A More Substantial “Romsey” Type.]
-
-The ring plate is three-ply, 12 sections to the layer, and its mate on
-which the dome is assembled is similarly formed, though left with the
-figure of a dodecagon to match the dome. The weight is carried on four
-rubber tired truck rollers, and there are lateral guide rollers on the
-plan of those in Fig. 179.
-
-The dome itself however, is wholly of galvanized iron, in 12 gores
-joined with standing seams, turned, riveted, and soldered. There is a
-short shutter at the zenith sliding back upon a frame, while the main
-shutter is removed from the outside by handles.
-
-[Illustration: FIG. 181.—Detail of Light Metal Dome for Small
-Observatory.]
-
-Observatories of the Romsey or allied types can be erected at very
-moderate cost, varying considerably from place to place, but running
-at present say from $200 to $600, and big enough to shelter refractors
-of 4 to 6 inches aperture. The revolving roofs will range from 9 to 12
-feet in diameter. If reflectors are in use, those of about double these
-apertures can be accommodated since the reflector is ordinarily much
-the shorter for equal aperture.
-
-The sliding roof, not to say the sliding shelter, forms of housing cost
-somewhat less, depending on the construction adopted. Going to brick
-may double the figures quoted, but such solidity is generally quite
-needless, though it is highly desirable that the cover of a valuable
-instrument should be fire-proof and not easily broken open. The
-stealing of objectives and accessories is not unknown, and vandalism
-is a risk not to be forgotten. But to even the matter up, housing a
-telescope is rather an easy thing to accomplish, and as a matter of
-fact for the price of a very modest motor car one can both buy and
-house an instrument big enough to be of genuine service.
-
-
-
-
-CHAPTER XI
-
-SEEING AND MAGNIFICATION
-
-
-Few things are more generally disappointing than one’s first glimpse
-of the Heavens through a telescope. The novice is fed up with maps of
-Mars as a great disc full of intricate markings, and he generally sees
-a little wriggling ball of light with no more visible detail than an
-egg. It is almost impossible to believe that, at a fair opposition,
-Mars under the power of even the smallest astronomical telescope really
-looks as big as the full moon. Again, one looks at a double star
-to see not two brilliant little discs resplendent in color, but an
-indeterminate flicker void of shape and hue.
-
-The fact is, that most of the time over most of the world seeing
-conditions are bad, so that the telescope does not have a fair chance,
-and on the whole the bigger the telescope the worse the chance. One
-famous English astronomer, possessed of a fine refractor that would be
-reckoned large even now-a-days, averred that he had seen but one first
-class night in fifteen years past.
-
-The case is really much less bad than this implies, for even in rather
-unfavorable climates many a night, at some o’clock or other, will
-furnish an hour or two of pretty good seeing, while now and then,
-without any apparent connection with the previous state of the weather,
-a night will turn up when the pictures in the popular astronomies come
-true, the stars shrink to steady points set in clean cut rings, and no
-available power seems too high.
-
-One can get a good idea of the true inwardness of bad seeing by trying
-to read a newspaper through an opera glass across a hot stove. If the
-actual movements in the atmosphere could be made visible they would
-present a strange scene of turbulence—rushing currents taking devious
-courses up and around obstacles, slowly moving whirlpools, upward
-slants such as gulls hug on the quarter of a liner, great downward
-rushes dreaded by the aviator, and over it all incessant ripples in
-every direction.
-
-And movements of air are usually associated with changes of
-temperature, as over the stove, varying the refraction and contorting
-the rays that come from a distant star until the image is quite ruined.
-
-The condition for excellence of definition is that the atmosphere
-through which we see shall be homogeneous, whatever its temperature,
-humidity, or general trend of movement. Irregular refraction is
-the thing to be feared, particularly if the variations are sudden
-and frequent. Hence the common troubles near the ground and about
-buildings, especially where there are roofs and chimneys to radiate
-heat—even in and about an observatory dome.
-
-Professor W. H. Pickering, who has had a varied experience in
-climatic idiosyncrasies, gives the Northern Atlantic seaboard the bad
-preëminence of having the worst observing conditions of any region
-within his knowledge. The author cheerfully concurs, yet now and
-then, quite often after midnight, the air steadies and, if the other
-conditions are good, definition becomes fairly respectable, sometimes
-even excellent.
-
-Temperature and humidity as such, seem to make little difference, and a
-steady breeze unless it shakes the instrument is relatively harmless.
-Hence we find the most admirable definition in situations as widely
-different as the Harvard station at Mandeville, Jamaica; Flagstaff,
-Arizona 7000 feet up and snow bound in winter; Italy, and Egypt. The
-first named is warm and with very heavy rainfall and dew, the second
-dry with rather large seasonal variation of temperature, and the others
-temperate and hot respectively.
-
-Perhaps the most striking evidence of the importance of uniformity
-was noted by Evershed at an Indian station where good conditions
-immediately followed the flooding of the rice fields with its tendency
-to stabilize the temperature. Mountain stations may be good as at
-Flagstaff, Mt. Hamilton, or Mt. Wilson, or very bad as Pike’s Peak
-proved to be, probably owing to local conditions.
-
-In fact much of the trouble comes from nearby sources, atmospheric
-waves and ripples rather than large movements, ripples indeed often
-small compared with the aperture of the telescope and sometimes in or
-not far outside of the tube itself.
-
-Aside from these difficulties, there are still others which have to do
-with the transparency of the atmosphere with respect to its suspended
-matter. This does not affect the definition as such, but it cuts down
-the light to a degree that may interfere seriously with the observation
-of faint stars and nebulæ. The smoke near a city aggravates the
-situation, but in particular it depends on general weather conditions
-which may be persistent or merely temporary.
-
-Often seeing conditions may be admirable save for this lack of
-transparency in the atmosphere, so that study of the moon, of planetary
-markings and even of double stars, not too faint, may go on quite
-unimpeded. The actual loss of light may reach however a magnitude or
-more, while the sky is quite cloudless and without a trace of fog or
-noticeable haziness by day.
-
-There have been a good many nights the past year (1921) when Alcor
-(80 Ursæ Majoris) the tiny neighbor of Mizar, very nearly of the 4th
-magnitude, has been barely or not at all visible while the seeing
-otherwise was respectably good. Ordinarily stars of 6^_m_ should be
-visible in a really clear night, and in a brilliant winter sky in the
-temperate zones, or in the clear air of the tropics, a good many eyes
-will do better than this, reaching 6^_m_.5 or even 7^_m_, occasionally
-a bit more.
-
-The relation of air waves and such like irregularities to telescopic
-vision was rather thoroughly investigated by Douglass more than twenty
-years ago (Pop. Ast. =6=, 193) with very interesting results. In
-substance, from careful observation with telescopes from 4 inches up
-to 24 inches aperture, he found that the real trouble came from what
-one may call ripples, disturbances from say 4 inches wave length down
-to ¾ inch or less. Long waves are rare and relatively unimportant
-since their general effect is to cause shifting of the image as a whole
-rather than the destruction of detail which accompanies the shorter
-waves.
-
-This rippling of the air is probably associated with the contact
-displacements in air currents such as on a big scale become visible
-in cloud forms. Clearly ripples, marked as they are by difference
-of refraction, located in front of a telescope objective, produce
-different focal lengths for different parts of the objective and render
-a clean and stable image quite out of the question.
-
-In rough terms Douglass found that waves of greater length than half
-the aperture did not materially deteriorate the image, although they
-did shift it as a whole, while waves of length less than one third the
-aperture did serious mischief to the definition, the greater as the
-ripples were shorter, and the image itself more minute in dimension or
-detail.
-
-Hence there are times when decreasing the aperture of an objective by
-a stop improves the seeing considerably by increasing the relative
-length of the air waves. Such is in fact found to be the case in
-practical observing, especially when the seeing with a large aperture
-is decidedly poor. In other words one may often gain more by increased
-steadiness than he loses by lessened “resolving power,” the result
-depending somewhat on the class of observation which chances to be
-under way.
-
-And this brings us, willy-nilly, to the somewhat abstruse matter of
-resolving power, depending fundamentally upon the theory of diffraction
-of light, and practically upon a good many other things that modify the
-character of the diffraction pattern, or the actual visibility of its
-elements.
-
-When light shines through a hole or a slit the light waves are bent at
-the margins and the several sets, eventually overlapping, interfere
-with each other so as to produce a pattern of bright and dark elements
-depending on the size and shape of the aperture, and distributed about
-a central bright image of that aperture. One gets the effect well in
-looking through an open umbrella at a distant street light. The outer
-images of the pattern are fainter and fainter as they get away from the
-central image.
-
-Without burdening the reader for the moment with details to be
-considered presently, the effect in telescopic vision is that a star
-of real angular diameter quite negligible, perhaps 0.″001 of arc, is
-represented by an image under perfect conditions like Fig. 154, of
-quite perceptible diameter, surrounded by a system of rings, faint but
-clear-cut, diminishing in intensity outwards. When the seeing is bad no
-rings are visible and the central disc is a mere bright blur several
-times larger than it ought to be.
-
-The varying appearance of the star image is a very good index of the
-quality of the seeing, so that, having a clear indication of this
-appearance, two astronomers in different parts of the world can gain a
-definite idea of each other’s relative seeing conditions. To this end
-a standard scale of seeing, due largely to the efforts of Prof. W. H.
-Pickering, has come into rather common use. (H. A. =61= 29). It is as
-follows, based on observations with a 5 inch telescope.
-
-
-STANDARD SCALE OF SEEING
-
-1. Image usually about twice the diameter of the third ring.
-
-2. Image occasionally twice the diameter of the third ring.
-
-3. Image of about the same diameter as the third ring, and brighter at
-the centre.
-
-4. Disc often visible, arcs (of rings) sometimes seen on brighter stars.
-
-5. Disc always visible, arcs frequently seen on brighter stars.
-
-6. Disc always visible, short arcs constantly seen.
-
-7. Disc sometimes sharply defined, (_a_) long arcs. (_b_) Rings
-complete.
-
-8. Disc always sharply defined, (_a_) long arcs. (_b_) Rings complete
-all in motion.
-
-9. Rings, (_a_) Inner ring stationary, (_b_) Outer rings momentarily
-stationary.
-
-10. Rings all stationary, (_a_) Detail between the rings sometimes
-moving. (_b_) No detail between the rings.
-
-The first three scale numbers indicate very bad seeing; the next two,
-poor; the next two, good; and the last three, excellent. One can
-get some idea of the extreme badness of scale divisions 1, 2, 3, in
-realizing that the third bright diffraction ring is nearly 4 times the
-diameter of the proper star-disc.
-
-It must be noted that for a given condition of atmosphere the seeing
-with a large instrument ranks lower on the scale than with a small one,
-since as already explained the usual air ripples are of dimensions that
-might affect a 5 inch aperture imperceptibly and a 15 inch aperture
-very seriously.
-
-Douglass (loc. cit.) made a careful comparison of seeing conditions for
-apertures up to 24 inches and found a systematic difference of 2 or 3
-scale numbers between 4 or 6 inches aperture, and 18 or 24 inches. With
-the smallest aperture the image showed merely bodily motion due to air
-waves that produced serious injury to the image in the large apertures,
-as might be expected.
-
-There is likewise a great difference in the average quality of seeing
-as between stars near the zenith and those toward the horizon, due
-again to the greater opportunity for atmospheric disturbances in the
-latter case. Pickering’s experiments (loc. cit.) show a difference
-of nearly 3 scale divisions between say 20° and 70° elevation. This
-difference, which is important, is well shown in Fig. 182, taken from
-his report.
-
-The three lower curves were from Cambridge observations, the others
-obtained at various Jamaica stations. They clearly show the systematic
-regional differences, as well as the rapid falling off in definition
-below altitude 40°, which points the importance of making provision for
-comfortable observing above this altitude.
-
-[Illustration: FIG. 182.—Variation of Seeing with Altitude.]
-
-[Illustration: FIG. 183.—Airy’s Diffraction Pattern.]
-
-The relation of the diffraction pattern as disclosed in the moments
-of best seeing to its theoretical form is a very interesting one. The
-diffraction through a theoretically perfect objective was worked out
-many years ago by Sir George Airy who calculated the exact distribution
-of the light in the central disc and the surrounding rings.
-
-This is shown from the centre outwards in Fig. 183, in which the
-ordinates of the curve represent relative intensities while the
-abscissæ represent to an arbitrary scale the distances from the axis.
-It will be at once noticed that the star image, brilliant at its
-centre, sinks, first rapidly and then more slowly, to a minimum and
-then very gradually rises to the maximum of the first bright ring, then
-as slowly sinks again to increase for the second ring and so on.
-
-[Illustration: FIG. 184.—Diffraction Solid for a Star.]
-
-For unity brightness in the centre of the star disc the maximum
-brightness of the first ring is 0.017, of the second 0.004 and the
-third 0.0016. The rings are equidistant and the star disc has a radius
-substantially equal to the distance between rings. One’s vision does
-not follow down to zero the intensities of the rings or of the margin
-of the disc, so that the latter has an apparent diameter materially
-less than the diameter to the first diffraction minimum, and the rings
-themselves look sharper and thinner than the figure would show, even
-were the horizontal scale much diminished. The eye does not descend in
-the presence of bright areas to its final threshold of perception.
-
-One gains a somewhat vivid idea of the situation by passing to three
-dimensions as in Fig. 184, the “diffraction solid” for a star, a
-conception due to M. André (Mem. de l’Acad. de Lyon =30=, 49). Here
-the solid represents in volume the whole light received and the height
-taken at any point, the intensity at that point.
-
-A cross section at any point shows the apparent diameter of the disc,
-its distance to the apex the remaining intensity, and the volume above
-the section the remaining total light. Substantially 85% of the total
-light belongs to the central cone, for the theoretical distribution.
-
-Granting that the eye can distinguish from the background of the sky,
-in presence of a bright point, only light above a certain intensity,
-one readily sees why the discs of faint stars look small, and why shade
-glasses are sometimes useful in wiping out the marginal intensities
-of the solid. There are physiological factors that alter profoundly
-the appearance of the actual star image, despite the fact that the
-theoretical diffraction image for the aperture is independent of the
-star’s magnitude.
-
-Practically the general reduction of illumination in the fainter stars
-cuts down the apparent diameters of their discs, and reduces the number
-of rings visible against the background of the sky.
-
-The scale of the diffraction system determines the resolving power of
-the telescope. This scale is given in Airy’s original paper (Cambr.
-Phil. Trans. =1834= p. 283), from which the angle α to any maximum or
-minimum in the ring system is defined by
-
-sin α = _n_λ/_R_
-
-in which λ is numerically the wave length of any light considered and
-_R_ is the radius of the objective.
-
-We therefore see that the ring system varies in dimension inversely
-with the aperture of the objective and directly with the wave length
-considered. Hence the bigger the objective the smaller the disc and
-its surrounding ring system; and the greater the wave length, i.e. the
-redder the light, the bigger the diffraction system. Evidently there
-should be color in the rings but it very seldom shows on account of the
-faintness of the illumination.
-
-Now the factor _n_= is for the first dark ring 0.61, and for the
-first bright ring 0.81, as computed from Airy’s general theory, and
-therefore if we reckon that two stars will be seen as separate when
-the central disc of one falls on the first dark ring of the other the
-angular distance will be
-
-Sinα = 0.61 λ/_R_′
-
-and, taking λ at the brightest part of the spectrum i.e., about 560
-μμ, in the yellow green, with α taken for sin α, we can compute this
-assumed separating power for any aperture. Thus 560 μμ being very
-nearly 1/45,500 inch, and assuming a 5 inch telescope, the instrument
-should on this basis show as double two stars whose centres are
-separated by 1.″1 of arc.
-
-In actual fact one can do somewhat better than this, showing that
-the visible diameter of the central disc is in effect less than the
-diameter indicated by the diffraction pattern, owing to the reasons
-already stated. Evidently the brightness of the star is a factor in the
-situation since if very bright the disc gains apparent size, and when
-very faint there is sufficient difficulty in seeing one star, let alone
-a pair.
-
-The most thorough investigation of this matter of resolving power was
-made by the Rev. W. R. Dawes many years ago (Mem. R.A.S. =35=, 158).
-His study included years of observation with telescopes of different
-sizes, and his final result was to establish what has since been known
-as “Dawes’ Limit.”
-
-To sum up Dawes’ results he established the fact that on the average a
-one inch aperture would enable one to separate two 6th magnitude stars
-the centers of which were separated by 4.56″. Or, to generalize from
-this basis, the separating power of any telescope is for very nearly
-equal stars, moderately bright, 4″.56/_A_ where _A_ is the aperture of
-the telescope in inches.
-
-Many years of experience have emphasized the usefulness of this
-approximate rule, but that it is only approximate must be candidly
-admitted. It is a limit decidedly under that just assigned on the basis
-of the theory of diffraction for the central bright wave-lengths of
-the spectrum. Attempts have been made to square the two figures by
-assuming in the diffraction theory a wave length of 1/55,000 inch, but
-this figure corresponds to a point well up into the blue, of so low
-luminosity that it is of no importance whatever in the visual use of a
-telescope.
-
-The fact is that the visibility of two neighboring bright points as
-distinct, depends on a complex of physical and physiological factors,
-the exact relations of which have never been unravelled. To start with
-we have the principles of diffraction as just explained, which define
-the relation of the stellar disc to the center of the first dark ring,
-but we know that under no circumstances can one see the disc out to
-this limit, since vision fails to take cognizance of the faint rim of
-the image. The apparent diameter of the diffraction solid therefore
-corresponds to a section taken some distance above the base, the exact
-point depending on the sensitiveness of the particular observer’s eye,
-the actual brilliancy of the center of the disc, and the corresponding
-factors for the neighboring star.
-
-[Illustration: FIG. 185.—Diffraction Solid for a Disc.]
-
-Under favorable circumstances one would not go far amiss in taking the
-visible diameter of the disc at about half that reckoned to the center
-of the first dark ring. This figure in fact corresponds to what has
-been shown to be within the grasp of a good observer under favorable
-conditions, as we shall presently see.
-
-On the other hand, if the stars are decidedly bright there is increase
-of apparent diameter of the disc due to the phenomenon known as
-irradiation, the spreading of light about its true image on the retina
-which corresponds quite closely to the halation produced by a bright
-spot on a photographic plate.
-
-If, on the contrary, the stars are very faint the total amount of
-light available is not sufficient to make contrast over and above the
-background sufficient to disclose the two points as separate, while if
-the pair is very unequal the brighter one will produce sufficient glare
-to quite over-power the light from the smaller one so that the eye
-misses it entirely.
-
-A striking case of this is found in the companion to Sirius, an
-extremely difficult object for ordinary telescopes although the
-distance to the companion is about 10.6″ and its magnitude is 8.4,
-making a superlatively easy double for the very smallest telescope
-save for the overpowering effect of the light of the large star.
-Another notoriously difficult object for small telescopes is δ Cygni, a
-beautiful double of which the smaller component falls unpleasantly near
-the first diffraction maximum of the primary in which it is apt to be
-lost.
-
-“Dawes’ Limit” is therefore subject to many qualifying factors. Lewis,
-in the papers already referred to (Obs. =37=, 378) did an admirable
-piece of investigation in going through the double star work of about
-two score trained observers working with telescopes all the way from 4
-inches to 36 inches aperture.
-
-From this accumulation of data several striking facts stand out. First
-there is great difference between individual observers working with
-telescopes of similar aperture as respects their agreement with “Dawes’
-Limit,” showing the effect of variation in the physiological factors as
-well as instrumental ones.
-
-Second, there is also a very large difference between the facility of
-observing equal bright pairs and equal faint pairs, or unequal pairs of
-any kind, again emphasizing the physiological as well as the physical
-factors.
-
-Finally, there is most unmistakable difference between small and large
-apertures in their capacity to work up to or past the standard of
-“Dawes’Limit.” The smaller telescopes are clearly the more efficient
-as would be anticipated from the facts just pointed out regarding the
-different effect of the ordinary and inescapable atmospheric waves on
-small and large instruments.
-
-The big telescopes are unquestionably as good optically speaking as
-the small ones but under the ordinary working conditions, even as good
-as those a double star observer seeks, the smaller aperture by reason
-of less disturbance from atmospheric factors does relatively much the
-better work, however good the big instrument may be under exceptional
-conditions.
-
-This is admirably shown by the discussion of the beautiful work of the
-late Mr. Burnham, than whom probably no better observer of doubles has
-been known to astronomy. His records of discovery with telescopes of
-6, 9.4, 12, 18½ and 36 inches show the relative ease of working to
-the theoretical limit with instruments not seriously upset by ordinary
-atmospheric waves.
-
-With the 6 inch aperture Burnham reached in the average 0.53 of Dawes’
-limit, quite near the rough figure just suggested, and he also fell
-well inside Dawes’ limit with the 9.4 inch instrument. With none
-of the others did he reach it and in fact fell short of it by 15 to
-60%. All observations being by the same notably skilled observer
-and representing discoveries of doubles, so that no aid could have
-been gained by familiarity, the issue becomes exceedingly plain
-that size with all its advantages in resolving power brings serious
-countervailing limitations due to atmosphere.
-
-But a large aperture has besides its possible separating power one
-advantage that can not be discounted in “light grasp,” the power of
-discerning faint objects. This is the thing in which a small telescope
-necessarily fails. The “light grasp” of the telescope obviously depends
-chiefly on the area of the objective, and visually only in very minor
-degree on the absorption of the thicker glass in the case of a large
-lens.
-
-According to the conventional scale of star magnitudes as now in
-universal use, stars are classified in magnitudes which differ from
-each other by a light ratio of 2.512. a number the logarithm of which
-is 0.4, a relation suggested by Pogson some forty years ago. A second
-magnitude star therefore gives only about 40% of the light of a first
-magnitude star, while a third magnitude star gives again a little less
-than 40% of the light of a second magnitude star and so on.
-
-But doubling the aperture of a telescope increases the available area
-of the objective four times and so on, the “light grasp” being in
-proportion to the square of the aperture. Thus a 10 inch objective will
-take in and deliver nearly 100 times as much light as would a 1 inch
-aperture. If one follows Pogson’s scale down the line he will find that
-this corresponds exactly to 5 stellar magnitudes, so that if a 1 inch
-aperture discloses, as it readily does, a 9th magnitude star, a 10 inch
-aperture should disclose a 14th magnitude star.
-
-Such is substantially in fact the case, and one can therefore readily
-tabulate the minimum visible for an aperture just as he can tabulate
-the approximate resolving power by reference to Dawes’ limit. Fig. 186
-shows in graphic form both these relations for ready reference, the
-variation of resolving power with aperture, and that of “light grasp,”
-reckoned in stellar magnitudes.
-
-It is hardly necessary to state that considerable individual and
-observational differences will be found in each of these cases, in the
-latter amounting to not less than 0.5 to 1.0 magnitude either way.
-The scale is based on the 9th magnitude star just being visible with
-1 inch aperture, whereas in fact under varying conditions and with
-various observers the range may be from the 8th to 10th magnitude. All
-these things, however convenient, must be taken merely at their true
-value as good working approximations.
-
-Even the diffraction theory can be taken only as an approximation since
-no optical surface is absolutely perfect and in the ordinary refracting
-telescope there is a necessary residual chromatic aberration beside
-whatever may remain of spherical errors.
-
-[Illustration: FIG. 186.—Light-grasp and Resolving Power.]
-
-It is a fact therefore, as has been shown by Conrady (M.N. =79=
-575) following up a distinguished investigation by Lord Rayleigh
-(Sci. Papers =1= 415), that a certain small amount of aberration can
-be tolerated without material effect on the definition, which is
-very fortunate considering that the secondary spectrum represents
-aberrations of about 1/2,000 of the focal length, as we have already
-seen.
-
-The chief effect of this, as of very slight spherical aberration,
-is merely to reduce the maximum intensity of the central disc of
-the diffraction pattern and to produce a faint haze about it which
-slightly illuminates the diffraction minima. The visible diameter
-of the disc and the relative distribution of intensity in it is not
-however materially changed so that the main effect is a little loss and
-scattering of light.
-
-With larger aberrations these effects are more serious but where the
-change in length of optical path between the ray proceeding through the
-center of the objective and that from the margin does not exceed ¼λ
-the injury to the definition is substantially negligible and virtually
-disappears when the image is focussed for the best definition, the loss
-of maximum intensity in the star disc amounting to less than 20%.
-
-Even twice this error is not a very serious matter and can be for
-the most part compensated by a minute change of focus as is very
-beautifully shown in a paper by Buxton(M. N. =81=, 547), which should
-be consulted for detail of the variations to be effected.
-
-Conrady finds a given change _dp_ in the difference in lengths of the
-optical paths, related to the equivalent linear change of focus, _df_,
-as follows:—
-
-  _df_ = 8_dp_(_f_/_A_)²
-
-A being the aperture and f the focal length, which indicates for
-telescopes of ordinary focal ratio a tolerance of the order of ±0.01
-inch before getting outside the limit λ for variation of path.
-
-For instruments of greater relative aperture the precision of focus
-and in general the requirements for lessened aberration are far more
-severe, proportional in fact to the square of this aperture. Hence
-the severe demands on a reflector for exact figure. An instrument
-working at F/5 or F/6 is extremely sensitive to focus and demands great
-precision of figure to fall within permissible values, say ¼λ to ½λ,
-for _dp_.
-
-Further, with a given value of _dp_ and the relation established by
-the chromatic aberration, _i.e._, about _f_/2000, a relation is also
-determined between _f_ and _A_, required to bring the aberration within
-limits. The equation thus found is
-
-  _f_ = 2.8_A_²
-
-This practically amounts to the common F/15 ratio for an aperture of
-approximately 5 inches. For smaller apertures a greater ratio can be
-well used, for larger, a relatively longer focus is indicated, the
-penalty being light spread into a halo over the diffraction image and
-reducing faint contrasts somewhat seriously.
-
-This is one of the factors aside from atmosphere, interfering with
-the full advantage of large apertures in refractors. While as already
-noted small amounts of spherical aberration may be to a certain
-extent focussed out, the sign of _df_ must change with the sign of
-the residual aberration, and a quick and certain test of the presence
-of spherical aberration is a variation in the appearance of the image
-inside and outside focus.
-
-To emphasize the importance of exact knowledge of existing aberrations
-note Fig. 187, which shows the results of Hartmann tests on a typical
-group of the world’s large objectives. All show traces of residual
-zones, but differing greatly in magnitude and position as the attached
-scales show. The most conspicuous aberrations are in the big Potsdam
-photographic refractor, the least are in the 24 inch Lowell refractor.
-The former has since been refigured by Schmidt and revised data are not
-yet available; the latter received its final figure from the Lundins
-after the last of the Clarks had passed on.
-
-Now a glance at the curves shows that the bad zone of the Potsdam glass
-was originally near the periphery, (I), hence both involved large area
-and, from Conrady’s equation, seriously enlarged _df_ due to the large
-relative aperture at the zone. An aberrant zone near the axis as in the
-stage (III) of the Potsdam objective or in the Ottawa 15 inch objective
-is much less harmful for corresponding reasons. Such differences have
-a direct bearing on the use of stops, since these may do good in case
-of peripheral aberration and harm when the faults are axial. Unless
-the aberrations are known no general conclusions can be drawn as to
-the effect of stops. Even in the Lowell telescope shown as a whole in
-Fig. 188, the late Dr. Lowell found stops to be useful in keeping down
-atmospheric troubles and reducing the illumination although they could
-have had no effect in relation to figure. Fig. 188 shows at the head
-of the tube a fitting for a big iris diaphragm, controlled from the
-eye-end, the value of which was well demonstrated by numerous observers.
-
-There are, too, cases in which a small instrument, despite intrinsic
-lack of resolving power, may actually do better work than a big one.
-Such are met in instances where extreme contrast of details is
-sought, as has been well pointed out by Nutting (Ap. J. =40=, 33) and
-the situation disclosed by him finds amplification in the extraordinary
-work done by Barnard with a cheap lantern lens of 1½ inch diameter
-and 5½ inches focus (Pop. Ast., =6=, 452).
-
-[Illustration: FIG. 187.—Hartmann Tests of Telescopes [From Hartmann’s
-Measures].]
-
-The fact is that every task must seek its own proper instrument. And in
-any case the interpretation of observed results is a matter that passes
-far beyond the bounds of geometrical optics, and involves physiological
-factors that are dominant in all visual problems.
-
-With respect to the visibility of objects the general diffraction
-theory again comes into play. For a bright line, for example, the
-diffraction figure is no longer chiefly a cone like Fig. 183,
-but a similar long wedge-shaped figure, with wave-like shoulders
-corresponding to the diffraction rings. The visibility of such a line
-depends not only on the distribution of intensity in the theoretical
-wedge but on the sensitiveness of the eye and the nature of the
-background and so forth, just as in the case of a star disc.
-
-If the eye is from its nature or state of adaptation keen enough
-on detail but not particularly sensitive to slight differences of
-intensity, the line will very likely be seen as if a section were made
-of the wedge near its thin edge. In other words the line will appear
-thin and sharp as the diffraction rings about a star frequently do.
-
-With an eye very sensitive to light and small differences of contrast
-the appearance of absolutely the same thing may correspond to a section
-through the wedge near its base, in other words to a broad strip
-shading off somewhat indistinctly at the edges, influenced again by
-irradiation and the character of the background.
-
-If there be much detail simultaneously visible the diffraction patterns
-may be mixed up in a most intricate fashion and one can readily see the
-confusion which may exist in correlating the work of various observers
-on things like planetary and lunar detail.
-
-In the planetary case the total image is a complex of illuminated
-areas of diffraction at the edges, which may be represented as the
-diffraction solid of Fig. 185, in which the dotted lines show what may
-correspond fairly to the real diameter of the planet, the edge shading
-off in a way again complicated by irradiation.
-
-[Illustration: FIG. 188.—The Lowell Refractor Fitted with Iris
-Diaphragm.]
-
-Fancy detail superimposed on a disc of this sort and one has a vivid
-idea of the difficulty of interpreting observations.
-
-It would be an exceedingly good thing if everyone who uses his
-telescope had the advantage of at least a brief course in microscopy,
-whereby he would gain very much in the practical understanding of
-resolving power, seeing conditions, and the interpretation of the
-image. The principles regarding these matters are in fact very much the
-same with the two great instruments of research.
-
-Aperture, linear in the case of the telescope and the so-called
-numerical in the case of the microscope, bear precisely the same
-relation to resolution, the minimum resolvable detail being in each
-case directly proportional to aperture in the senses here employed.
-
-Further, although the turbulence of intervening atmosphere does
-not interfere with the visibility of microscopic detail, a similar
-disturbing factor does enter in the form of irregular and misplaced
-illumination. It is a perfectly easy matter to make beautifully
-distinct detail quite vanish from a microscopic image merely by
-mismanagement of the illumination, just as unsteady atmosphere will
-produce substantially the same effect in the telescopic image.
-
-In the matter of magnification the two cases run quite parallel, and
-magnification pushed beyond what is justified by the resolving power
-of the instrument does substantially little or no good. It neither
-discloses new detail nor does it bring out more sharply detail which
-can be seen at all with a lower power.
-
-The microscopist early learns to shun high power oculars, both from
-their being less comfortable to work with, and from their failing to
-add to the efficiency of the instrument except in some rare cases
-with objectives of very high resolving power. Furthermore in the
-interpretation of detail the lessons to be learned from the two
-instruments are quite the same, although one belongs to the infinitely
-little and the other to the infinitely great.
-
-Nothing is more instructive in grasping the relation between resolving
-power, magnification, and the verity of detail, than the study under
-the microscope of some well known objects. For example, in Fig. 189
-is shown a rough sketch of a common diatom, _Navicula Lyra_. The
-tiny siliceous valve appears thus under an objective of slightly
-insufficient resolving power. The general form of the object is
-clearly perceived, as well as the central markings, standing boldly out
-in the form which suggests the specific name. No trace of any finer
-detail appears and no amount of dexterity in arranging the illumination
-or increase of magnifying power will show any more than here appears,
-the drawing being one actually made with the camera lucida, using an
-objective of numerical aperture just too small to resolve the details
-of the diatoms on this particular slide.
-
-Figure 189_a_ shows what happens when, with the same magnifying power,
-an objective of slightly greater aperture is employed. Here the whole
-surface of the valve is marked with fine striations, beautifully
-sharp and distinct like the lines of a steel engraving. There is a
-complete change of aspect wrought by an increase of about 20% in the
-resolving power. Again nothing further can be made out by an increase
-of magnification, the only effect being to make the outlines a little
-hazier and the view therefore somewhat less satisfactory.
-
-[Illustration: FIG. 189.—The Stages of Resolution.]
-
-Finally in Fig. 189_b_ we have again the same valve under the same
-magnifying power, but here obtained from an objective of numerical
-aperture 60% above that used for the main figure. The sharp striæ now
-show their true character. They had their origin in lines of very
-clearly distinguished dots, which are perfectly distinct, and are due
-to the resolving power at last being sufficient to show the detail
-which previously merely formed a sharp linear diffraction pattern
-entirely incapable of being resolved into anything else by the eye,
-however much it might be magnified.
-
-Here one has, set out in unmistakable terms, the same kind of
-differences which appear in viewing celestial detail through telescopes
-of various aperture. What cannot be seen at all with a low aperture
-may be seen with higher ones under totally different aspects; while in
-each case the apparent sharpness and clarity of the image is somewhat
-extraordinary.
-
-Further in Fig. 189_b_ in using the resolving power of the objective
-of high numerical aperture, the image may be quite wrecked by a little
-carelessness in focussing, or by mismanagement of light, so that one
-would hardly know that the valve had markings other than those seen
-with the objectives of lower aperture, and under these circumstances
-added magnification would do more harm than good. In precisely the same
-way mismanagement of the illumination in Fig. 189_a_ would cause the
-striæ to vanish and with _Navicula Lyra_, as with many other diatoms,
-the resolution into striæ is a thing which often depends entirely on
-careful lighting, and the detail flashes into distinctness or vanishes
-with a suddenness which is altogether surprising. For “lighting” read
-“atmosphere,” and you have just the sort of conditions that exist in
-telescope vision.
-
-With respect to magnifying powers what has already been said is
-sufficient to indicate that on the whole the lowest power which
-discloses to the eye the detail within the reach of the resolving power
-of the objective is the most satisfactory.
-
-Every increase above this magnifies all the optical faults of the
-telescope and the atmospheric difficulties as well, beside decreasing
-the diameter of the emergent pencil which enters the eye, and thereby
-causing serious loss of acuity. For the eye like any other optical
-instrument loses resolving power with decrease of effective aperture,
-and, besides, a very narrow beam entering it is subject to the
-interference of entoptic defects, such as floating motes and the like,
-to a serious extent.
-
-Figure 190 shows from Cobb’s experiments (Am. Jour. of Physiol., =35=,
-335) the effect of reduction of ocular aperture upon acuity. The curve
-shows very plainly that for emergent pencils below a millimeter (1/25
-inch) in diameter, visual acuity falls off almost in direct proportion
-to the decreasing aperture. Below this figure there can be only
-incidental gains, such as may be due to opening up double stars and
-simultaneously so diminishing the general illumination as to render the
-margins of the star discs a little less conspicuous.
-
-An emergent pencil of this diameter is not quite sufficient for the
-average eye to utilize fully the available resolving power and some
-excess of magnification even though it actually diminishes visual
-acuity materially, may be of some service.
-
-[Illustration: FIG. 190.—Resolving Power of the Eye.]
-
-Increased acuity will of course be gained for the same magnification
-in using an objective of greater diameter, to say nothing of increased
-resolving power, at the cost, of course, of relatively greater
-atmospheric troubles.
-
-To come down to figures as to the resolving power of the eye, often
-repeated experiments have shown that two points offering strong
-contrast with the background can be noted as separate by the normal eye
-when at an angular separation of about 3′ of arc. People, as we have
-seen, differ considerably in acuity so that now and then individuals
-will considerably better this figure, while others, far less keen
-sighted, may require a separation of 4′ or even 5′.
-
-The pair of double stars ε_{1}, ε_{2}, Lyræ, separated by 3′ 27″
-mags. nearly 4 and 5 respectively, can be seen as separate by those
-of fairly keen vision, while Mizar and Alcor, 11′ apart, seem thrown
-wide to nearly every one. On the other hand the writer has never known
-anybody who could separate the two components of Asterope of the
-Pleiades, distant a scant 2½ but of mags. 6.5 and 7.0 only, while
-Pleione and Atlas, distance about 5¼′, mags. 6.5 and 4, are very
-easy.
-
-Assuming for liberality that the separation constant is in the
-neighborhood of 5′ one can readily estimate the magnification that for
-any telescope will take full advantage of its resolving power. As we
-have already seen this resolving power is practically 4.″56/_A_ for
-equal stars moderately bright. An objective of 4.56′ inches aperture
-has a resolving constant of 1″ and to develop this should take a
-magnification of say 300, about 65 to the inch of aperture, requiring a
-focal length of ocular about 0.20 to 0.25 inch for telescopes of normal
-relative aperture, and pushing the emergent pencil down to little more
-than 0.02 inch,—rather further than is physiologically desirable.
-Except for these extreme stunts of separation, half to two thirds this
-power is preferable and conditions under which one can advantageously
-go above this limit are very rare indeed.
-
-A thoroughly good objective or mirror will stand quite 100
-magnification to the inch without, as the microscopist would say,
-“breaking down the image,” but in at least nine cases out of ten the
-result will be decidedly unsatisfactory.
-
-As the relative aperture of the instrument increases, other things
-being equal, one is driven to oculars of shorter and shorter focus
-to obtain the same magnification and soon gets into trouble. Very
-few oculars below 0.20 inch in focus are made, and such are rarely
-advisable, although occasionally in use down to 0.15 inch or
-thereabouts. The usual F/15 aperture is a figure quite probably as much
-due to the undesirability of extremely short focus oculars as to the
-easier corrections of the objective.
-
-In the actual practice of experienced observers the indications of
-theory are well borne out. Data of the habits of many observers of
-double stars are of record and the accomplished veteran editor of _The
-Observatory_, Mr. T. Lewis, took the trouble in one of his admirable
-papers on “Double Star Astronomy” (Obs. =36=, 426) to tabulate from the
-original sources the practice of a large group of experts. The general
-result was to show the habitual use with telescopes of moderate size
-of powers around 50 per inch of aperture, now and then on special
-occasions raised to the neighborhood of 70 per inch.
-
-But the data showed unequivocally just what has been already indicated,
-that large apertures, suffering severely as they generally do from
-turbulence of the air, will not ordinarily stand their due proportion
-of magnification. With the refractors of 24 inches aperture and
-upwards the records show that even in this double star work, where, if
-anywhere, high power counts, the general practice ran in the vicinity
-of 30 per inch of aperture.
-
-Analyzing the data more completely in this respect Mr. Lewis found that
-the best practise of the skilled observers studied was approximately
-represented by the empirical equation
-
-_m_ = 140 √_A_
-
-Of course the actual figures must vary with the conditions of location
-and the general quality of the seeing, as well as the work in hand. For
-other than double star work the tendency will be generally toward lower
-powers. The details which depend on shade perception rather than visual
-acuity are usually hurt rather than helped when magnified beyond the
-point at which they are fairly resolved, quite as in the case of the
-microscope.
-
-Now and then they may be made more distinct by the judicious use of
-shade glasses. Quite apart from the matter of the high powers which can
-advantageously be used on a telescope, one must for certain purposes
-consider the lowest powers which are fairly applicable. This question
-really turns on the largest utilizable emergent pencil from the eye
-piece. It used to be commonly stated that ⅛ inch for the emergent
-pencil was about a working maximum, leading to a magnification of 8
-per inch of aperture of the objective. This in view of our present
-knowledge of the eye and its properties is too low an estimate of
-pupillary aperture. It is a fact which has been well known for more
-than a decade that in faint light, when the eye has become adapted to
-its situation, the pupil opens up to two or three times this diameter
-and there is no doubt that a fifth or a fourth of an inch aperture
-can be well utilized, provided the eye is properly dark-adapted. For
-scrutinizing faint objects, comet sweeping and the like, one should
-therefore have one ocular of very wide field and magnifying power of 4
-or 5 per inch of aperture, the main point being to secure a field as
-wide is practicable. One may use for such purposes either a very wide
-field Huyghenian, or, if cross wires are to be used, a Kellner form.
-Fifty degrees of field is perfectly practicable with either. As regards
-the rest of the eyepiece equipment the observer may well suit his own
-convenience and resources. Usually one ocular of about half the maximum
-power provided will be found extremely convenient and perhaps oftener
-used than either the high or low power. Oculars of intermediate power
-and adapted for various purposes will generally find their way into any
-telescopic equipment. And as a last word do not expect to improve bad
-conditions by magnifying. If the seeing is bad with a low power, cap
-the telescope and await a better opportunity.
-
-
-
-
-APPENDIX
-
-WORK FOR THE TELESCOPE
-
-
-To make at first hand the acquaintance of the celestial bodies is, in
-and of itself, worth the while, as leading the mind to a new sense of
-ultimate values. To tell the truth the modern man on the whole knows
-the Heavens less intimately than did his ancestors. He glances at his
-wrist-watch to learn the hour and at the almanac to identify the day.
-The rising and setting of the constellations, the wandering of the
-planets among the stars, the seasonal shifting of the sun’s path—all
-these are a sealed book to him, and the intricate mysteries that lie in
-the background are quite unsuspected.
-
-The telescope is the lifter of the cosmic veil, and even for merely
-disclosing the spectacular is a source of far-reaching enlightenment.
-But for the serious student it offers opportunities for the genuine
-advancement of human knowledge that are hard to underestimate. It is
-true that the great modern observatories can gather information on
-a scale that staggers the private investigator. But in this matter
-fortune favors the pertinacious, and the observer who settles to a line
-of deliberate investigation and patiently follows it is likely to find
-his reward. There is so much within the reach of powerful instruments
-only, that these are in the main turned to their own particular spheres
-of usefulness.
-
-For modest equipment there is still plenty of work to do. The study
-of variable stars offers a vast field for exploration, most fruitful
-perhaps with respect to the irregular and long-period changes of which
-our own Sun offers an example. Even in solar study there are transient
-phenomena of sudden eruptions and of swift changes that escape the eye
-of the spectro-heliograph, and admirable work can be done, and has been
-done, with small telescopes in studying the spectra of sun spots
-
-Temporary stars visible to the naked eye or to the smallest instruments
-turn up every few years and their discovery has usually fallen to the
-lot of the somewhat rare astronomer, professional or amateur, who knows
-the field of stars as he knows the alphabet. The last three important
-novæ fell to the amateurs—two to the same man. Comets are to be had
-for the seeking by the persistent observer with an instrument of fair
-light-grasp and field; one distinguished amateur found a pair within a
-few days, acting on the theory that small comets are really common and
-should be looked for—most easily by one who knows his nebulæ, it should
-be added.
-
-And within our small planetary system lies labor sufficient for
-generations. We know little even about the superficial characters of
-the planets, still less about their real physical condition. We are not
-even sure about the rotation periods of Venus and Neptune. The clue to
-many of the mysteries requires eternal vigilance rather than powerful
-equipment, for the appearance of temporary changes may tell the whole
-story. The old generation of astronomers who believed in the complete
-inviolability of celestial order has been for the most part gathered to
-its fathers, and we now realize that change is the law of the universe.
-Within the solar system there are planetary surfaces to be watched,
-asteroids to be scanned for variability or change of it, meteor swarms
-to be correlated with their sources, occultations to be minutely
-examined, and when one runs short of these, our nearest neighbor the
-Moon offers a wild and physically unknown country for exploration. It
-is suspected with good reason of dynamic changes, to say nothing of the
-possible last remnants of organic life.
-
-Much of this work is well within the useful range of instruments of
-three to six inches aperture. The strategy of successful investigation
-is in turning attention upon those things which are within the scope of
-one’s equipment, and selecting those which give promise of yielding to
-a well directed attack. And to this end efforts correlated with those
-of others are earnestly to be advised. It is hard to say too much of
-the usefulness of directed energies like those of the Variable Star
-Association and similar bodies. They not only organize activities to
-an important common end, but strengthen the morale of the individual
-observer.
-
-
-
-
-INDEX
-
-
-  A
-
-  Abbé, roof prism, 162
-
-  Aberration, compensated by minute change of focus, 266
-    illuminates the diffraction minima, 265
-    relation determines of focus and aperture, 266
-
-  Achromatic long relief ocular, 146
-    objective, 77
-
-  Achromatism, condition for, 78
-    determination of, 78
-    imperfection of, 87
-
-  Adjustment where Polaris invisible, 235
-
-  Air waves, length of, 255
-
-  Alt-azimuth mount for reflector, 102
-    mounts, with slow motions, 102
-    setting up an, 228
-
-  Anastigmats, 84
-
-  Annealing, pattern of strain, 68
-
-  Astigmatism, 84, 209
-    of figure, 210
-
-  Astronomy, dawn of popular, 19
-
-
-  B
-
-  Bacon, Roger, alleged description of telescopes, 6
-
-  Barlow lens, 152
-
-  “Bent,” objective, 86
-
-  Binocular, 2
-    advantage of, exaggerated, 151
-    for strictly astronomical use, 152
-    telescopes for astronomical use, 163
-
-
-  C
-
-  Camouflage, in optical patents, 97
-
-  Cassegrain, design for reflecting telescope, 22
-
-  Cassegrain, sculptor and founder of statues, 22
-
-  Cell, taking off from a telescope, 202
-
-  Chromatic aberration, 11, 76
-    investigation of, 210
-    correction, differences in, 91
-    error of the eye, 90
-
-  Clairault’s condition, 81
-    two cemented forms for, 81
-
-  Clarks, portable equatorial mounting, 109
-    terrestrial prismatic eyepiece, 158
-
-  Clock, the cosmic, 233
-
-  Clock drive, 110, 174
-
-  Clock mechanism, regulating rate of motor, 179
-
-  Coddington lens, 137
-
-  Cœlostat constructions, 126
-    tower telescopes, 127
-
-  Color correction, commonly used, 211
-    examined by spectroscope, 211
-    of the great makers, 90
-
-  Coma-free, condition combined with Clairault’s, 83
-
-  Comet seeker, Caroline Herschel’s 118
-    seekers with triple objective, 119
-
-  Crowns distinguished from flints, 64
-
-  Curves, struggle for non-spherical, 18
-
-
-  D
-
-  Davon micro-telescope, 148
-
-  Dawes’ Limit, 261
-    in physiological factors, 263
-
-  Declination circle, 108
-    adjustment of, 239
-
-  Declination circle, adjustment by, 237
-    facilitates setting up instrument, 110
-
-  Definition condition for excellence of, 254
-    good in situations widely different, 254
-
-  DeRheita, 12
-    constructed binoculars, 13
-    terrestrial ocular, 13
-
-  Descartes’ dioptrics, publication of, 11
-    lens with elliptical curvature, 12
-
-  Dew cap, 219
-
-  Diaphragms, importance of, 43
-
-  Diffraction figure for bright line, 269
-    pattern, 256
-    solid, apparent diameter of, 262
-    solid of planet, 269
-    solid for a star, 260
-    spectra, 190
-    system, scale of, 260
-    varies inversely with aperture, 260
-    through objective, 258
-
-  Digges, account suggests camera obscura, 7
-
-  Dimensions, customary, telescope of, 24
-
-  Discs, inspection of glass, 66
-    roughing to form, 69
-
-  Distortion, 86
-
-  Dolland, John, 28
-      published his discovery of achromatism, 29
-    Peter, early triple objective, 29
-
-  Dome wholly of galvanized iron, 250
-
-  Domes, 246
-
-  Driving clock, a simple, 174
-    pendulum controlled, 177
-    clocks spring operated, 175
-
-
-  E
-
-  English equatorial, 110
-    mounts, mechanical stability of, 113
-
-  Equatorial, adjustments of, 230
-
-  Equatorial, coudé, 124
-    mount, different situations in using, 229
-    mount, first by Short, 104
-    mount, pier overhung, 115
-    mount in section, 107
-    two motions necessary in, 106
-
-  Equilibrating levers, devised by T. Grubb, 39
-
-  Evershed, direct vision solar spectroscope, 189
-
-  Eye lens, simple, preferred by Sir W. Herschel, 136
-
-  Eyepiece, compensating, 142
-    Huygenian, 139
-    Huygenian, achromatism of, 140
-    Huygenian, with cross wires, 140
-    Huygenian, field of, 141
-    Huygenian focal length of, 143
-    measuring focus of, 136
-    microscope form, 147, 148
-    monocentric, 139
-    a simple microscope, 134
-    Tolles solid, 141
-
-
-  F
-
-  Field, curvature of, 85
-    glass, arrangement of parts, 151
-      Galilean, 150
-      lens diameter possible, 150
-
-  Field lens, 139
-
-  Figuring locally, 73
-    process of, 73
-
-  Filar micrometer, 172
-
-  Finder, 108, 132
-    adjustment of, 230
-
-  Fine grinding, 69
-
-  Fixed eyepiece mounts, 118
-
-  Flints, highly refractive due to Guinand, 36
-
-  Foucault, 39
-    development of silver on glass reflector, 41
-    knife edge test, 212
-
-  Foucault, methods of working and testing, 41
-
-  Fraunhofer, 36
-    applied condition of absence of coma, 82
-    form of objectives, 37
-    long list of notable achievements, 38
-
-  “Front view” telescope, 32
-    mechanical difficulty of, 33
-
-  Furnaces, glass, classes of, 59
-
-
-  G
-
-  Galilean telescope, small field of, 9
-
-  Galileo, exhibited telescope to senators of Venice, 8
-    grasps the general principles, 7
-    produces instrument magnifying 32 times, 8
-
-  Gascoigne, William, first using genuine micrometer, 12
-
-  Gauss, Objective, 82
-
-  Gerrish, application of drive, 181
-    motor drive, 179
-
-  Ghosts, 137
-
-  Glass, dark, as sunshade, 166
-    forming and annealing, 62
-    inspection of raw, 61
-    losses by volatilization, 58
-    materials of, 59
-    origin of, 57
-    persistent bubbles in, 58
-    a solid solution, 57
-
-  Grating spectroscopes, 190
-
-  Gratings, spectroscope, 189
-
-  Gregory, James, described construction which bears his name, 19
-    failed of material success, 20
-
-  Grubb, Sir Howard, objectives, 74
-
-  Guinand, Pierre Louis, improvements in optical glass, 36
-
-
-  H
-
-  Hadley, disclosed test for true figure, 27
-    John, real inventor of reflector, 25
-
-  Hadley’s reflector, tested with satisfactory results, 26
-
-  Hall, Chester Moor, designed first achromatic telescope, 27
-    had telescopes made as early as 1733, 27
-
-  Hand telescope, magnifying power, 150
-    monocular, 151
-
-  Hartmann test, 213
-    on large objectives, 267
-    principle of, 214
-
-  Hartness, turret telescope, 130, 131
-
-  Heliometer, principle of, 171
-
-  Hensoldt, prism form, 163
-
-  Herschel’s discovery of Uranus, 32
-    forty foot telescope, 34
-    Sir John, 35
-    Sir John, proposed defining condition, 81
-    Sir William, 31
-
-  Herschel’s time, instruments of, 35
-
-  Hevelius, construction for objective of 150 feet, 17
-    directions for designing Galilean and Keplerian telescopes, 14
-    invention of first periscope, 15
-    Johannes, 13
-    mention of advantage of plano convex lens, 14
-    mentions telescope due to DeRheita, 14
-
-  Housing reflector of 36 inch aperture, 243
-    rolling on track, 242
-    simplest instrument for fixed, 241
-
-  Huygens, Christian, devised methods of grinding & polishing, 16
-
-  Huygens’ eyepiece, introduction of, 24
-
-  Huygens, sketch of Mars, 16
-
-
-  I
-
-  Image, correct extra focal, 208
-    critical examination of, 204
-
-  Image, curvature of, 87
-    seen without eyepiece, 134
-    showing unsymmetrical coloring, 208
-
-  Interference rings, eccentric, 205
-
-  Irradiation, 262
-
-
-  J
-
-  Jansen, Zacharius, 4
-
-
-  K
-
-  Kellner, ocular, 145
-
-  Kepler, astronomical telescope, 10
-    differences of from Galilean form, 10
-
-  Knife edge test of parabolic mirror, 212
-
-
-  L
-
-  Lacquer, endurance of coating, 223
-
-  Latitude scale, 232
-
-  Lenses, determinate forms for, 80
-
-  Lens, magnifying power of, 134
-    “crossed,” 24
-    polishing the fine ground, 70
-    power of, 78
-    triple cemented, a useful ocular, 138
-    simple achromatic, 137
-    single, has small field, 137
-    spotted, cleaning of, 217
-
-  Light grasp and resolving power, 265
-    small telescope fails in, 264
-
-  Light ratio of star magnitudes, 264
-
-  Light transmitted by glass, 53
-
-  Lippershey, Jan, 2
-    discovery, when made, 5
-    retainer to, 3
-
-  Lunette à Napoleon Troisiéme, 154, 155, 162
-
-
-  M
-
-  Magnifying power, directly as ratio of increase in tangent, 135
-    powers, increase of, 273
-
-  Marius, Simon, 5
-    used with glasses from spectacles, 5
-
-  Marius, picked up satellites of Jupiter, 5
-
-  Meridian photometer, 194
-
-  Metius, James, 4
-
-  Metius, tale of, 4
-
-  Micrometer, double image, 171
-    square bar, 171
-
-  Micrometers, 168
-
-  Micrometry, foundations of, 12
-
-  Mirror’s, aberrations of, 92
-    adjustment of, 206
-    concave spherical, 92
-    final burnishing of, 226
-    hyperboloidal, 96
-    lacquer coating for surface, 221
-    mounting, by Browning, 49
-    parabolic oblique, shows aberration, 95
-    surface, prevention of injury to, 220
-
-  Mittenzwey ocular, 141
-
-  Mountain stations, good or very bad, 254
-
-  Mounts, alt-azimuth and equatorial, 98
-
-  Myopia, glasses for, came slowly, 2
-
-
-  N
-
-  Navicula Lyra, stages of resolution of, 271
-
-  Newton, abandoned parabolic mirror, 21
-    blunder in experiment, 20
-    gave little information about material for mirrors, 23
-    Isaac, attempt at a reflector, 20
-
-  Normal spectra, 190
-
-
-  O
-
-  Objective, adjustable mount for, 44
-    adjusting screws of, 44
-    Clark’s form, 83
-    cleansing, 203
-    examination of, 202
-
-  Objective, four-part, 85
-    Fraunhofer flint-ahead, 83
-    how to clean, 216
-    spacers, to take out, 217
-    typical striæ in, 203
-
-  Objective prism, photographing with, 185, 187
-
-  Objectives, crown glass equiconvex, 80
-    over-achromatized, 90
-    rated on focal length for green 24
-
-  Observatories, cost of Romsey, 252
-
-  Observatory at small expense, 249
-    Romsey, description of, 249
-    with simple sliding roof, 245
-
-  Observing box, 229
-
-  Oblique fork alt-azimuth, 100
-
-  Ocular, apparent angular field of, 146
-    terrestrial, 147
-    Tolles terrestrial, 147
-    typical form, 45
-
-  Oculars, radius of curvature of image in, 146
-    undesirability of short focus, 275
-
-  Open fork mount, 115
-    well suited to big reflectors, 117
-
-  Optical axis, to adjust declination of, 238
-
-  Optical glass, classes of, 63
-    data and analysis of, 64
-    industry, due to single man, 36
-    production of, 60
-
-  Orthoscopic ocular, 145
-
-
-  P
-
-  Parallactic mount, 104
-
-  Petition for annulment of Dolland’s patent, 29
-
-  Photometer, artificial star Zöllner, 194
-    extinction, 198
-    photoelectric cell, 199
-    precision of astronomical, 199
-    selenium cell, 199
-    Zöllner, 197
-
-  Photometers, three classes in stellar, 193
-
-  “Photo-visual, objective,” 89
-
-  Pillar-and-claw stand, 98
-
-  Pillar mount, 240
-
-  Pitch, optician’s, 71
-
-  Placement for tripod legs, 236
-
-  Polar and coudé forms of reflector, 125
-    axis, adjustment of by level, 232
-    axis, alignment to meridian, 232
-    axis, setting with finder altitude of, 234
-    telescope, 119, 122
-
-  Polaris, hour angle of, 233
-    a variable star, 199
-
-  Polarizing photometer, 193
-
-  Pole, position, 234
-
-  Polishing machine, 70
-    surface of tool, 72
-    tool, 71
-
-  Porro’s second form, 157
-    work, original description of, 156
-
-  Porta, description unintelligible, 7
-
-  Portable equatorial, adjustment of, 230
-    telescopes, mounting of, 228
-
-  Porter polar reflector, 130
-
-  Position angle micrometer of Lowell Observatory, 173
-
-  Powers, lowest practicable, 276
-
-  Prismatic inversion, Porro’s first form, 155
-
-  Prismatic inverting system, the first, 154
-
-  Prisms, Dove’s, 154
-
-  Prism field glasses, stereoscopic effect of, 159
-
-  Prism glass, 152
-    loss of light in, 160
-    objectives of, 161
-    weak points of, 160
-
-
-  R
-
-  Resolving constant, magnification to develop, 275
-    power and verity of detail, 2
-    power of the eye, 274
-
-  Reticulated micrometer, 169
-
-  Reversion prism, 153
-
-  Right ascension circle, 108
-
-  Ring micrometer, 169
-    computation of results of, 170
-
-  Ring system faults due to strain, 205
-
-  “Romsey” observatory type, 248
-
-  Rack motion in altitude, 100
-
-  Ramsden, ocular, 144
-
-  Reflection, coefficient of, from silvered surface, 54
-
-  Reflector costs, 55
-    cover for, 242
-    development in England, 41
-    for astrophysical work, 56
-    light-grasp of, 53
-    relative aperture of, 50
-    section of Newtonian, 45
-    skeleton construction, 49
-    suffers from scattered light, 56
-    working field of, 55
-
-  Refractive index, 63
-
-  Refractors and reflectors, relative advantages of, 52
-    few made after advent of reflector, 27
-    in section, 43
-    light transmission of, 53
-
-  Refractors, relative equivalent apertures of, 54
-    tubes of, 42
-
-
-  S
-
-  Scheiner, Christopher, use of Kepler’s telescope, 11
-    devised parallactic mount, 11
-
-  Secondary spectrum, 87
-    new glasses reducing, 88
-
-  Seeing, 257
-    conditions, for difference of aperture, 257
-    conditions generally bad, 253
-    standard scale of, 256
-    true inwardness of bad, 253
-
-  Separating power, to compute, 261
-
-  Short, James, mastered art of figuring paraboloid, 27
-    took up Gregorian construction with success, 27
-
-  Shortened telescope, 152
-
-  Sights, on portable mount, 229
-
-  Silver films, condition of, 54
-
-  Silvering, Ludin’s process, 225
-    processes, 222
-    process, Dr. Brashear’s, 222
-
-  Sine condition, Abbé’s, 82
-
-  Slit, spectroscope, Abbé type, 184
-
-  Snow cœlostat telescope, 127
-
-  Solar diagonal, 166
-    eye piece diaphragms in, 168
-    early spectroscopes, 188
-    polarizing eyepiece, 167
-    spectroscope, 187
-
-  Spacers, 44, 218
-
-  Spectacle lenses, combination of, 2
-
-  Spectacles for presbyopia, 2
-    invention of, 1
-
-  Spectra, visibility of stellar, 183
-
-  Spectro-heliograph, principle of, 191
-    simple type of Hale’s, 191
-
-  Spectroscope, 182
-    construction of astronomical, 182
-    of Lowell refractor, 185
-    ocular, McClean form, 183
-
-  Specula, small, methods of support, 49
-
-  Speculum metal composition of, 24
-
-  Sphenoid prisms, 158, 163
-
-  Spherical aberration, 11
-    amount of, 80
-    annulling in both directions, 84
-    examination for, 207
-    quick test of, 267
-    remedy for, 79
-    concave mirror, errors of, 22
-
-  Star, appearance of, 204
-    artificial, 66, 203
-    diagonal, 165
-    disc, apparent diameter of, 259
-    image of reflector, 206
-
-  Steinheil, achromatic ocular, 144
-    Karl August, silvering specula, 39
-
-  Striæ, location of, 67
-
-  Surface, treatment of deterioration of, 218
-
-
-  T
-
-  Taylor, triplets with reduced secondary spectrum, 89
-
-  Telescopes, choice and purchase of, 201
-    Early in 1610 made in England, 6
-    first, 3
-    the first astronomical, 9
-    improvement of early, 11
-    lineage of, 1
-    name devised, 9
-
-  Telescopes, portable and fixed, 108
-    1609, for sale in Paris, 5
-    size and mounting of early, 14
-
-  Telescopic vision, discovery of, 2
-
-  Templets, designed curves of, 69
-
-  Tests for striæ and annealing, 68
-
-  Transparency, lack of in atmosphere, 255
-
-  Triplet, cemented, 85
-
-  Turret housing of reflector, 244
-
-
-  V
-
-  Variable stars, 192
-
-
-  W
-
-  Wedge calibrated by observation, 197
-    photographic, 197
-    photometer, 197
-
-  Wind, shelter from, 240
-
-
-  Z
-
-  Zeiss, binocular of extreme stereoscopic effect, 161
-
-  Zöllner, photometer modification of, 198
-
-  Zonal aberration, 209
-
-
-       *       *       *       *       *
-
-
-Transcriber's Notes
-
-Obvious typographical errors have been silently corrected. Variations
-in hyphenation and accents have been standardised but all other
-spelling and punctuation remains unchanged.
-
-Italics are represented thus _italic_, bold thus =bold=, subscript thus
-_{s} and underline thus underline=.
-
-In caption of Fig. 49.—Spherical Aberration of Concave Lens. Concave
-has been changed to Convex
-
-In “An objective of 4.56′ inches aperture has a resolving constant of
-1″ and to develop this should take a magnification of say 300,” 1″ has
-been hand altered in the original and may be 1′.
-
-The table “Characteristics of Optical Glasses″ has been divided to fit
-within the width restriction.
-
-
-
-
-
-End of the Project Gutenberg EBook of The Telescope, by Louis Bell
-
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-The Project Gutenberg EBook of The Telescope, by Louis Bell
-
-This eBook is for the use of anyone anywhere in the United States and most
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-Title: The Telescope
-
-Author: Louis Bell
-
-Release Date: December 16, 2016 [EBook #53740]
-
-Language: English
-
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-*** START OF THIS PROJECT GUTENBERG EBOOK THE TELESCOPE ***
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-</pre>
-
-<hr class="chap" />
-
-
-
-
-
-<p class="half-title">THE TELESCOPE</p>
-
-
-
-<div class="figcenter">
-<img src="images/i-002.jpg"  alt="Original of plain text under" />
-</div>
-<div class="bbox">
-<p class="center"><i><big>McGraw-Hill Book Co. Inc.</big></i><br />
-
-<small>PUBLISHERS OF BOOKS FOR</small></p>
-
-<p class="center">
-Coal Age ▿ Electric Railway Journal<br />
-Electrical World ▿ Engineering News-Record<br />
-American Machinist ▿ Ingeniería Internacional<br />
-Engineering &amp; Mining Journal ▿ Power<br />
-Chemical &amp; Metallurgical Engineering<br />
-Electrical Merchandising</p></div>
-
-<hr class="chap" />
-
-
-<div class="figcenter">
-<img src="images/i_frontis.jpg" alt="" />
-<div class="caption"> Galileo’s Telescopes. (<i>Frontispiece</i>)<br />
-(<i>Bull. de la Soc. Astron. de France.</i>)</div>
-</div>
-
-
-
-
-<h1>THE TELESCOPE</h1>
-
-<p class="center spaced">BY<br />
-
-LOUIS BELL, <span class="smcap">Ph.D.</span><br />
-
-<span class="xs">CONSULTING ENGINEER; FELLOW, AMERICAN ACADEMY OF ARTS &amp; SCIENCES; PAST-PRESIDENT,<br />
-THE ILLUMINATING ENGINEERING SOCIETY; MEMBER,<br />
-AMERICAN ASTRONOMICAL SOCIETY</span></p>
-
-<p class="center spaced"><span class="smcap"><small>First Edition</small></span></p>
-
-<p class="center"><span class="smcap">McGRAW-HILL BOOK COMPANY, Inc.</span><br />
-NEW YORK: 370 SEVENTH AVENUE<br />
-<small>LONDON: 6 &amp; 8 BOUVERIE ST., E. C. 4</small><br />
-1922</p>
-
-
-
-
-
-<p class="center spaced"><span class="smcap"><small>Copyright, 1922, by the<br />
-McGraw-Hill Book Company, Inc.</small></span></p>
-
-<p class="center">
-<small><small>THE MAPLE PRESS YORK PA</small></small></p>
-
-<hr class="chap" />
-
-<p><span class="pagenum"><a name="Page_iii" id="Page_iii">[Pg iii]</a></span></p>
-
-
-
-
-<div class="chapter"></div>
-<h2><a name="PREFACE" id="PREFACE">PREFACE</a></h2>
-
-
-<p>This book is written for the many observers, who use telescopes
-for study or pleasure and desire more information about
-their construction and properties. Not being a “handbook” in
-two or more thick quartos, it attempts neither exhaustive technicalities
-nor popular descriptions of great observatories and their
-work. It deals primarily with principles and their application to
-such instruments as are likely to come into the possession, or
-within reach, of students and others for whom the Heavens have
-a compelling call.</p>
-
-<p>Much has been written of telescopes, first and last, but it is for
-the most part scattered through papers in three or four languages,
-and quite inaccessible to the ordinary reader. For his benefit the
-references are, so far as is practicable, to English sources, and
-dimensions are given, regretfully, in English units. Certain
-branches of the subject are not here discussed for lack of space
-or because there is recent literature at hand to which reference
-can be made. Such topics are telescopes notable chiefly for their
-dimensions, and photographic apparatus on which special treatises
-are available.</p>
-
-<p>Celestial photography is a branch of astronomy which stands
-on its own feet, and although many telescopes are successfully
-used for photography through the help of color screens, the
-photographic telescope proper and its use belongs to a field
-somewhat apart, requiring a technique quite its own.</p>
-
-<p>It is many years, however, since any book has dealt with the
-telescope itself, apart from the often repeated accounts of the
-marvels it discloses. The present volume contains neither pictures
-of nebulæ nor speculations as to the habitibility of the
-planets; it merely attempts to bring the facts regarding the
-astronomer’s chief instrument of research somewhere within
-grasp and up to the present time.</p>
-
-<p>The author cordially acknowledges his obligations to the
-important astronomical journals, particularly the Astro-physical
-Journal, and Popular Astronomy in this country; The Observatory,
-and the publications of the Royal Astronomical Society<span class="pagenum"><a name="Page_iv" id="Page_iv">[Pg iv]</a></span>
-in England; the Bulletin de la Société Astronomique de France;
-and the Astronomische Nachrichten; which, with a few other journals
-and the official reports of observatories form the body of
-astronomical knowledge. He also acknowledges the kindness of
-the various publishers who have extended the courtesy of illustrations,
-especially Macmillan &amp; Co. and the Clarendon Press,
-and above all renders thanks to the many friends who have
-cordially lent a helping hand—the Director and staff of the
-Harvard Observatory, Dr. George E. Hale, C. A. R. Lundin,
-manager of the Alvan Clark Corporation, J. B. McDowell, successor
-of the Brashear Company, J. E. Bennett, the American
-representative of Carl Zeiss, Jena, and not a few others.</p>
-
-<p class="right">
-<span class="smcap">Louis Bell.</span></p>
-
-<p><span class="smcap">Boston, Mass.</span>,<br />
-<i>February, 1922</i>.<br />
-</p>
-
-<hr class="chap" />
-
-<p><span class="pagenum"><a name="Page_v" id="Page_v">[Pg v]</a></span></p>
-
-
-
-
-<div class="chapter"></div>
-<h2><a name="CONTENTS" id="CONTENTS">CONTENTS</a></h2>
-
-
-
-
-<div class="center">
-<table border="0" cellpadding="4" cellspacing="0" summary="">
-<tr>
-  <td align="right" colspan="3"><span class="smcap"><small>Page</small></span></td>
-</tr>
-<tr>
-  <td align="left" colspan="2"><span class="smcap"><a href="#PREFACE">Preface</a></span></td>
-  <td align="left">vii</td>
-</tr>
-<tr>
-  <td align="center"><span class="smcap"><small>Chap</small>.</span></td>
-</tr>
-<tr>
-  <td align="right"><a href="#CHAPTER_I">I</a>.</td>
-  <td align="left"><span class="smcap">The Evolution of the Telescope</span></td>
-  <td align="right">1</td>
-</tr>
-<tr>
-  <td align="right"><a href="#CHAPTER_II">II</a>.</td>
-  <td align="left"><span class="smcap">The Modern Telescope</span></td>
-  <td align="right">31</td>
-</tr>
-<tr>
-  <td align="right"><a href="#CHAPTER_III">III</a>.</td>
-  <td align="left"><span class="smcap">Optical Glass and Its Working</span></td>
-  <td align="right">57</td>
-</tr>
-<tr>
-  <td align="right"><a href="#CHAPTER_IV">IV</a>.</td>
-  <td align="left"><span class="smcap">The Properties of Objectives and Mirrors</span></td>
-  <td align="right">76</td>
-</tr>
-<tr>
-  <td align="right"><a href="#CHAPTER_V">V</a>.</td>
-  <td align="left"><span class="smcap">Mountings</span></td>
-  <td align="right">98</td>
-</tr>
-<tr>
-  <td align="right"><a href="#CHAPTER_VI">VI</a>.</td>
-  <td align="left"><span class="smcap">Eye-pieces</span></td>
-  <td align="right">134</td>
-</tr>
-<tr>
-  <td align="right"><a href="#CHAPTER_VII">VII</a>.</td>
-  <td align="left"><span class="smcap">Hand Telescopes and Binoculars</span></td>
-  <td align="right">150</td>
-</tr>
-<tr>
-  <td align="right"><a href="#CHAPTER_VIII">VIII</a>.</td>
-  <td align="left"><span class="smcap">Accessories</span></td>
-  <td align="right">165</td>
-</tr>
-<tr>
-  <td align="right"><a href="#CHAPTER_IX">IX</a>.</td>
-  <td align="left"><span class="smcap">The Testing and Care of Telescopes</span></td>
-  <td align="right">201</td>
-</tr>
-<tr>
-  <td align="right"><a href="#CHAPTER_X">X</a>.</td>
-  <td align="left"><span class="smcap">Setting up and Housing the Telescope</span></td>
-  <td align="right">228</td>
-</tr>
-<tr>
-  <td align="right"><a href="#CHAPTER_XI">XI</a>.</td>
-  <td align="left"><span class="smcap">Seeing and Magnification</span></td>
-  <td align="right">253</td>
-</tr>
-<tr>
-  <td align="left" colspan="2"><span class="smcap"><a href="#APPENDIX">Appendix</a></span></td>
-  <td align="right">279</td>
-</tr>
-<tr>
-  <td align="left" colspan="2"><span class="smcap"><a href="#INDEX">Index</a></span></td>
-  <td align="right">281</td>
-</tr>
-</table></div>
-<hr class="chap" />
-
-<p><span class="pagenum"><a name="Page_1" id="Page_1">[Pg 1]</a></span></p>
-
-
-
-<div class="chapter"></div>
-<p class="half-title">THE TELESCOPE</p>
-
-
-
-<hr class="chap" />
-<h2><a name="CHAPTER_I" id="CHAPTER_I">CHAPTER I</a><br />
-
-<small>THE EVOLUTION OF THE TELESCOPE</small></h2>
-
-
-<p>In the credulous twaddle of an essay on the Lost Arts one may
-generally find the telescope ascribed to far antiquity. In place
-of evidence there is vague allusion of classical times or wild
-flights of fancy like one which argued from the Scriptural statement
-that Satan took up Christ into a high mountain and
-showed him all the kingdoms of the earth, that the Devil had a
-telescope—bad optics and worse theology.</p>
-
-<p>In point of fact there is not any indication that either in classical
-times, or in the black thousand years of hopeless ignorance
-that followed the fall of Roman civilization, was there any
-knowledge of optical instruments worth mentioning.</p>
-
-<p>The peoples that tended their flocks by night in the East alone
-kept alive the knowledge of astronomy, and very gradually, with
-the revival of learning, came the spirit of experiment that led
-to the invention of aids to man’s natural powers.</p>
-
-<p>The lineage of the telescope runs unmistakably back to
-spectacles, and these have an honorable history extending over
-more than six centuries to the early and fruitful days of the
-Renaissance.</p>
-
-<p>That their origin was in Italy near the end of the thirteenth
-century admits of little doubt. A Florentine manuscript letter
-of 1289 refers to “Those glasses they call spectacles, lately
-invented, to the great advantage of poor old men when their
-sight grows weak,” and in 1305 Giordano da Rivalto refers to
-them as dating back about twenty years.</p>
-
-<p>Finally, in the church of Santa Maria Maggiore in Florence lay
-buried Salvino d’Amarto degli Armati, (obiit 1317) under an
-epitaph, now disappeared, ascribing to him the invention of
-spectacles. W. B. Carpenter, F. R. S., states that the inventor
-tried to keep the valuable secret to himself, but it was discovered
-and published before his death. At all events the discovery
-moved swiftly. By the early fourteenth century it had spread to<span class="pagenum"><a name="Page_2" id="Page_2">[Pg 2]</a></span>
-the Low Countries where it was destined to lead to great results,
-and presently was common knowledge over all civilized Europe.</p>
-
-<p>It was three hundred years, however, between spectacles
-and the combination of spectacle lenses into a telescope, a lapse
-of time which to some investigators has seemed altogether
-mysterious. The ophthalmological facts lead to a simple explanation.
-The first spectacles were for the relief of presbyopia, the
-common and lamentable affection of advancing years, and for
-this purpose convex lenses of very moderate power sufficed, nor
-was material variation in power necessary. Glasses having a
-uniform focus of a foot and a half or thereabouts would serve
-every practical purpose, but would be no material for telescopes.</p>
-
-<p>Myopia was little known, its acquired form being rare in a
-period of general illiteracy, and glasses for its correction, especially
-as regards its higher degrees, probably came slowly and
-were in very small demand, so that the chance of an optical
-craftsman having in hand the ordinary convex lenses and those
-of strong negative curvature was altogether remote. Indeed it
-was only in 1575 that Maurolycus published a clear description
-of myopia and hypermetropia with the appropriate treatment by
-the use of concave and convex lenses. Until both of these, in
-quite various powers, were available, there was small chance of
-hitting upon an instrument that required their use in a highly
-special combination.</p>
-
-<p>At all events there is no definite trace of the discovery of
-telescopic vision until 1608 and the inventor of record is
-unquestionably one Jan Lippershey, a spectacle maker of Middelburg
-in Zeeland, a native of Wesel. On Oct. 2, 1608 the States-General
-took under consideration a petition which had been
-presented by Lippershey for a 30-year patent to the exclusive
-right of manufacture of an instrument for seeing at a distance, or
-for a suitable pension, under the condition that he should make
-the instrument only for his country’s service.</p>
-
-<p>The States General pricked up its ears and promptly appointed
-on Oct. 4 a committee to test the new instrument from a tower of
-Prince Maurice’s palace, allotting 900 florins for the purchase of
-the invention should it prove good. On the 6th the committee
-reported favorably and the Assembly agreed to give Lippershey
-900 florins for his instrument, but desired that it be arranged for
-use with both eyes.</p>
-
-<p>Lippershey therefore pushed forward to the binocular form and<span class="pagenum"><a name="Page_3" id="Page_3">[Pg 3]</a></span>
-two months later, Dec. 9, he announced his success. On the
-15th the new instrument was examined and pronounced good,
-and the Assembly ordered two more binoculars, of rock crystal,
-at the same price. They denied a patent on the ground that the
-invention was known to others, but paid Lippershey liberally as a
-sort of retainer to secure his exclusive services to the State. In
-fact even the French Ambassador, wishing to obtain an instrument
-from him for his King, had to secure the necessary authorization
-from the States-General.</p>
-
-<div class="figcenter">
-<img src="images/i_003.jpg" alt="" />
-<div class="caption"><i>Bull. de la Soc. Astron. de France.</i><br />
-<span class="smcap">Fig. 1.</span>—Jan Lippershey, Inventor of the Telescope.</div>
-</div>
-
-<p>It is here pertinent to enquire what manner of optic tube
-Lippershey showed to back up his petition, and how it had come
-to public knowledge. As nearly as we may know these first telescopes
-were about a foot and a half long, as noted by Huygens, and
-probably an inch and a half or less in aperture, being constructed
-of an ordinary convex lens such as was used in spectacles for the
-aged, and of a concave glass suitable for a bad case of short
-sightedness, the only kind in that day likely to receive attention.</p>
-
-<p><span class="pagenum"><a name="Page_4" id="Page_4">[Pg 4]</a></span></p>
-
-<p>It probably magnified no more than three or four diameters
-and was most likely in a substantial tube of firmly rolled, glued,
-and varnished paper, originally without provision for focussing,
-since with an eye lens of rather low power the need of adjustment
-would not be acute.</p>
-
-<p>As to the invention being generally known, the only definite
-attempt to dispute priority was made by James Metius of
-Alkmaar, who, learning of Lippershey’s petition, on Oct. 17, 1608,
-filed a similar one, alleging that through study and labor extending
-over a couple of years he, having accidentally hit upon the
-idea, had so far carried it out that his instrument made distant
-objects as distinct as the one lately offered to the States by a
-citizen and spectacle maker of Middelburg.</p>
-
-<p>He apparently did not submit an instrument, was politely
-told to perfect his invention before his petition was further considered,
-and thereafter disappears from the scene, whatever his
-merits. If he had actually noted telescopic vision he had neither
-appreciated its enormous importance nor laid the facts before
-others who might have done so.</p>
-
-<p>The only other contemporary for whom claims have been made
-is Zacharius Jansen, also a spectacle maker of Middelburg, to
-whom Pierre Borel, on entirely second hand information, ascribed
-the discovery of the telescope. But Borel wrote nearly fifty
-years later, after all the principals were dead, and the evidence
-he collected from the precarious memories of venerable witnesses
-is very conflicting and points to about 1610 as the date when
-Jansen was making telescopes—like many other spectacle
-makers.<a name="FNanchor_1_1" id="FNanchor_1_1"></a><a href="#Footnote_1_1" class="fnanchor">[1]</a></p>
-
-<p>Borel also gave credence to a tale that Metius, seeking
-Jansen, strayed into Lippershey’s shop and by his inquiries gave
-the shrewd proprietor his first hint of the telescope, but set the
-date at 1610. A variation of this tale of the mysterious stranger,
-due to Hieronymus Sirturus, contains the interesting intimation
-that he may have been of supernatural origin—not further specified.
-There are also the reports, common among the ignorant
-or envious, that Lippershey’s discovery was accidental, even
-perhaps made by his children or apprentice.</p>
-
-<p>Just how it actually was made we do not know, but there
-is no reason to suppose that it was not in the commonplace way<span class="pagenum"><a name="Page_5" id="Page_5">[Pg 5]</a></span>
-of experimenting with and testing lenses that he had produced,
-perhaps those made to meet a vicious case of myopia in one of
-his patrons.</p>
-
-<p>When the discovery was made is somewhat clearer. Plainly
-it antedated Oct. 2, and in Lippershey’s petition is a definite
-statement that an instrument had already been tested by some,
-at least, of the members of the States-General. A somewhat
-vague and gossipy note in the <i>Mercure Française</i> intimates that
-one was presented to Prince Maurice “about September of the
-past year” (1608) and that it was shown to the Council of State
-and to others.</p>
-
-<p>Allowing a reasonable time between Lippershey’s discovery
-and the actual production of an example suitable for exhibition
-to the authorities, it seems likely that the invention dates back
-certainly into the summer of 1608, perhaps even earlier.</p>
-
-<p>At all events there is every indication that the news of it
-spread like wild-fire. Unless Lippershey were unusually careful
-in keeping his secret, and there are traditions that he was not,
-the sensational discovery would have been quickly known in the
-little town and every spectacle maker whose ears it reached would
-have been busy with it.</p>
-
-<p>If the dates given by Simon Marius in his <i>Mundus Jovialis</i>
-be correct, a Belgian with an air of mystery and a glass of which
-one of the lenses was cracked, turned up at the Frankfort fair
-in the autumn of 1608 and at last allowed Fuchs, a nobleman of
-Bimbach, to look through the instrument. Fuchs noted that it
-magnified “several” times, but fell out with the Belgian over the
-price, and returning, took up the matter with Marius, fathomed
-the construction, tried it with glasses from spectacles, attempted
-to get a convex lens of longer focus from a Nuremburg maker,
-who had no suitable tools, and the following summer got a fairly
-good glass from Belgium where such were already becoming
-common.</p>
-
-<p>With this Marius eventually picked up three satellites of
-Jupiter—the fourth awaited the arrival of a superior telescope
-from Venice. Early in 1609 telescopes “about a foot long”
-were certainly for sale in Paris, a Frenchman had offered one in
-Milan by May of that year, a couple of months later one was in
-use by Harriot in England, an example had reached Cardinal
-Borghese, and specimens are said to have reached Padua. Fig. 2
-from the “<i>Mundus Jovialis</i>,” shows Marius with his “Perspicil<span class="pagenum"><a name="Page_6" id="Page_6">[Pg 6]</a></span>ium,”
-the first published picture of the new instrument. Early
-in 1610 telescopes were being made in England, but if the few
-reports of performance, even at this date, are trustworthy, the
-“Dutch trunk” of that period was of very indifferent quality and
-power, far from being an astronomical instrument.</p>
-
-
-<div class="figcenter">
-<img src="images/i_006.jpg" alt="" />
-<div class="caption"><i>The Observatory.</i><br />
-<span class="smcap">Fig. 2.</span>—Simon Marius and his Telescope.</div>
-</div>
-
-<p>One cannot lay aside this preliminary phase of the evolution
-of the telescope without reference to the alleged descriptions of
-telescopic apparatus by Roger Bacon, (c. 1270), Giambattista
-della Porta (1558), and Leonard Digges (1571), details of which
-may be found in Grant’s <i>History of Physical Astronomy</i> and many
-other works.</p>
-
-<p>Of these the first on careful reading conveys strongly the conviction
-that the author had a pretty clear idea of refraction from
-the standpoint of visual angle, yet without giving any evidence
-of practical acquaintance with actual apparatus for doing the
-things which he suggests.</p>
-
-<p>Given a suitable supply of lenses, it is reasonably certain that
-Bacon was clever enough to have devised both telescope and<span class="pagenum"><a name="Page_7" id="Page_7">[Pg 7]</a></span>
-microscope, but there is no evidence that he did so, although his
-manifold activities kept him constantly in public view. It does
-not seem unlikely, however, that his suggestions in manuscripts,
-quite available at the time, may have led to the contemporaneous
-invention of spectacles.</p>
-
-<p>Porta’s comments sound like an echo of Bacon’s, plus a rather
-muddled attempt to imagine the corresponding apparatus.
-Kepler, certainly competent and familiar with the principles
-of the telescope, found his description entirely unintelligible.
-Porta, however, was one of the earliest workers on the <i>camera
-obscura</i> and upon this some of his cryptic statements may have
-borne.</p>
-
-<p>Somewhat similar is the situation respecting Digges. His son
-makes reference to a Ms. of Roger Bacon as the source of the
-marvels he describes. The whole account, however, strongly
-suggests experiments with the <i>camera obscura</i> rather than with the
-telescope.</p>
-
-<p>The most that can be said with reference to any of the three
-is that, if he by any chance fell upon the combination of lenses
-that gave telescopic vision, he failed to set down the facts in any
-form that could be or was of use to others. There is no reason
-to believe that the Dutch discovery, important as it was, had
-gone beyond the empirical observation that a common convex
-spectacle lens and a concave one of relatively large curvature
-could be placed in a tube, convex ahead, at such a distance apart
-as to give a clear enlarged image of distant objects.</p>
-
-<p>It remained for Galileo (1564-1647) to grasp the general
-principles involved and to apply them to a real instrument of
-research. It was in May 1609 that, on a visit to Venice, he heard
-reports that a Belgian had devised an instrument which made
-distant objects seem near, and this being quickly confirmed by a
-letter from Paris he awakened to the importance of the issue and,
-returning to Padua, is said to have solved the problem the very
-night of his arrival.</p>
-
-<p>Next day he procured a plano-convex and a plano-concave
-lens, fitted them to a lead tube and found that the combination
-magnified three diameters, an observation which indicates about
-what it was possible to obtain from the stock of the contemporary
-spectacle maker.<a name="FNanchor_2_2" id="FNanchor_2_2"></a><a href="#Footnote_2_2" class="fnanchor">[2]</a> The relation between the power and the foci<span class="pagenum"><a name="Page_8" id="Page_8">[Pg 8]</a></span>
-of the lenses he evidently quickly fathomed for his next recorded
-trial reached about eight diameters.</p>
-
-<p>With this instrument he proceeded to Venice and during a
-month’s stay, August, 1609, exhibited it to the senators of the
-republic and throngs of notables, finally disclosing the secret of
-its construction and presenting the tube itself to the Doge
-sitting in full council. This particular telescope was about
-twenty inches long and one and five eighths inches in aperture,
-showing plainly that Galileo had by this time found, or more
-likely made, an eye lens of short focus, about three inches, quite
-probably using a well polished convex lens of the ordinary sort
-as objective.</p>
-
-<div class="figcenter">
-<img src="images/i_008.jpg" alt="" />
-<div class="caption"><i>Lodge “Pioneers of Science.”</i><br />
-<span class="smcap">Fig. 3.</span>—Galileo.</div>
-</div>
-
-<p>Laden with honors he returned to Padua and settled down to
-the hard work of development, grinding many lenses with his
-own hands and finally producing the instrument magnifying
-some 32 times, with which he began the notable succession of
-discoveries that laid the foundation of observational astronomy.
-This with another of similar dimensions is still preserved at the<span class="pagenum"><a name="Page_9" id="Page_9">[Pg 9]</a></span>
-Galileo Museum in Florence, and is shown in the Frontispiece.
-The larger instrument is forty-nine inches long and an inch and
-three quarters aperture, the smaller about thirty-seven inches long
-and of an inch and five-eighths aperture. The tubes are of
-paper, the glasses still remain, and these are in fact the first astronomical
-telescopes.</p>
-
-<p>Galileo made in Padua, and after his return to Florence in the
-autumn of 1610, many telescopes which found their way over
-Europe, but quite certainly none of power equalling or exceeding
-these.</p>
-
-<p>In this connection John Greaves, later Savilian Professor of Astronomy
-at Oxford, writing from Sienna in 1639, says: “Galileus
-never made but two good glasses, and those were of old Venice
-glass.” In these best telescopes, however, the great Florentine
-had clearly accomplished a most workmanlike feat. He had
-brought the focus of his eye lens down to that usual in modern
-opera glasses, and has pushed his power about to the limit for
-simple lenses thus combined.</p>
-
-<p>The lack of clear and homogeneous glass, the great difficulty
-of forming true tools, want of suitable commercial abrasives,
-impossibility of buying sheet metals or tubing (except lead),
-and default of now familiar methods of centering and testing
-lenses, made the production of respectably good instruments a
-task the difficulty of which it is hard now to appreciate.</p>
-
-<p>The services of Galileo to the art were of such profound importance,
-that his form of instrument may well bear his name, even
-though his eyes were not the first that had looked through it.
-Such, too, was the judgment of his contemporaries, and it was
-by the act of his colleagues in the renowned Acaddemia dei
-Lincei, through the learned Damiscianus, that the name “Telescope”
-was devised and has been handed down to us.</p>
-
-<p>A serious fault of the Galilean telescope was its very small
-field of view when of any considerable power. Galileo’s largest
-instrument had a field of but 7′15″, less than one quarter the
-moon’s diameter. The general reason is plain if one follows the
-rays through the lenses as in Fig. 4 where <i>AB</i> is the distant object,
-<i>o</i> the objective, <i>e</i> the eye lens, <i>ab</i> the real image in the absence of <i>e</i>,
-and <i>a′b′</i> the virtual magnified image due to <i>e</i>.</p>
-
-<p>It will be at once seen that the axes of the pencils of rays from
-all parts of the object, as shown by the heavy lines, act as if they
-diverged from the optical center of the objective, but diverging<span class="pagenum"><a name="Page_10" id="Page_10">[Pg 10]</a></span>
-still more by refraction through the concave eye lens <i>e</i>, fall mostly
-outside the pupil of the observer’s eye. In fact the field is
-approximately measured by the angle subtended by the pupil
-from the center of <i>o</i>.</p>
-
-<p>To the credit of the Galilean form may be set down the convenient
-erect image, a sharp, if small, field somewhat bettered
-by a partial compensation of the aberrations of the objective by
-the concave eye lens, and good illumination. For a distant
-object the lenses were spaced at the difference of their focal
-lengths, and the magnifying power was the ratio of these, <i>f<sub>o</sub>/f<sub>e</sub></i>.</p>
-
-<div class="figcenter">
-<img src="images/i_010a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 4.</span>—Diagram of Galileo’s Telescope.</div>
-</div>
-<p>But the difficulty of obtaining high power with a fairly sizeable
-field was ultimately fatal and the type now survives only in the
-form of opera and field glasses, usually of 2 to 5 power, and in an
-occasional negative eye lens for erecting the image in observatory
-work. Practically all the modern instruments have achromatic
-objectives and commonly achromatic oculars.</p>
-
-<div class="figcenter">
-<img src="images/i_010b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 5.</span>—Diagram of Kepler’s Telescope.</div>
-</div>
-
-<p>The necessary step forward was made by Johann Kepler
-(1571-1630), the immortal discoverer of the laws of planetary
-motion. In his <i>Dioptrice</i> (1611) he set forth the astronomical
-telescope, substantially, save for the changes brought by
-achromatism, as it has been used ever since. His arrangement
-was that of Fig. 5 in which the letters have the same significance
-as in Fig. 4.</p>
-
-<p>There are here three striking differences from the Galilean
-form. There is a real image in the front focus of the eye lens <i>e</i>,
-the rays passing it are refracted inwards instead of outwards,
-to the great advantage of the field, and any object placed in the
-image plane will be magnified together with the image. The<span class="pagenum"><a name="Page_11" id="Page_11">[Pg 11]</a></span>
-first two points Kepler fully realized, the third he probably did
-not, though it is the basis of the micrometer. The lenses <i>o</i> and
-<i>e</i> are obviously spaced at the sum of their focal lengths, and as
-before the magnifying power is the ratio of these lengths, the visible
-image being inverted.</p>
-
-<p>Kepler, so far as known, did not actually use the new telescope,
-that honor falling about half a dozen years later, to Christopher
-Scheiner, a Jesuit professor of mathematics at Ingolstadt, best
-known as a very early and most persistent, not to say verbose,
-observer of sun spots. His <i>Rosa Ursina</i> (1630) indicates free
-use of Kepler’s telescope for some years previously, in just what
-size and power is uncertain.<a name="FNanchor_3_3" id="FNanchor_3_3"></a><a href="#Footnote_3_3" class="fnanchor">[3]</a> Fontana of Naples also appears
-to have been early in the field.</p>
-
-<p>But the new instrument despite its much larger field and far
-greater possibilities of power, brought with it some very serious
-problems. With increased power came greatly aggravated
-trouble from spherical aberration and chromatic aberration as
-well, and the additive aberrations of the eye lens made matters
-still worse. The earlier Keplerian instruments were probably
-rather bad if the drawings of Fontana from 1629 to 1636
-fairly represent them.</p>
-
-<p>If one may judge from the course of developments, the first
-great impulse to improvement came with the publication of
-Descartes’ (1596-1650) study of dioptrics in 1637. Therein
-was set forth much of the theory of spherical aberration and
-astronomers promptly followed the clues, practical and impractical,
-thus disclosed.</p>
-
-<p>Without going into the theory of aberrations the fact of importance
-to the improvement of the early telescope is that the
-longitudinal spherical aberration of any simple lens is directly proportional
-to its thickness due to curvature. Hence, other things
-being equal, the longer the focus for the same aperture the less the
-spherical aberration both absolutely and relatively to the image.
-Further, although Descartes knew nothing of chromatic aberration,
-and the colored fringe about objects seen through the telescope
-must then have seemed altogether mysterious, it, also, was
-greatly relieved by lengthening the focus.</p>
-
-<p><span class="pagenum"><a name="Page_12" id="Page_12">[Pg 12]</a></span></p>
-
-<p>For the chromatic circle produced by a simple lens of given
-diameter has a radial width substantially irrespective of the focal
-length. But increasing the focal length increases in exact proportion
-the size of the image, correspondingly decreasing the relative
-effect of the chromatic error.</p>
-
-<p>Descartes also suggested several designs of lenses which would
-be altogether free of spherical aberration, formed with elliptical
-or hyperbolic curvature, and for some time fruitless efforts were
-made to realize this in practice. It was in fact to be near a
-century before anyone successfully figured non-spherical surfaces.
-It was spherical quite as much as chromatic aberration that
-drove astronomers to long telescopes.</p>
-
-<p>Meanwhile the astronomical telescope fell into better hands
-than those of Scheiner. The first fully to grasp its possibilities
-was William Gascoigne, a gallant young gentleman of Middleton,
-Yorkshire, born about 1620 (some say as early as 1612) and who
-died fighting on the King’s side at Marston Moor, July 2, 1644.
-To him came as early as 1638 the inspiration of utilizing the real
-focus of the objective for establishing a telescopic sight.</p>
-
-<div class="figcenter">
-<img src="images/i_012.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 6.</span>—Diagram of Terrestrial Ocular.</div>
-</div>
-
-<p>This shortly took the form of a genuine micrometer consisting
-of a pair of parallel blades in the focus, moved in opposite directions
-by a screw of duplex pitch, with a scale for whole revolutions,
-and a head divided into 100 parts for partial revolutions. With
-this he observed much from 1638 to 1643, measured the diameters
-of sun, moon and planets with a good degree of precision, and
-laid the foundations of modern micrometry. He was equipped
-by 1639 with what was then called a large telescope.</p>
-
-<p>His untimely death, leaving behind an unpublished treatise
-on optics, was a grave loss to science, the more since the manuscript
-could not be found, and, swept away by the storms of war,
-his brilliant work dropped out of sight for above a score of years.</p>
-
-<p>Meanwhile De Rheita (1597-1660), a Capuchin monk, and an
-industrious and capable investigator, had been busy with the<span class="pagenum"><a name="Page_13" id="Page_13">[Pg 13]</a></span>
-telescope, and in 1645 published at Antwerp a somewhat bizarre
-treatise, dedicated to Jesus Christ, and containing not a little
-practical information. De Rheita had early constructed binoculars,
-probably quite independently, had lately been diligently
-experimenting with Descartes’ hyperbolic lens, it is needless to
-say without much success, and was meditating work on a colossal
-scale—a glass to magnify 4,000 times.</p>
-
-<p>But his real contribution to optics was the terrestrial ocular.
-This as he made it is shown in Fig. 6 where <i>a b</i> is the image
-formed by the objective in front of the eye lens r, s and t two
-equal lenses separated by their focal lengths and <i>a′ b′</i> the resultant
-reinverted image. This form remained in common use until
-improved by Dolland more than a century later.</p>
-
-<div class="figcenter">
-<img src="images/i_013.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 7.</span>—Johannes Hevelius.</div>
-</div>
-
-<p>A somewhat earlier form ascribed to Father Scheiner had
-merged the two lenses forming the inverting system of Fig.
-6, into a single lens used at its conjugate foci.</p>
-
-<p>Closely following De Rheita came Johannes Hevelius (1611-1687)
-of Danzig, one of the really important observers of the<span class="pagenum"><a name="Page_14" id="Page_14">[Pg 14]</a></span>
-seventeenth century. His great treatise <i>Selenographia</i> published
-in 1647 gives us the first systematic study of the moon, and a brief
-but illuminating account of the instruments of the time and
-their practical construction.</p>
-
-<p>At this time the Galilean and Keplerian forms of telescope were
-in concurrent use and Hevelius gives directions for designing and
-making both of them. Apparently the current instruments were
-not generally above five or six feet long and from Hevelius’ data
-would give not above 30 diameters in the Galilean form. There
-is mention, however, of tubes up to 12 feet in length, and of the
-advantage in clearness and power of the longer focus plano-convex
-lens. Paper tubes, evidently common, are condemned,
-also those of sheet iron on account of their weight, and wood was
-to be preferred for the longer tubes.</p>
-
-<p>Evidently Hevelius had at this time no notion of the effect of
-the plano-convex form of lens as such in lessening aberration, but
-he mentions a curious form of telescope, actually due to De Rheita,
-in which the objective is double, apparently of two plano-convex
-lenses, the weaker ahead, and used with a concave eye lens.
-If properly proportioned such a doublet would have less than a
-quarter the spherical aberration of the equivalent double convex
-lens.</p>
-
-<p>Hevelius also mentions the earlier form of re-inverting telescope
-above referred to, and speaks rather highly of its performance.
-To judge from his numerous drawings of the moon made in 1643
-and 1644, his telescopes were much better than those of Scheiner
-and Fontana, but still woefully lacking in sharp definition.</p>
-
-<p>Nevertheless the copper plates of the <i>Selenographia</i>, representing
-every phase of the moon, placed the lunar details with remarkable
-accuracy and formed for more than a century the best lunar
-atlas available. One acquires an abiding respect for the patience
-and skill of these old astronomers in seeing how much they did
-with means utterly inadequate.</p>
-
-<p>One may get a fair idea of the size, appearance, and mounting
-of telescopes in this early day from Fig. 8, which shows a somewhat
-advanced construction credited by Hevelius to a suggestion in
-Descartes’ <i>Dioptrica</i>. Appearances indicate that the tube was
-somewhere about six feet long, approximately two inches in
-aperture, and that it had a draw tube for focussing. The offset
-head of the mount to allow observing near the zenith is worth
-an extra glance.</p>
-
-<p><span class="pagenum"><a name="Page_15" id="Page_15">[Pg 15]</a></span></p>
-
-<p>Incidentally Hevelius, with perhaps pardonable pride, also
-explains the “Polemoscope,” a little invention of his own, made, he
-tells us, in 1637. It is nothing else than the first periscope,
-constructed as shown in Fig. 9, a tube <i>c</i> with two right angled
-branches, a fairly long one <i>e</i> for the objective <i>f</i>, a 45° mirror at <i>g</i>,
-another at <i>a</i>, and finally the concave ocular at <i>b</i>. It was of
-modest size, of tubes 1⅔ inch in diameter, the longer tube being
-22 inches and the upper branch 8 inches, a size well suited for
-trench or parapet.</p>
-
-<div class="figright">
-<img src="images/i_015.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 8.</span>—A Seventh Century Astronomer and his Telescope.</div>
-</div>
-
-<p><span class="pagenum"><a name="Page_16" id="Page_16">[Pg 16]</a></span></p>
-
-<p>Even in these days of his youth Hevelius had learned much of
-practical optics as then known, had devised and was using very
-rational methods of observing sun-spots by projection in a darkened
-room, and gives perhaps the first useful hints at testing
-telescopes by such solar observations and on the planets. He was
-later to do much in the development and mounting of long telescopes
-and in observation, although, while progressive in other
-respects, he very curiously never seemed to grasp the importance
-of telescopic sights and consistently refused to use them.</p>
-
-<p>Telescope construction was now to fall into more skillful hands.
-Shortly after 1650 Christian Huygens (1629-1695), and his
-accomplished brother Constantine awakened to a keen interest
-in astronomy and devised new and excellent methods of forming
-accurate tools and of grinding and polishing lenses.</p>
-
-<div class="figcenter">
-<img src="images/i_016.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 9.</span>—The first Periscope.</div>
-</div>
-<p>By 1655 they had completed an instrument of 12 feet focus with
-which the study of Saturn was begun, Titan the chief satellite
-discovered, and the ring recognized. Pushing further, they
-constructed a telescope of 23 feet focal length and 2⅓ inches
-aperture, with which four years later Christian Huygens finally
-solved the mystery of Saturn’s ring.</p>
-
-<p>Evidently this glass, which bore a power of 100, was of good
-defining quality, as attested by a sketch of Mars late in 1695
-showing plainly Syrtis Major, from observation of which Huygens
-determined the rotation period to be about 24 hours.</p>
-
-<p>The Huygens brothers were seemingly the first fully to grasp
-the advantage of very long focus in cutting down the aberrations,
-the aperture being kept moderate. Their usual proportions were
-about as indicated above, the aperture being kept somewhere
-nearly as the square root of the focus in case of the larger glasses.</p>
-
-<p><span class="pagenum"><a name="Page_17" id="Page_17">[Pg 17]</a></span></p>
-
-<p>In the next two decades the focal length of telescopes was
-pushed by all hands to desperate extremes. The Huygens
-brothers extended themselves to glasses up to 210 feet focus and
-built many shorter ones, a famous example of which, of 6 inches
-aperture and 123 feet focal length, presented to the Royal
-Society, is still in its possession. Auzout produced even longer
-telescopes, and Divini and Campani, in Rome, of whom the last
-named made Cassini’s telescopes for the Observatory of Paris,
-were not far behind. The English makers were similarly busy,
-and Hevelius in Danzig was keeping up the record.</p>
-
-<div class="figcenter">
-<img src="images/i_017.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 10.</span>—Christian Huygens.</div>
-</div>
-
-<p>Clearly these enormously long telescopes could not well be
-mounted in tubes and the users were driven to aerial mountings,
-in which the objective was at the upper end of a spar or girder
-and the eye piece at the lower. Figure 11 shows an actual construction
-by Hevelius for an objective of 150 feet focal length.</p>
-
-<p>In this case the main support was a T beam of wooden planks
-well braced together. Additional stiffness was given by light
-wooden diaphragms at short intervals with apertures of about
-8 inches next to the objective, and gradually increasing downwards.
-The whole was lined up by equalizing tackle in the vertical
-plane, and spreaders with other tackle at the joints of the 40<span class="pagenum"><a name="Page_18" id="Page_18">[Pg 18]</a></span>foot
-sections of the main beam. The mast which supported
-the whole was nearly 90 feet high.</p>
-
-<p>So unwieldly and inconvenient were these long affairs that,
-quite apart from their usual optical imperfections, it is little
-wonder that they led to no results commensurate with their size.
-In fact nearly all the productive work was done with telescopes
-from 20 to 35 feet long, with apertures roughly between 2 and
-3 inches.</p>
-
-<div class="figcenter">
-<img src="images/i_018.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 11.</span>—Hevelius’ 150-foot Telescope.</div>
-</div>
-
-<p>Dominique Cassini to be sure, scrutinizing Saturn in 1684 with
-objectives by Campani, of 100 and 136 feet focus picked up the
-satellites Tethys and Dione, but he had previously found Iapetus
-with a 17-foot glass, and Rhea with one of 34 feet. The longer
-glasses above mentioned had aerial mounts but the smaller
-ones were in tubes supported on a sort of ladder tripod. A 20-foot
-objective, power 90, gave Cassini the division in Saturn’s ring.</p>
-
-<p>A struggle was still being kept up for the non-spherical curves
-urged by Descartes. It is quite evident that Huygens had a go<span class="pagenum"><a name="Page_19" id="Page_19">[Pg 19]</a></span>
-at them, and Hevelius thought at one time that he had mastered
-the hyperbolic figure, but his published drawings give no indication
-that he had reduced spherical aberration to any perceptible
-degree. At this time the main thing was to get good glass and
-give it true figure and polish, in which Huygens and Campani
-excelled, as the work on Saturn witnesses.</p>
-
-<p>These were the days of the dawn of popular astronomy and
-many a gentleman was aroused to at least a casual interest in
-observing the Heavens. Notes Pepys in his immortal <i>Diary</i>:
-“I find Reeves there, it being a mighty fine bright night, and so
-upon my leads, though very sleepy, till one in the morning, looking
-on the moon and Jupiter, with this twelve foot glass, and
-another of six foot, that he hath brought with him to-night,
-and the sights mighty pleasant, and one of the glasses I will buy.”</p>
-
-<p>Little poor Pepys probably saw, by reason of his severe
-astigmatism, but astronomy was
-in the air with the impulse that
-comes to every science after a
-period of brilliant discovery. Another
-such stimulus came near the
-end of the eighteenth century,
-with the labors of Sir William
-Herschel.</p>
-
-<div class="figright">
-<img src="images/i_019.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 12.</span>—Gregory’s Diagram of his Telescope.</div>
-</div>
-
-<p>Just at this juncture comes one
-of the interesting episodes of telescopic
-history, the ineffectual and
-abandoned experiments on reflecting
-instruments.</p>
-
-<p>In 1663 James Gregory (1638-1675)
-a famous Scottish mathematician,
-published his <i>Optica
-Promota</i>, in which he described
-the rather elegant construction
-which bears his name, a perforated parabolic mirror with an
-elliptical mirror forward of the focus returning an image to the
-ocular through the perforation. It was convenient in that it
-gave an erect image, and it was sound theoretically, and, as the
-future proved, practically, but the curves were quite too much
-for the contemporary opticians. Figure 12 shows the diagrammatic
-construction as published.</p>
-
-<p>The next year Gregory started Reive, a London optician,<span class="pagenum"><a name="Page_20" id="Page_20">[Pg 20]</a></span>
-doubtless the same mentioned by Pepys, on the construction of a
-6 foot telescope. This rather ambitious effort failed of material
-success through the inability of Reive to give the needed figures
-to the mirrors,<a name="FNanchor_4_4" id="FNanchor_4_4"></a><a href="#Footnote_4_4" class="fnanchor">[4]</a> and of it nothing further appears until the ingenious
-Robert Hooke (1635-1703) executed in 1674 a Gregorian,
-apparently without any notable results. There is a well
-defined tradition that Gregory himself was using one in 1675, at
-the time of his death, but the invention then dropped out of sight.</p>
-
-<p>No greater influence on the art attended the next attempt at a
-reflector, by Isaac Newton (1643-1727). This was an early outcome
-of his notable discovery of the dispersion of light by prisms,
-which led him to despair of improving refracting telescopes and
-turned his mind to reflectors.</p>
-
-<p>Unhappily in an experiment to determine whether refraction
-and dispersion were proportional he committed the singular
-blunder of raising the refractive index of a water-filled prism to
-equality with glass by dissolving sugar of lead in it. Without
-realizing the impropriety of thus varying two quite unknown
-quantities at once in his crucial experiment, he promptly jumped
-to the conclusion that refraction and dispersion varied in exact
-proportion in all substances, so that if two prisms or lenses
-dispersed light to the same extent they must also equally refract
-it. It would be interesting to know just how the fact of his
-bungling was passed along to posterity. As a naïve apologist
-once remarked, it was not to be found in his “<i>Optics</i>.”
-But Sir David Brewster and Sir John Herschel, both staunch
-admirers of the great philosopher, state the fact very positively.
-If one may hazard a guess it crept out at Cambridge and was
-passed along, perhaps to Sir William Herschel, via the unpublished
-history of research that is rich in picturesque details of the
-mare’s nests of science. At all events a mistake with a great
-name behind it carries far, and the result was to delay the
-production of the achromatic telescope by some three quarters
-of a century.</p>
-
-<p>Turning from refractors he presented to the Royal Society
-just after his election as Fellow in 1672, the little six-inch model of
-his device which was received with acclamation and then lay on
-the shelf without making the slightest impression on the art, for
-full half a century.</p>
-
-<p><span class="pagenum"><a name="Page_21" id="Page_21">[Pg 21]</a></span></p>
-
-<p>Newton, by dropping the notion of direct view through the
-tube, hit upon by far the simplest way of getting the image outside
-it, by a plane mirror a little inside focus and inclined at 45°,
-but injudiciously abandoned the parabolic mirror of his original
-paper on dispersion. His invention therefore as actually
-made public was of the combination with a spherical concave
-mirror of a plane mirror of elliptical form at 45°, a construction
-which in later papers he defended as fully adequate.<a name="FNanchor_5_5" id="FNanchor_5_5"></a><a href="#Footnote_5_5" class="fnanchor">[5]</a></p>
-
-<div class="figcenter">
-<img src="images/i_021.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 13.</span>—Newton’s Model of his Reflector.</div>
-</div>
-
-<p>His error in judgment doubtless came from lack of practical
-astronomical experience, for he assumed that the whole real
-trouble with existing telescopes was chromatic aberration, which
-in fact worried the observer little more than the faults due to
-other causes, since the very low luminosity toward the ends<span class="pagenum"><a name="Page_22" id="Page_22">[Pg 22]</a></span>
-of the spectrum enormously lessens the indistinctness due to
-dispersion.</p>
-
-<p>As a matter of fact the long focus objective of small aperture
-did very creditable work, and its errors would not compare
-unfavorably with those of a spherical concave mirror of the wide
-aperture planned by Newton. Had he actually made one of
-his telescopes of fair dimensions and power the definition would
-infallibly have been wrecked by the aberrations due to spherical
-figure.<a name="FNanchor_6_6" id="FNanchor_6_6"></a><a href="#Footnote_6_6" class="fnanchor">[6]</a></p>
-
-<div class="figcenter">
-<img src="images/i_022.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 14.</span>—De Bercé’s sketch of Cassegrain’s Telescope.</div>
-</div>
-
-<p>It is quite likely that appreciation of this, and the grave doubts
-of both Newton and Huygens as to obtaining a proper parabolic
-curve checked further developments. About the beginning of
-the year 1672 M. Cassegrain communicated to M. de Bercé a
-design for a reflecting telescope, which eventually found its way
-into the <i>Philosophical Transactions</i> of May in that year, after
-previous publication in the <i>Journal des Sçavans</i>. Figure 14 shows
-de Bercé’s rough original sketch. It differed from Gregory’s
-construction in that the latter’s elliptical concave mirror placed
-outside the main focus, was replaced by a convex mirror placed
-inside focus. The image was therefore inverted.</p>
-
-<p>The inventor is referred to in histories of science as “Cassegrain,
-a Frenchman.” He was in fact Sieur Guillaume Cassegrain,
-sculptor in the service of Louis Quatorze, modeller and founder
-of many statues. In 1666 he was paid 1200 livres for executing<span class="pagenum"><a name="Page_23" id="Page_23">[Pg 23]</a></span>
-a bust of the King modelled by Bertin, and later made many
-replicas from the antique for the decoration of His Majesty’s
-gardens at Versailles. He disappeared from the royal records in
-1684 and probably died within a year or two of that date.</p>
-
-<p>At the period here concerned he apparently, like de Bercé, was
-of Chartres. Familiar with working bronzes and with the art
-of the founder, he was a very likely person to have executed
-specula. Although there is no certainty that he actually made a
-telescope, a contemporary reference in the <i>Journal des Sçavans</i>
-speaks of his invention as a “petite lunette d’approche,” and one
-does not usually suggest the dimensions of a thing non-existent.
-How long he had been working upon it prior to the period about
-the beginning of 1672 when he disclosed the device to de Bercé
-is unknown.</p>
-
-<p>Probably Newton’s invention was the earlier, but the two were
-independent, and it was somewhat ungenerous of Newton to
-criticise Cassegrain, as he did, for using spherical mirrors, on the
-strength of de Bercé’s very superficial description, when he himself
-considered the parabolic needless.</p>
-
-<p>However, nothing further was done, and the devices of Gregory,
-Newton and Cassegrain went together into the discard for some
-fifty years.</p>
-
-<p>These early experiments gave singularly little information
-about material for mirrors and methods of working it, so little
-that those who followed, even up to Lord Rosse, had to work
-the problems out for themselves. We know from his original
-paper that Newton used bell-metal, whitened by the addition of
-arsenic, following the lore of the alchemists.</p>
-
-<p>These speculative worthies used to alloy copper with arsenic,
-thinking that by giving it a whitish cast they had reached a sort
-of half way point on the road to silver. Very silly at first
-thought, but before the days of chemical analysis, when the
-essential properties of the metals were unknown, the way of the
-scientific experimenter was hard.</p>
-
-<p>What the “steely matter, imployed in London” of which
-Newton speaks in an early paper was, we do not know—very
-likely one of the hard alloys much richer in tin than is ordinary
-bell-metal. Nor do we know to what variety of speculum metal
-Huygens refers in his correspondence with Newton.</p>
-
-<p>As to methods of working it Newton only disclosed his scheme
-of pitch-polishing some thirty years after this period, while it is<span class="pagenum"><a name="Page_24" id="Page_24">[Pg 24]</a></span>
-a matter of previous record, that Huygens had been in the habit
-of polishing his true tools on pitch from some date unknown.
-Probably neither of them originated the practice. Opticians
-are a peculiarly secretive folk and shop methods are likely to be
-kept for a long time before they leak out or are rediscovered.</p>
-
-<p>Modern speculum metal is substantially a definite compound
-of four atoms copper and one tin (SnCu<sub>4</sub>), practically 68 per
-cent copper and 32 per cent tin, and is now, as it was in all
-previous modifications, a peculiarly mean material to cast and
-work. Thus exit the reflector.</p>
-
-<div class="figleft">
-<img src="images/i_024.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 15.</span>—Diagram of Huygens’ Eyepiece.</div>
-</div>
-
-<p>The long telescope continued to grow longer with only slow
-improvement in quality, but the next
-decade was marked by the introduction
-of Huygens’ eyepiece, an immense
-improvement over the single
-lens which had gone before, and with
-slight modifications in use today.</p>
-
-<p>This is shown in section in Fig. 15.
-It consists of a field lens <i>A</i>, plano-convex,
-and an eye lens <i>B</i> of one-third
-the focal length, the two being placed
-at the difference of their focal lengths
-apart with (in later days) a stop half way between them. The
-eye piece is pushed inside the main focus until the rays which fall
-on the field lens focus through the eye lens.</p>
-
-<p>The great gain from Huygens’ view-point was a very much
-enlarged clear field—about a four-fold increase—and in fact the
-combination is substantially achromatic, particularly important
-now when high power oculars are needed.</p>
-
-<p>Still larger progress was made in giving the objective a better
-form with respect to spherical aberration, the “crossed” lens being
-rather generally adopted. This form is double convex, and if of
-ordinary glass, with the rear radius six times the front radius, and
-gives even better results than a plano-convex in its best position-plane
-side to the rear. Objectives were rated on focal length for
-the green rays, that is, the bright central part of the spectrum, the
-violet rays of course falling short and the red running beyond.</p>
-
-<p>To give customary dimensions, a telescope of 3 inches aperture,
-with magnifying power of 100, would be of about 30 feet focus
-with the violet nearly 6 inches short and the red a similar amount
-long. It is vast credit to the early observers that with such<span class="pagenum"><a name="Page_25" id="Page_25">[Pg 25]</a></span>
-slender means they did so much. But in fact the long telescope
-had reached a mechanical <i>impasse</i>, so that the last quarter of the
-seventeenth century and the first quarter of the next were marked
-chiefly by the development of astronomy of position with instruments
-of modest dimensions.</p>
-
-<div class="figcenter">
-<img src="images/i_025.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 16.</span>—The First Reflector. John Hadley, 1722.</div>
-</div>
-
-<p>In due time the new order came and with astounding suddenness.
-Just at the end of 1722 James Bradley (1692-1762)
-measured the diameter of Venus with an objective of 212 ft.
-3 in. focal length; about three months later John Hadley (1682-1744)
-presented to the Royal Society the first reflecting telescope
-worthy the name, and the old order practically ended.</p>
-
-<p>John Hadley should in fact be regarded as the real inventor of
-the reflector in quite the same sense that Mr. Edison has been
-held, <i>de jure</i> and <i>de facto</i>, the inventor of the incandescent elec<span class="pagenum"><a name="Page_26" id="Page_26">[Pg 26]</a></span>tric
-lamp. Actually Hadley’s case is the stronger of the two,
-for the only things which could have been cited against him were
-abandoned experiments fifty years old. Moreover he took successfully
-the essential step at which Gregory and Newton had
-stumbled or turned back—parabolizing his speculum.</p>
-
-<p>The instrument he presented was of approximately 6 inches
-aperture and 62⅝ inches focal length, which he had made
-and tested some three years previously; on a substantial alt-azimuth
-mount with slow motions. He used the Newtonian
-oblique mirror and the instrument was provided with both
-convex and concave eye lenses, with magnifications up to
-about 230.</p>
-
-<p>The whole arrangement is shown in Fig. 16 which is for the most
-part self explanatory. It is worth noting that the speculum
-is positioned in the wooden tube by pressing it forward against
-three equidistant studs by three corresponding screws at the rear,
-that a slider moved by a traversing screw in a wide groove
-carries the small mirror and the ocular, that there is a convenient
-door for access to the mirror, and also a suitable finder. The
-motion in altitude is obtained by a key winding its cord against
-gravity. That in azimuth is by a roller support along a horizontal
-runway carried by an upright, and is obtained by the key
-with a cord pull off in one direction, and in the other, by springs
-within the main upright, turning a post of which the head carries
-cheek pieces on which rest the trunnions of the tube.</p>
-
-<p>A few months later this telescope was carefully tested, by
-Bradley and the Rev. J. Pound, against the Huygens objective
-of 123 feet focus possessed by the Royal Society, and with
-altogether satisfactory results. Hadley’s reflector would show
-everything which could be seen by the long instrument, bearing as
-much power and with equal definition, though somewhat lessened
-light. In particular they saw all five satellites of Saturn, Cassini’s
-division, which the inventor himself had seen the previous
-year even in the northern edge of the ring beyond the planet, and
-the shadow of the ring upon the ball.</p>
-
-<p>The casting of the large speculum was far from perfect, with
-many spots that failed to take polish, but the figure must have
-been rather good. A spherical mirror of these dimensions would
-give an aberration blur something like twenty times the width of
-Cassini’s division, and the chance of seeing all five satellites
-with it would be negligibly small.</p>
-
-<p><span class="pagenum"><a name="Page_27" id="Page_27">[Pg 27]</a></span></p>
-
-<p>Further, Hadley presently disclosed to others not only the
-method he used in polishing and parabolizing specula, but his
-method of testing for true figure by the aberrations disclosed as
-he worked the figure away from the sphere—a scheme frequently
-used even to this day.</p>
-
-<p>The effect of Hadley’s work was profound. Under his guidance
-others began to produce well figured mirrors, in particular
-Molyneux and Hawksbee; reflecting telescopes became fairly
-common; and in the beginning of the next decade James Short,
-(1710-1768), possessed of craftsmanship that approached wizardry,
-not only fully mastered the art of figuring the paraboloid,
-but at once took up the Gregorian construction with its
-ellipsoidal small mirror, with much success.</p>
-
-<p>His specula were of great relative aperture, F/4 to F/6, and
-from the excellent quality of his metal some of them have retained
-their fine polish and definition after more than a century. He is
-said to have gone even up to 12 inches in diameter. His exact
-methods of working died with him. Even his tools he ordered
-to be destroyed before his death.</p>
-
-<p>The Cassegrain reflector, properly having a parabolic large
-mirror and a hyperbolic small one, seems very rarely to have been
-made in the eighteenth century, though one certainly came into
-the hands of Ramsden (1735-1800).</p>
-
-<p>Few refractors for astronomical use were made after the advent
-of the reflector, which was, and is, however, badly suited for the
-purposes of a portable spy-glass, owing to trouble from stray
-light. The refractor therefore permanently held its own in this
-function, despite its length and uncorrected aberrations.</p>
-
-<p>Relief was near at hand, for hardly had Short started on his
-notable career when Chester Moor Hall, Esq. (1704-1771) a
-gentleman of Essex, designed and caused to be constructed the first
-achromatic telescope, with an objective of crown and flint glass.
-He is stated to have been studying the problem for several years,
-led to it by the erroneous belief (shared by Gregory long before)
-that the human eye was an example of an achromatic instrument.</p>
-
-<p>Be this as it may Hall had his telescopes made by George Bast
-of London at least as early as 1733, and according to the best
-available evidence several instruments were produced, one of them
-of above 2 inches aperture on a focal length of about 20 inches
-(F/8) and further, subsequently such instruments were made and
-sold by Bast and other opticians.</p>
-
-<p><span class="pagenum"><a name="Page_28" id="Page_28">[Pg 28]</a></span></p>
-
-<p>These facts are clear and yet, with knowledge of them among
-London workmen as well as among Hall’s friends, the invention
-made no impression, until it was again brought to light, and
-patented, by the celebrated John Dolland (1706-1761) in the
-year 1758.</p>
-
-<p>Physical considerations give a clue to this singular neglect.
-The only glasses differing materially in dispersion available in
-Hall’s day were the ordinary crown, and such flint as was in use
-in the glass cutting trade,—what we would now know as a light
-flint, and far from homogeneous at that.</p>
-
-<div class="figcenter">
-<img src="images/i_028.jpg" alt="" />
-<div class="caption"><i>Lodge “Pioneers of Science.”</i><br />
-<span class="smcap">Fig. 17.</span>—John Dolland.</div>
-</div>
-
-<p>Out of such material it was practically very hard (as the
-Dollands quickly found) to make a double objective decently free
-from spherical aberration, especially for one working, as Hall quite<span class="pagenum"><a name="Page_29" id="Page_29">[Pg 29]</a></span>
-assuredly did, by rule of thumb. With the additional handicap
-of flint full of faults it is altogether likely that these first achromatics,
-while embodying the correct principles, were not good
-enough to make effective headway against the cheaper and
-simpler spy-glass of the time.</p>
-
-<p>Dolland, although in 1753 he strongly supported Newton’s
-error in a Royal Society paper against Euler’s belief in achromatism,
-shifted his view a couple of years later and after a
-considerable period of skilful and well ordered experimenting published
-his discovery of achromatism early in 1758, for which a
-patent was granted him April 19, while in the same year the Royal
-Society honored him with the Copley medal. From that time
-until his death, late in 1761, he and his son Peter Dolland (1730-1820)
-were actively producing achromatic glasses.</p>
-
-<p>The Dollands were admirable craftsmen and their early product
-was probably considerably better than were Hall’s objectives but
-they felt the lack of suitable flint and soon after John Dolland’s
-death, about 1765, the son sought relief in the triple objective of
-which an early example is shown in Fig. 18, and
-which, with some modifications, was his standard
-form for many years.</p>
-
-<div class="figright">
-<img src="images/i_029.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 18.</span>—Peter Dolland’s Triple Objective.</div>
-</div>
-
-<p>Other opticians began to make achromatics,
-and, Peter Dolland having threatened action
-for infringement, a petition was brought by 35
-opticians of London in 1764 for the annulment
-of John Dolland’s patent, alleging that he was
-not the original inventor but had knowledge
-of Chester Moor Hall’s prior work. In the
-list was George Bast, who in fact did make
-Hall’s objectives twenty five years before
-Dolland, and also one Robert Rew of Coldbath
-Fields, who claimed in 1755 to have informed Dolland of
-the construction of Hall’s objective.</p>
-
-<p>This was just the time when Dolland came to the right about
-face on achromatism, and it may well be that from Rew or
-elsewhere he may have learned that a duplex achromatic lens
-had really been produced. But his Royal Society paper shows
-that his result came from honest investigations, and at worst he
-is in about the position of Galileo a century and a half before.</p>
-
-<p>The petition apparently brought no action, perhaps because
-Peter Dolland next year sued Champneys, one of the signers, and<span class="pagenum"><a name="Page_30" id="Page_30">[Pg 30]</a></span>
-obtained judgment. It was in this case that the judge (Lord
-Camden) delivered the oft quoted dictum: “It was not the
-person who locked up his invention in his scrutoire that ought to
-profit by a patent for such invention, but he who brought it
-forth for the benefit of the public.<a name="FNanchor_7_7" id="FNanchor_7_7"></a><a href="#Footnote_7_7" class="fnanchor">[7]</a>”</p>
-
-<p>This was sound equity enough, assuming the facts to be as
-stated, but while Hall did not publish the invention admittedly
-made by him, it had certainly become known to many. Chester
-Moor Hall was a substantial and respected lawyer, a bencher of
-the Inner Temple, and one is inclined to think that his alleged
-concealment was purely constructive, in his failing to contest
-Dolland’s claim.</p>
-
-<p>Had he appeared at the trial with his fighting blood up, there is
-every reason to believe that he could have established a perfectly
-good case of public use quite aside from his proof of technical
-priority. However, having clearly lost his own claims through
-<i>laches</i>, he not improbably was quite content to let the tradesmen
-fight it out among themselves. Hall’s telescopes were in
-fact known to be in existence as late as 1827.</p>
-
-<p>As the eighteenth century drew toward its ending the reflecting
-telescope, chiefly in the Gregorian form, held the field in astronomical
-work, the old refractor of many draw tubes was the spy-glass
-of popular use, and the newly introduced achromatic was
-the instrument of “the exclusive trade.” No glass of suitable
-quality for well corrected objectives had been produced, and that
-available was not to be had in discs large enough for serious
-work. A 3-inch objective was reckoned rather large.</p>
-
-<hr class="chap" />
-
-<p><span class="pagenum"><a name="Page_31" id="Page_31">[Pg 31]</a></span></p>
-
-
-
-
-<div class="chapter"></div>
-<h2><a name="CHAPTER_II" id="CHAPTER_II">CHAPTER II</a><br />
-
-<small>THE MODERN TELESCOPE</small></h2>
-
-
-<p>The chief link between the old and the new, in instrumental
-as well as observational astronomy, was Sir William Herschel
-(1738-1822). In the first place he carried the figuring of his
-mirrors to a point not approached by his predecessors, and second,
-he taught by example the immense value of aperture in definition
-and grasp of light. His life has never been adequately written,
-but Miss Clerke’s “<i>The Herschels and Modern Astronomy</i>” is
-extremely well worth the reading as a record of achievement that
-knew not the impossible.</p>
-
-<div class="figcenter">
-<img src="images/i_031.jpg" alt="" />
-<div class="caption"> <i>Miss Clerke’s Herschel &amp; Modern Astronomy</i> (<i>Macmillan</i>).<br />
-<span class="smcap">Fig. 19.</span>—Sir William Herschel.</div>
-</div>
-
-<p>He was the son of a capable band-master of Hanover, brought
-up as a musician, in a family of exceptional musical abilities,
-and in 1757 jumped his military responsibilities and emigrated to
-England, to the world’s great gain. For nearly a decade he
-struggled upward in his art, taking meanwhile every opportunity
-for self education, not only in the theory of music but in mathematics
-and the languages, and in 1767 we find him settled in
-fashionable Bath, oboist in a famous orchestra, and organist of
-the Octagon Chapel. His abilities brought him many pupils,<span class="pagenum"><a name="Page_32" id="Page_32">[Pg 32]</a></span>
-and ultimately he became director of the orchestra in which he
-had played, and the musical dictator of the famous old resort.</p>
-
-<p>In 1772 came his inspiration in the loan of a 2-foot Gregorian
-reflector, and a little casual star-gazing with it. It was the
-opening of the kingdom of the skies, and he sought to purchase a
-telescope of his own in London, only to find the price too great for
-his means. (Even a 2-foot, of 4&frac12; inches aperture, by Short
-was listed at five-and-thirty guineas.) Then after some futile
-attempts at making a plain refractor he settled down to hard
-work at casting and polishing specula.</p>
-
-<p>Although possessed of great mechanical abilities the difficult
-technique of the new art long baffled him, and he cast and worked
-some 200 small discs in the production of his first successful
-telescopes, to say nothing of a still greater number in larger sizes
-in his immediately subsequent career.</p>
-
-<p>As time went on he scored a larger proportion of successes,
-but at the start good figure seems to have been largely fortuitous.
-Inside of a couple of years, however, he had mastered
-something of the art and turned out a 5-foot instrument which
-seems to have been of excellent quality, followed later by a 7-foot
-(aperture 6&frac14; inches) even better, and then by others still bigger.</p>
-
-<p>The best of Herschel’s specula must have been of exquisite
-figure. His 7-foot was tested at Greenwich against one of Short’s
-of 9&frac12; inches aperture much to the latter’s disadvantage. His
-discovery with the 7-foot, of the “Georgium Sidus” (Uranus) in
-1781 won him immediate fame and recognition, beside spurring
-him to greater efforts, especially in the direction of larger apertures,
-of which he had fully grasped the importance.</p>
-
-<p>In 1782 he successfully completed a 12-inch speculum of 20 feet
-focus, followed in 1788 by an 18-inch of the same length. The
-previous year he first arranged his reflector as a “front view”
-telescope—the so-called Herschelian. Up to this time he, except
-for a few Gregorians, had used Newton’s oblique mirror.</p>
-
-<p>The heavy loss of light (around 40 per cent) in the second
-reflection moved him to tilt the main mirror so as to throw the
-focal point to the edge of the aperture where one could look downward
-upon the image through the ocular as shown in Fig. 20.
-Here <i>SS</i> is the great speculum, <i>O</i> the ocular and <i>i</i> the image
-formed near the rim of the tube. In itself the tilting would
-seriously impair the definition, but Herschel wisely built his
-telescopes of moderate relative aperture (F/10 to F/20), so that<span class="pagenum"><a name="Page_33" id="Page_33">[Pg 33]</a></span>
-this difficulty was considerably lessened, while the saving of
-light, amounting to nearly a stellar magnitude, was important.</p>
-
-<p>Meanwhile he was hard at work on his greatest mirror, of
-48 inches clear aperture and 40 feet focal length, the father of the
-great line of modern telescopes. It was finished in the summer of
-1789. The speculum was 49&frac12; inches in over-all diameter, 3&frac12;
-inches thick and weighed as cast 2118 lbs. The completion of
-this instrument, which would rank as large even today, was made
-notable by the immediate discovery of two new satellites of
-Saturn, Enceladus and Mimas.</p>
-
-<p>It also proved of very great value in sweeping for nebulæ,
-but its usefulness seems to have been much limited by the flexure
-of the mirror under its great weight, and by its rapid tarnishing.
-It required repolishing, which meant refiguring, at least every two
-years, a prodigious task.<a name="FNanchor_8_8" id="FNanchor_8_8"></a><a href="#Footnote_8_8" class="fnanchor">[8]</a></p>
-
-<div class="figright">
-<img src="images/i_033.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 20.</span>—Herschel’s Front View Telescope.</div>
-</div>
-
-<p>It was used as a front view instrument and was arranged as
-shown in Fig. 21. Obviously the front view form has against it
-the mechanical difficulty of supporting the observer up to quite
-the full focal length of the instrument in air, a difficulty vastly
-increased were the mount an equatorial one, so that for the great
-modern reflectors the Cassegrain form, looked into axially upward,
-and in length only a third or a quarter of the principal focus, is
-almost universal.</p>
-
-<p>As soon as the excellent results obtained by Herschel became
-generally known, a large demand arose for his telescopes, which
-he filled in so far as he could spare the time from his regular<span class="pagenum"><a name="Page_34" id="Page_34">[Pg 34]</a></span>
-work, and not the least of his services to science was the distribution
-of telescopes of high quality and consequent strong stimulus
-to general interest in astronomy.</p>
-
-<p>Two of his instruments, of 4-and 7-feet focus respectively, fell
-into the worthy hands of Schröter at Lilienthal and did sterling
-service in making his great systematic study of the lunar surface.
-At the start even Herschel’s 7-foot telescope brought 200 guineas,
-and the funds thus won he promptly turned to research.</p>
-
-<div class="figcenter">
-<img src="images/i_034.jpg" alt="" />
-<div class="caption"><i>Miss Clerke’s Herschel &amp; Modern Astronomy</i> (<i>Macmillan</i>).
-<span class="smcap"><br />Fig. 21.</span>—Herschel’s Forty-foot Telescope.</div>
-</div>
-
-<p>We sometimes think of the late eighteenth century as a time
-of license unbounded and the higher life contemned, but Herschel
-wakened a general interest in unapplied science that has hardly
-since been equalled and never surpassed. Try to picture social
-and official Washington rushing to do honor to some astronomer
-who by luck had found the trans-Neptunian planet; the diplomatic
-corps crowding his doors, and his very way to the Naval
-Observatory blocked by the limousines of the curious and admiring,
-and some idea may be gained of what really happened to the
-unassuming music master from Bath who suddenly found himself
-famous.</p>
-
-<p>Great as were the advances made by Herschel the reflector<span class="pagenum"><a name="Page_35" id="Page_35">[Pg 35]</a></span>
-was destined to fall into disuse for many years. The fact was
-that the specula had to be refigured, as in the case of the great 40-foot
-telescope, quite too often to meet the requirements of the
-ordinary user, professional or amateur. Only those capable of
-doing their own figuring could keep their instruments conveniently
-in service.</p>
-
-<p>Sir W. Herschel always had relays of specula at hand for his
-smaller instruments, and when his distinguished son, Sir John
-F. W. Herschel, went on his famous observing expedition to the
-Cape of Good Hope in 1834-38 he took along his polishing
-machine and three specula for his 20-foot telescope. And he
-needed them indeed, for a surface would sometimes go bad
-even in a week, and regularly became quite useless in 2 or 3
-months.</p>
-
-<p>Makers who used the harder speculum metal, very brittle and
-scarcely to be touched by a file, fared better, and some small
-mirrors, well cared for, have held serviceable polish for many
-years. Many of these instruments of Herschel’s time, too, were
-of very admirable performance.</p>
-
-<p>Some of Herschel’s own 7-foot telescopes give evidence of
-exquisite figure and he not only commonly used magnifying powers
-up to some 80 per inch of aperture, a good stiff figure for a
-telescope old or new, but went above 2,000, even nearly to 6,000
-on one of his 6&frac12;-inch mirrors without losing the roundness of the
-star image. “Empty magnification” of course, gaining no detail
-whatever, but evidence of good workmanship.</p>
-
-<p>Many years later the Rev. W. R. Dawes, the famous English
-observer, had a 5-inch Gregorian, commonly referred to as “The
-Jewel,” on which he used 430 diameters, and pushed to 2,000 on
-Polaris without distortion of the disc. Comparing it with a 5-foot
-(approximately 4-inch aperture) refractor, he reports the Gregorian
-somewhat inferior in illuminating power; “But in
-sharpness of definition, smallness of discs of stars, and hardness
-of outline of planets it is superior.” All of which shows that
-while methods and material may have improved, the elders did
-not in the least lack skill.</p>
-
-<p>The next step forward, and a momentous one, was to be taken
-in the achromatic refractor. Its general principles were understood,
-but clear and homogeneous glass, particularly flint glass,
-was not to be had in pieces of any size. “Optical glass,” as we
-understand the term, was unknown.</p>
-
-<p><span class="pagenum"><a name="Page_36" id="Page_36">[Pg 36]</a></span></p>
-
-<p>It is a curious and dramatic fact that to a single man was due
-not only the origin of the art but the optical glass industry of the
-world. If the capacity for taking infinite pains be genius, then
-the term rightfully belongs to Pierre Louis Guinand. He was a
-Swiss artisan living in the Canton of Neuchatel near Chaux-de-Fonds,
-maker of bells for repeaters, and becoming interested in
-constructing telescopes imported some flint glass from England
-and found it bad.</p>
-
-<p>He thereupon undertook the task of making better, and from
-1784 kept steadily at his experiments, failure only spurring him
-on to redoubled efforts. All he could earn at his trade went into
-his furnaces, until gradually he won success, and his glass began
-to be heard of; for by 1799 he was producing flawless discs of
-flint as much as 6 inches in diameter.</p>
-
-<p>What is more, to Guinand is probably due the production of
-the denser, more highly refractive flints, especially valuable for
-achromatic telescopes. The making of optical glass has always
-been an art rather than a science. It is one thing to know the
-exact composition of a glass and quite another to know in what
-order and proportion the ingredients went into the furnace, to
-what temperature they were carried, and for how long, and just
-how the fused mass must be treated to free the products from
-bubbles and striæ.</p>
-
-<p>Even today, though much has been learned by scientific investigation
-in the past few years, it is far from easy to produce two
-consecutive meltings near enough in refractive power to be
-treated as optically identical, or to produce large discs optically
-homogeneous. What Guinand won by sheer experience was
-invaluable. He was persuaded in 1805 to move to Munich and
-eventually to join forces with Fraunhofer, an association which
-made both the German optical glass industry and the modern
-refractor.</p>
-
-<p>He returned to Switzerland in 1814 and continued to produce
-perfect discs of larger and larger dimensions. One set of 12 inches
-worked up by Cauchoix in Paris furnished what was for some
-years the world’s largest refractor.</p>
-
-<p>Guinaud died in 1824, but his son Henry, moving to Paris,
-brought his treasure of practical knowledge to the glass works
-there, where it has been handed down, in effect from father to
-son, gaining steadily by accretion, through successive firms to
-the present one of Parra-Mantois.</p>
-
-<p><span class="pagenum"><a name="Page_37" id="Page_37">[Pg 37]</a></span></p>
-
-<p>Bontemps, one of the early pupils of Henry Guinand, emigrated
-to England at the Revolution of 1848 and brought the art to the
-famous firm of Chance in Birmingham. Most of its early secrets
-have long been open, but the minute teachings of experience are
-a tremendously valuable asset even now.</p>
-
-<div class="figcenter">
-<img src="images/i_037.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 22.</span>—Dr. Joseph von Fraunhofer, the Father of Astrophysics.</div>
-</div>
-
-<p>To Fraunhofer, the greatest master of applied optics in the
-nineteenth century, is due the astronomical telescope in substantially
-its present form. Not only did he become under
-Guinand’s instruction extraordinarily skillful in glass making
-but he practically devised the art of working it with mathematical
-precision on an automatic machine, and the science of correctly
-designing achromatic objectives.</p>
-
-<p>The form which he originated (Fig. 23) was the first in which
-the aberrations were treated with adequate completeness, and,
-particularly for small instruments, is unexcelled even now.<span class="pagenum"><a name="Page_38" id="Page_38">[Pg 38]</a></span>
-The curvatures here shown are extreme, the better to show their
-relations. The front radius of the crown is about 2&frac12; times
-longer than the rear radius, the front of the flint is slightly flatter
-than the back of the crown, and the rear of the flint is only
-slightly convex.</p>
-
-<p>Fraunhofer’s workmanship was of the utmost exactness and it
-is not putting the case too strongly to say that a first class example
-of the master’s craft, in good condition, would
-compare well in color-correction, definition, and
-field, with the best modern instruments.</p>
-
-<div class="figleft">
-<img src="images/i_038.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 23.</span></div>
-</div>
-
-<p>The work done by the elder Struve at Dorpat
-with Fraunhofer’s first large telescope (9.6 inches
-aperture and 170 inches focal length) tells the
-story of its quality, and the Königsberg heliometer,
-the first of its class, likewise, while even
-today some of his smaller instruments are still doing
-good service.</p>
-
-<p>It was he who put in practice the now general
-convention of a relative aperture of about F/15,
-and standardized the terrestrial eyepiece into the design quite
-widely used today. The improvements since his time have been
-relatively slight, due mainly to the recent production of varieties
-of optical glass unknown a century ago. Fraunhofer was born
-in Straubing, Bavaria, March 6, 1787. Self-educated like
-Herschel, he attained to an extraordinary combination of
-theoretical and practical knowledge that went far in laying the
-foundations of astrophysics.</p>
-
-<p>The first mapping of the solar spectrum, the invention of the
-diffraction grating and its application to determining the wave
-length of light, the first exact investigation of the refraction and
-dispersion of glass and other substances, the invention of the
-objective prism, and its use in studying the spectra of stars and
-planets, the recognition of the correspondence of the sodium lines
-to the D lines in the sun, and the earliest suggestion of the
-diffraction theory of resolution later worked out by Lord
-Rayleigh and Professor Abbé, make a long list of notable
-achievements.</p>
-
-<p>To these may be added his perfecting of the achromatic telescope,
-the equatorial mounting and its clockwork drive, the
-improvement of the heliometer, the invention of the stage mi<span class="pagenum"><a name="Page_39" id="Page_39">[Pg 39]</a></span>crometer,
-several types of ocular micrometers, and the automatic
-ruling engine.</p>
-
-<p>He died at the height of his creative powers June 7, 1826, and
-lies buried at Munich under the sublime ascription, by none
-better earned, <i>Approximavit Sidera</i>.</p>
-
-<p>From Fraunhofer’s time, at the hands of Merz his immediate
-successor, Cauchoix in France, and Tully in England, the achromatic
-refractor steadily won its way. Reflecting telescopes,
-despite the sensational work of Lord Rosse on his 6-foot mirror of
-53 feet focus (unequalled in aperture until the 6-foot of the
-Dominion Observatory seventy years later), and the even more
-successful instrument of Mr. Lassell (4 feet aperture, 39 feet
-focus), were passing out of use, for the reason already noted,
-that repolishing meant refiguring and the user had to be at once
-astronomer and superlatively skilled optician.</p>
-
-<p>These large specula, too, were extremely prone to serious flexure
-and could hardly have been used at all except for the equilibrating
-levers devised by Thomas Grubb about 1834, and used
-effectively on the Rosse instrument. These are in effect a group
-of upwardly pressing counterbalanced planes distributing among
-them the downward component of the mirror’s weight so as to
-keep the figure true in any position of the tube.</p>
-
-<p>Such was the situation in the 50’s of the last century, when the
-reflector was quite unexpectedly pushed to the front as a practical
-instrument by almost simultaneous activity in Germany and
-France. The starting point in each was Liebig’s simple chemical
-method of silvering glass, which quickly and easily lays on a thin
-reflecting film capable of a beautiful polish.</p>
-
-<p>The honor of technical priority in its application to silvering
-telescope specula worked in glass belongs to Dr. Karl August
-Steinheil (1801-1870) who produced about the beginning of
-1856 an instrument of 4-inch aperture reported to have given
-with a power of 100 a wonderfully good image. The publication
-was merely from a news item in the “<i>Allgemeine Zeitung</i>”
-of Augsburg, March 24, 1856, so it is little wonder that the
-invention passed for a time unnoticed.</p>
-
-<p>Early the next year, Feb. 16, 1857, working quite independently,
-exactly the same thing was brought before the French Academy
-of Sciences by another distinguished physicist, Jean Bernard
-Léon Foucault, immortal for his proof of the earth’s rotation by<span class="pagenum"><a name="Page_40" id="Page_40">[Pg 40]</a><br /><a name="Page_41" id="Page_41">[Pg 41]</a></span>
-the pendulum experiment, his measurement of the velocity of
-light, and the discovery of the electrical eddy currents that bear
-his name.</p>
-
-<div class="figcenter">
-<img src="images/i_040a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 24.</span>—Dr. Karl August Steinheil.</div>
-</div>
-
-<div class="figcenter">
-<img src="images/i_040b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 25.</span>—Jean Bernard Léon Foucault.<br />
-The Inventors of the Silver-on-Glass Reflector.</div>
-</div>
-
-<p>To Foucault, chiefly, the world owes the development of the
-modern silver-on-glass reflector, for not being a professional
-optician he had no hesitation in making public his admirable
-methods of working and testing, the latter now universally
-employed. It is worth noting that his method of figuring was,
-physically, exactly what Jesse Ramsden (1735-1800) had pointed
-out in 1779, (Phil. Tr. 1779, 427) geometrically. One of
-Foucault’s very early instruments mounted equatorially by
-Sécrétan is shown in Fig. 26.</p>
-
-
-<div class="figcenter">
-<img src="images/i_041.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 26.</span>—Early Foucault Reflector.</div>
-</div>
-
-<p>The immediate result of the admirable work of Steinheil and
-Foucault was the extensive use of the new reflector, and its rapid
-development as a convenient and practical instrument, especially
-in England in the skillful hands of With, Browning, and Calver.
-Not the least of its advantages was its great superiority over the
-older type in light-grasp, silver being a better reflector than specu<span class="pagenum"><a name="Page_42" id="Page_42">[Pg 42]</a></span>lum
-metal in the ratio of very nearly 7 to 5. From this time on
-both refractors and reflectors have been
-fully available to the user of telescopes.</p>
-
-<p>In details of construction both have
-gained somewhat mechanically. As we
-have seen, tubes were often of wood, and
-not uncommonly the mountings also. At
-the present time metal work of every kind
-being more readily available, tubes and
-mountings of telescopes of every size are
-quite universally of metal, save for the
-tripod-legs of the portable instruments.
-The tubes of the smaller refractors, say 3 to
-5 inches in aperture, are generally of brass,
-though in high grade instruments this is
-rapidly being replaced by aluminum, which
-saves considerable weight. Tubes above 5
-or 6 inches are commonly of steel, painted
-or lacquered. The beautifully polished
-brass of the smaller tubes, easily damaged
-and objectionably shiny, is giving way to
-a serviceable matt finish in hard lacquer.
-Mountings, too, are now more often in
-iron and steel or aluminum than in brass,
-the first named quite universally in the
-working parts, for which the aluminum is
-rather soft.</p>
-
-<p>The typical modern refractor, even of
-modest size, is a good bit more of a machine
-than it looks at first glance. In principle
-it is outlined in Fig. 5, in practice it is
-much more complex in detail and requires
-the nicest of workmanship. In fact if one
-were to take completely apart a well-made
-small refractor, including its optical
-and mechanical parts one would reckon up
-some 30 to 40 separate pieces, not counting
-screws, all of which must be accurately
-fitted and assembled if the instrument is
-to work properly.</p>
-
-<div class="figcenter">
-<img src="images/i_042.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 27.</span>—Longitudinal Section of Modern Refractor.</div>
-</div>
-
-<p>Fig. 27 shows such an instrument in<span class="pagenum"><a name="Page_43" id="Page_43">[Pg 43]</a></span>
-section from end to end, as one would find it could he lay it open
-longitudinally.</p>
-
-<p><i>A</i> is the objective cap covering the objective <i>B</i> in its adjustable
-cell <i>C</i>, which is squared precisely to the axis of the main tube <i>D</i>.
-Looking along this one finds the first of the diaphragms, <i>E</i>.</p>
-
-<p>These are commonly 3 to 6 in number spaced about equally
-down the tube, and are far more important than they look.
-Their function is not to narrow the beam of light that reaches
-the ocular, but to trap light which might enter the tube obliquely
-and be reflected from its sides into the ocular, filling it with stray
-glare.</p>
-
-<p>No amount of simple blackening will answer the purpose, for
-even dead black paint such as opticians use reflects at very oblique
-incidence quite 10 to 20 per cent of the beam. The importance
-of both diaphragms and thorough blackening has been
-realized for at least a century and a half, and one can hardly
-lay too much stress upon the matter.</p>
-
-<p>The diaphragms should be so proportioned that, when looking
-up the tube from the edge of an aperture of just the size and position
-of the biggest lens in the largest eyepiece, no part of the
-edge of the objective is cut off, and no part of the side of the
-tube is visible beyond the nearest diaphragm.</p>
-
-<p>Going further down the tube past a diaphragm or two one
-comes to the clamping screws <i>F</i>. These serve to hold the instrument
-to its mounting. They may be set in separate bases
-screwed in place on the inside of the tube, or may be set in the
-two ends of a lengthwise strap thus secured. They are placed at
-the balance point as nearly as may be, generally nearer the eye
-end than the objective.</p>
-
-<p>Then, after one or more diaphragms, comes the guide ring <i>G</i>,
-which steadies the main draw tube <i>H</i>, and the rack <i>I</i> by which it
-is moved for the focussing in turning the milled head of the pinion
-<i>J</i>. The end ring <i>K</i> of the main tube furnishes the other bearing
-of <i>H</i>, and both <i>G</i> and <i>K</i> are commonly recessed for accurately
-fitted cloth lining rings <i>L</i>, <i>L</i>, to give the draw tube the necessary
-smoothness of motion.</p>
-
-<p>For the same reason <i>I</i> and <i>J</i> have to be cut and fitted with the
-utmost exactness so as to work evenly and without backlash.
-<i>H</i> is fitted at its outer end with a slide ring and tube <i>M</i>, generally
-again cloth lined to steady the sliding eyepiece tube <i>N</i>. This is
-terminated by the spring collar <i>O</i>, in which fits the eyepiece <i>P</i>,<span class="pagenum"><a name="Page_44" id="Page_44">[Pg 44]</a></span>
-generally of the two lens form; and finally comes the eyepiece cap
-<i>Q</i> set at the proper distance from the eye lens and with an aperture
-of carefully determined size.</p>
-
-<p>One thus gets pretty well down in the alphabet without going
-much into the smaller details of construction. Both objective
-mount and ocular are somewhat complex in fact, and the former
-is almost always made adjustable in instruments of above 3 or
-4 inches aperture, as shown in Fig. 28, the form used by Cooke, the
-famous maker of York, England. Unless the optical axis of the
-objective is true with the tube bad images result.</p>
-
-<div class="figcenter">
-<img src="images/i_044.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 28.</span>—Adjustable Cell for Objective.</div>
-</div>
-
-<p>To the upper end of the tube is fitted a flanged counter-cell
-<i>c</i>, to an outward flange <i>f</i>, tapped for 3 close pairs of adjusting
-screws as <i>s</i><sub>1</sub>, <i>s</i><sub>11</sub> spaced at 120° apart. The objective cell itself,
-<i>b</i>, is recessed for the objective which is held in place by an
-interior or exterior ring <i>d</i>. The two lenses of the achromatic
-objective are usually very slightly separated by spacers, either
-tiny bits of tinfoil 120° apart, or a very thin ring with its upper
-edge cut down save at 3 points.</p>
-
-<p>This precaution is to insure that the lenses are quite uniformly
-supported instead of touching at uncertain points, and quite
-usually the pair as a whole rests below on three corresponding
-spacers. Of each pair of adjusting screws one as 1 in the pair <i>s</i><sub>11</sub>
-is threaded to push the counter cell out, the adjacent one, 2, to pull
-it in, so that when adjustment is made the objective is firmly held.
-Of the lenses that form the objective, the concave flint is commonly
-at the rear and the convex crown in front.</p>
-
-<p><span class="pagenum"><a name="Page_45" id="Page_45">[Pg 45]</a></span></p>
-
-<p>At the eye end the ocular ordinarily consists of two lenses
-each burnished into a brass screw ring, a tube, flange, cap, and
-diaphragm arranged as shown in Fig. 29. There are many
-varieties of ocular as will presently be shown, but this is a typical
-form. Figure 30 shows a complete modern refractor of four
-inches aperture on a portable equatorial stand with slow motion
-in right ascension and diagonal eye piece.</p>
-
-<p>Reflectors, used in this country less than they deserve, are,
-when properly mounted, likewise possessed of many parts. The
-smaller ones, such as are likely to come into the reader’s hands,
-are almost always in the Newtonian form, with a small oblique
-mirror to bring the image outside the tube.</p>
-
-<div class="figcenter">
-<img src="images/i_045.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 29.</span>—The Eye-Piece and its Fittings.</div>
-</div>
-
-<p>The Gregorian form has entirely vanished. Its only special
-merit was its erect image, which gave it high value as a terrestrial
-telescope before the days of achromatics, but from its
-construction it was almost impossible to keep the field from being
-flooded with stray light, and the achromatic soon displaced it.
-The Cassegranian construction on the other hand, shorter and
-with aberrations much reduced, has proved important for obtaining
-long equivalent focus in a short mount, and is almost universally
-applied to large reflectors, for which a Newtonian mirror
-is also generally provided.</p>
-
-<p>Figure 31 shows in section a typical reflector of the Newtonian
-form. Here <i>A</i> is the main tube, fitted near its outer end with a
-ring <i>B</i> carrying the small elliptical mirror <i>C</i>, which is set at 45°
-to the axis of the tube. At the bottom of the tube is the parabolic
-main mirror <i>D</i>, mounted in its cell <i>E</i>. Just opposite the
-45° small mirror is a hole in the tube to which is fitted the eye<span class="pagenum"><a name="Page_46" id="Page_46">[Pg 46]</a></span>
-piece mounting <i>F</i>, carrying the eyepiece <i>G</i>, fitted to a spring
-collar <i>H</i>, screwed into a draw tube <i>I</i>, sliding in its mounting and
-brought to focus by the rack-and-pinion <i>J</i>.</p>
-
-<div class="figcenter">
-<img src="images/i_046.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 30.</span>—Portable Equatorial Refractor (Brashear).</div>
-</div>
-
-<p>At <i>K</i>, <i>K</i>, are two rings fixed to the tube and bearing smoothly
-against the rings <i>L L</i> rigidly fixed to the bar <i>M</i> carried by the
-polar axis of the mount. The whole tube can therefore be rotated
-about its axis so as to bring the eye piece into a convenient posi<span class="pagenum"><a name="Page_47" id="Page_47">[Pg 47]</a><br /><a name="Page_48" id="Page_48">[Pg 48]</a></span>tion
-for observation. One or more handles, <i>N</i>, are provided for
-this purpose.</p>
-
-<div class="figcenter">
-<img src="images/i_047.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 31.</span>—Longitudinal Section of Newtonian Reflector.</div>
-</div>
-
-<p>Brackets shown in dotted lines at <i>O</i>, <i>O</i>, carry the usual finder,
-and a hinged door <i>P</i> near the lower end of the tube enables one to
-remove or replace the close fitting metal cover that protects the
-main mirror when not in use. Similarly a cover is fitted to the
-small mirror, easily reached from the upper end of the tube. The
-proportions here shown are approximately those commonly
-found in medium sized instruments, say 7 to 10 inches aperture.
-The focal ratio is somewhere about <i>F</i>/6, the diagonal mirror is
-inside of focus by about the diameter of the main mirror, and
-its minor axis is from ⅕ to &frac14; that diameter.</p>
-
-<div class="figcenter">
-<img src="images/i_048.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 32.</span>—Reflector with Skeleton Tube (Brashear).</div>
-</div>
-<p>Note that the tube is not provided with diaphragms. It
-is merely blackened as thoroughly as possible, although stray
-light is quite as serious here as in a refractor. One could fit<span class="pagenum"><a name="Page_49" id="Page_49">[Pg 49]</a></span>
-diaphragms effectively only in a tube of much larger diameter
-than the mirror, which would be inconvenient in many
-ways.</p>
-
-<p>A much better way of dealing with the difficulty is shown in Fig.
-32 in which the tube is reduced to a skeleton, a construction common
-in large instruments. Nothing is blacker than a clear
-opening into the darkness of night, and in addition there can be
-no localized air currents, which often injure definition in an ordinary
-tube.</p>
-
-<div class="figright">
-<img src="images/i_049.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 33.</span></div>
-</div>
-
-<p>Instruments by different makers vary somewhat in detail. A
-good type of mirror mounting is
-that shown in Fig. 33, and used
-for many years past by Browning,
-one of the famous English makers.
-Here the mirror <i>A</i>, the back of
-which is made accurately plane,
-is seated in its counter-cell <i>B</i>, of
-which a wide annulus <i>F</i>, <i>F</i>, is also a good plane, and is lightly held
-in place by a retaining ring. This counter cell rests in the outer
-cell <i>C</i> on three equidistant studs regulated by the concentric
-push-and-pull adjusting screws <i>D</i>, <i>D</i>, <i>E</i>, <i>E</i>. The outer cell
-may be solid, or a skeleton for lightness and better equalization
-of temperature.</p>
-
-<p>Small specula may be well supported on any flat surface substantial
-enough to be thoroughly rigid, with one or more thicknesses
-of soft, thick, smooth cloth between, best of all Brussels
-carpet. Such was the common method of support in instruments
-of moderate dimensions prior to the day of glass specula. Sir
-John Herschel speaks of thus carrying specula of more than a
-hundred-weight, but something akin to Browning’s plan is
-generally preferable.</p>
-
-<p>There is also considerable variety in the means used for supporting
-the small mirror centrally in the tube. In the early
-telescopes it was borne by a single stiff arm which was none too
-stiff and produced by diffraction a long diametral flaring ray in
-the images of bright stars.</p>
-
-<p>A great improvement was introduced by Browning more than
-a half century ago, in the support shown in Fig. 34. Here the
-ring <i>A</i>, (<i>B</i>, Fig. 31) carries three narrow strips of thin spring
-steel, <i>B</i>, extending radially inward to a central hub which carries
-the mirror <i>D</i>, on adjusting screws <i>E</i>. Outside the ring the ten<span class="pagenum"><a name="Page_50" id="Page_50">[Pg 50]</a></span>sion
-screws <i>C</i> enable the mirror to be accurately centered and
-held in place. Rarely, the mirror is replaced by a totally reflecting
-right angled prism which saves some light, but unless for
-small instruments is rather heavy and hard to obtain of the requisite
-quality and precision of figure. A typical modern reflector
-by Brashear, of 6 inches aperture, is shown in Fig. 35, complete
-with circles and driving clock, the latter contained in the hollow
-iron pier, an arrangement usual in American-made instruments.</p>
-
-<div class="figcenter">
-<img src="images/i_050.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 34.</span>—Support of Diagonal Mirror (Browning.)</div>
-</div>
-
-<p>Recent reflectors, particularly in this country, have four supporting
-strips instead of three, which gives a little added stiffness,
-and produces in star images but four diffraction rays instead of
-the six produced by the three strip arrangement, each strip
-giving a diametral ray.</p>
-
-<p>In some constructions the ring <i>A</i> is arranged to carry the eyepiece
-fittings, placed at the very end of the tube and arranged for
-rotating about the optical axis of the telescope. This allows the
-ocular to be brought to any position without turning the whole
-tube. In small instruments a fixed eyepiece can be used without
-much inconvenience if located on the north side of the tube (in
-moderate north latitudes).</p>
-
-<p>Reflectors are easily given a much greater relative aperture
-than is practicable in a single achromatic objective. In fact
-they are usually given apertures of <i>F</i>/5 to <i>F</i>/8 and now and then
-are pushed to or even below <i>F</i>/3. Such mirrors have been
-successfully used for photography;<a name="FNanchor_9_9" id="FNanchor_9_9"></a><a href="#Footnote_9_9" class="fnanchor">[9]</a> and less frequently for visual
-observation, mounted in the Cassegranian form, which commonly
-increases the virtual focal length at least three or four times. A
-telescope so arranged, with an aperture of a foot or more as in<span class="pagenum"><a name="Page_51" id="Page_51">[Pg 51]</a></span>
-some recent examples, makes a very powerful and compact
-instrument.</p>
-
-<div class="figcenter">
-<img src="images/i_051.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 35.</span>—Small Equatorially Mounted Reflector.</div>
-</div>
-
-<p>This is the form commonly adopted for the large reflectors of
-recent construction, a type being the 60-inch telescope of the
-Mount Wilson Observatory of which the primary focus is 25&frac14;
-feet and the ordinary equivalent focus as a Cassegranian 80
-feet.</p>
-
-<p><span class="pagenum"><a name="Page_52" id="Page_52">[Pg 52]</a></span></p>
-
-<p>Comparatively few small reflectors have been made or used
-in the United States, although the climatic conditions here are
-more favorable than in England, where the reflector originated
-and has been very fully developed. The explanation may lie
-in our smaller number of non-professional active astronomers
-who are steadily at observational work, and can therefore use
-reflectors to the best advantage.</p>
-
-<p>The relative advantages of refractors and reflectors have
-long been a matter of acrimonious dispute. In fact, more of the
-genuine <i>odium theologicum</i> has gone into the consideration of this
-matter than usually attaches to differences in scientific opinion.
-A good many misunderstandings have been due to the fact that
-until recently few observers were practically familiar with both
-instruments, and the professional astronomer was a little inclined
-to look on the reflector as fit only for amateurs. The comparison
-is somewhat clarified at present by the fact that the old speculum
-metal reflector has passed out of use, and the case now stands as
-between the ordinary refracting telescope such as has just been
-described, and the silver-on-glass reflector discussed immediately
-thereafter.</p>
-
-<p>The facts in the case are comparatively simple. Of two
-telescopes having the same clear aperture, one a reflector and the
-other a refractor, each assumed to be thoroughly well figured, as it
-can be in fact today, the theoretical resolving power is the same,
-for this is determined merely by the aperture, so that the only
-possible difference between the two would be in the residual imperfection
-in the performance of the refractor due to its not being
-perfectly achromatic. This difference is substantially a negligible
-one for many, but not all, purposes.</p>
-
-<p>Likewise, the general definition of the pair, assuming first-class
-workmanship, would be equal. Of the two, the single
-surface of the mirror is somewhat more difficult to figure with the
-necessary precision than is any single surface of the refractor, but
-reflectors can be, and are, given so perfect a parabolic figure that
-the image is in no wise inferior to that produced by the best
-refractors, and the two types of telescopes will stand under
-favorable circumstances the same proportional magnifying
-powers.</p>
-
-<p>The mirror is much more seriously affected by changes of
-temperature and by flexure than is the objective, since in the
-former case the successive surfaces of the two lenses in the achro<span class="pagenum"><a name="Page_53" id="Page_53">[Pg 53]</a></span>matic
-combination to a considerable extent compensate each
-other’s slight changes of curvature, which act only by still slighter
-changes of refraction, while the mirror surface stands alone and
-any change in curvature produces double the defect on the reflected
-ray.</p>
-
-<p>It is therefore necessary, as we shall see presently, to take
-particular precautions in working with a reflecting telescope,
-which is, so to speak, materially more tender as regards external
-conditions than the refractor. As regards light-grasp, the power
-of rendering faint objects visible, there is more room for honest
-variety of opinion. It was often assumed in earlier days that a
-reflector was not much brighter than a refractor of half the
-aperture, <i>i.e.</i>, of one quarter the working area.</p>
-
-<p>This might have been true in the case of an old speculum metal
-reflector in bad condition, but is certainly a libel on the silver-on-glass
-instrument, which Foucault on the other hand claimed to be,
-aperture for aperture, brighter than the refractor. Such a
-relation might in fact temporarily exist, but it is far from
-typical.</p>
-
-<p>The real relation depends merely on the light losses demonstrably
-occurring in the two types of telescopes. These are now
-quite well known. The losses in a refractor are those due to
-absorption of light in the two lenses, plus those due to the four
-free surfaces of these lenses. The former item in objectives of
-moderate size aggregates hardly more than 2 to 3 per cent.
-The latter, assuming the polish to be quite perfect, amount to
-18 to 20 per cent of the incident light, for the glasses commonly
-used.</p>
-
-<p>The total light transmitted is therefore not over 80 per cent
-of the whole, more often somewhat under this figure. For
-example, a test by Steinheil of one of Fraunhofer’s refractors
-gave a transmission of 78 per cent, and other tests show similar
-results.</p>
-
-<p>The relation between the light transmitted by glass of various
-thickness is very simple. If unit thickness transmits m per cent
-of the incident light then n units in thickness will pass m<sup>n</sup> per
-cent. Thus if one half inch passes .98, two inches will transmit
-.98<sup>4</sup>, or .922. Evidently the bigger the objective the greater the
-absorptive loss. If the loss by reflection at a single surface
-leaves m per cent to be transmitted then n surfaces will transmit
-<span class="pagenum"><a name="Page_54" id="Page_54">[Pg 54]</a></span>m<sup>n</sup>. And m being usually about .95, the four surfaces of an objective
-let pass nearly .815, and the thicker objective as a whole
-transmits approximately 75 per cent.</p>
-
-<p>As to the reflector the whole relation hinges on the coefficient
-of reflection from a silvered surface, under the circumstances of
-the comparison.</p>
-
-<p>In the case of a reflecting telescope as a whole, there are
-commonly two reflections from silver and if the coefficient of
-reflection is m then the total light reflected is m². Now the
-reflectivity of a silver-on-glass film has been repeatedly measured.
-(Chant Ap. J. <b>21</b>, 211) found values slightly in excess of 95
-per cent, Rayleigh (Sci. Papers <b>2, 4</b>) got 93.9, Zeiss (Landolt u.
-Bornstein, Tabellen) about 93.0 for light of average wave
-length.</p>
-
-<p>Taking the last named value, a double reflection would return
-substantially 86.5 per cent of the incident light. No allowance
-is here made for any effect of selective reflection, since for the
-bright visual rays, which alone we are considering, there is very
-slight selective effect. In the photographic case it must be
-taken into account, and the absorption in glass becomes a
-serious factor in the comparison, amounting for the photographic
-rays to as much as 30 to 40 per cent in large instruments. Now
-in comparing reflector and refractor one must subtract the
-light stopped by the small mirror and its supports, commonly
-from 5 to 7 per cent. One is therefore forced to the conclusion
-that with silver coatings fresh and very carefully polished
-reflector and refractor will show for equal aperture equal light
-grasp.</p>
-
-<p>But as things actually go even fresh silver films are quite often
-below .90 in reflectivity and in general tarnish rather rapidly,
-so that in fact the reflector falls below the refractor by just about
-the amount by which the silver films are out of condition. For
-example Chant (loc. cit.) found after three months his reflectivity
-had fallen to .69. A mirror very badly tarnished by fifteen weeks
-of exposure to dampness and dust, uncovered, was found by the
-writer down to a scant .40.</p>
-
-<p>The line of Fig. 36 shows the relative equivalent apertures of
-refractors corresponding to a 10 inch reflector at coefficients of
-reflection for a single silvered surface varying from .95 to .50 at
-which point the film would be so evidently bad as to require immediate
-renewal. The relation is obviously linear when the
-transmission of the objective is, as here, assumed constant. The<span class="pagenum"><a name="Page_55" id="Page_55">[Pg 55]</a></span>
-estimates of skilled observers from actual comparisons fall in well
-with the line, showing reflectivities generally around .80 to .85
-for well polished films in good condition.</p>
-
-<p>The long and short of the situation is that a silvered reflector
-deteriorates and at intervals varying from a few months to a year
-or two depending on situation, climate, and usage, requires
-repolishing or replacement of the film. This is a fussy job, but
-quickly done if everything goes well.</p>
-
-<div class="figcenter">
-<img src="images/i_055.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 36.</span>—Relative Light-grasp of Reflector and Refractor.</div>
-</div>
-
-<p>As to working field the reflector as ordinarily proportioned is at
-a disadvantage chiefly because it works at <i>F</i>/5 or <i>F</i>/6 instead of
-at <i>F</i>/15. At equal focal ratios there is no substantial difference
-between reflector and refractor in this respect, unless one goes
-into special constructions, as in photographic telescopes.</p>
-
-<p>In two items, first cost and convenience in observing, the
-reflector has the advantage in the moderate sizes. Roughly,
-the reflector simply mounted costs about one half to a quarter the
-refractor of equal light grasp and somewhat less resolving power,
-the discrepancy getting bigger in large instruments (2 feet aperture
-and upwards).</p>
-
-<p><span class="pagenum"><a name="Page_56" id="Page_56">[Pg 56]</a></span></p>
-
-<p>As to case of observing, the small refractor is a truly neck-wringing
-instrument for altitudes above 45° or thereabouts, just
-the situation in which the equivalent reflector is most convenient.
-In considering the subject of mounts these relations will appear
-more clearly.</p>
-
-<p>Practically the man who is observing rather steadily and can
-give his telescope a fixed mount can make admirable use of a
-reflector and will not find the perhaps yearly or even half yearly
-re-silvering at all burdensome after he has acquired the knack—chiefly
-cleanliness and attention to detail.</p>
-
-<p>If, like many really enthusiastic amateurs, he can get only an
-occasional evening for observing, and from circumstances has to
-use a portable mount set up on his lawn, or even roof, when
-fortune favors an evening’s work, he will find a refractor always
-in condition, easy to set up, and requiring a minimum of time to
-get into action. The reflector is much the more tender instrument,
-with, however, the invaluable quality of precise achromatism,
-to compensate for the extra care it requires for its best
-performance. It suffers more than the refractor, as a rule, from
-scattered light, for imperfect polish of the film gives a field
-generally presenting a brighter background than the field of a
-good objective. After all the preference depends greatly on the
-use to which the telescope is to be put. For astrophysical work
-in general, Professor George E. Hale, than whom certainly no one
-is better qualified to judge, emphatically endorses the reflector.
-Most large observatories are now-a-days equipped with both
-refractors and reflectors.</p>
-
-<hr class="chap" />
-
-<p><span class="pagenum"><a name="Page_57" id="Page_57">[Pg 57]</a></span></p>
-
-
-
-
-<div class="chapter"></div>
-<h2><a name="CHAPTER_III" id="CHAPTER_III">CHAPTER III</a><br />
-
-<small>OPTICAL GLASS AND ITS WORKING</small></h2>
-
-
-<p>Glass, one of the most remarkable and useful products of
-man’s devising, had an origin now quite lost in the mists of
-antiquity. It dates back certainly near a thousand years before
-the Christian era, perhaps many centuries more. Respecting its
-origin there are only traditions of the place, quite probably Syria,
-and of the accidental melting together of sand and soda. The
-product, sodium silicate, readily becomes a liquid, i.e., “water-glass,”
-but the elder Pliny, who tells the story, recounts the later
-production of a stable vitreous body by the addition of a mineral
-which was probably a magnesia limestone.</p>
-
-<p>This combination would give a good permanent glass, whether
-the story is true or not, and very long before Pliny’s time glass
-was made in great variety of composition and color. In fact
-in default of porcelain glass was used in Roman times relatively
-more than now. But without knowledge of optics there was no
-need for glass of optical quality, it was well into the Renaissance
-before its manufacture had reached a point where anything of the
-sort could be made available even in small pieces, and it is barely
-over a century since glass-making passed beyond the crudest
-empiricism.</p>
-
-<p>Glass is substantially a solid solution of silica with a variety of
-metallic oxides, chiefly those of sodium, potassium, calcium and
-lead, sometimes magnesium, boron, zinc, barium and others.</p>
-
-<p>By itself silica is too refractory to work easily, though
-silica glass has some very valuable properties, and the alkaline
-oxides in particular serve as the fluxes in common use. Other
-oxides are added to obtain various desired properties, and some
-impurities may go with them.</p>
-
-<p>The melted mixture is thus a somewhat complex solution containing
-frequently half a dozen ingredients. Each has its own
-natural melting and vaporizing point, so that while the blend
-remains fairly uniform it may tend to lose some constituent while
-molten, or in cooling to promote the crystallization of another, if
-held too near its particular freezing point. Some combinations are
-more likely to give trouble from this cause than others, and while<span class="pagenum"><a name="Page_58" id="Page_58">[Pg 58]</a></span>
-a very wide variety of oxides can be coerced into solution with
-silica, a comparatively limited number produce a homogeneous
-and colorless glass useful for optical purposes.</p>
-
-<p>Many mixtures entirely suitable for common commercial purposes
-are out of the question for lens making, through tendency
-to surface deterioration by weathering, lack of homogeneous
-quality, or objectionable coloration. A very small amount of
-iron in the sand used at the start gives the green tinge familiar
-in cheap bottles, which materially decreases the transparency.
-The bottle maker often adds oxide of manganese to the mixture,
-which naturally of itself gives the glass a pinkish tinge, and so
-apparently whitens it by compensating the one absorption by
-another. The resulting glass looks all right on a casual glance,
-but really cuts off a very considerable amount of light.</p>
-
-<p>A further difficulty is that glass differs very much in its degree
-of fluidity, and its components sometimes seem to undergo mutual
-reactions that evolve persistent fine bubbles, besides reacting
-with the fireclay of the melting pot and absorbing impurities
-from it.</p>
-
-<p>The molten glass is somewhat viscous and far from homogeneous.
-Its character suggests thick syrup poured into water, and
-producing streaks and eddies of varying density. Imagine such a
-mixture suddenly frozen, and you have a good idea of a common
-condition in glass, transparent, but full of striæ. These are
-frequent enough in poor window glass, and are almost impossible
-completely to get rid of, especially in optical glass of some of the
-most valuable varieties.</p>
-
-<p>The great improvement introduced by Guinand was constant
-stirring of the molten mass with a cylinder of fire clay, bringing
-bubbles to the surface and keeping the mass thoroughly mixed
-from its complete fusion until, very slowly cooling, it became too
-viscous to stir longer.</p>
-
-<p>The fine art of the process seems to be the exact combination of
-temperature, time, and stirring, suitable for each composition
-of the glass. There are, too, losses by volatilization during
-melting, and even afterwards, that must be reckoned with in the
-proportions of the various materials put into the melting, and in
-the temperatures reached and maintained.</p>
-
-<p><span class="pagenum"><a name="Page_59" id="Page_59">[Pg 59]</a></span></p>
-
-<p>One cannot deduce accurately the percentage mixture of the
-raw materials from an analysis of the glass, and it is notorious
-that the product even of the best manufacturers not infrequently
-fails to run quite true to type. Therefore the optical properties
-of each melting have carefully to be ascertained, and the product
-listed either as a very slight variant from its standard type, or
-as an odd lot, useful, but quite special in properties. Some of
-these odd meltings in fact have optical peculiarities the regular
-reproduction of which would be very desirable.</p>
-
-<p>The purity of the materials is of the utmost importance in
-producing high grade glass for optical or other purposes. The
-silica is usually introduced in the form of the purest of white
-sand carrying only a few hundredths of one per cent of impurities
-in the way of iron, alumina and alkali. The ordinary alkalis
-go in preferably as carbonates, which can be obtained of great
-purity; although in most commercial glass the soda is used in the
-form of “salt-cake,” crude sodium sulphate.</p>
-
-<p>Calcium, magnesium, and barium generally enter the melt as
-carbonates, zinc and lead as oxides. Alumina, like iron, is generally
-an impurity derived from felspar in the sand, but occasionally
-enters intentionally as pure natural felspar, or as chemically
-prepared hydrate. A few glasses contain a minute amount of
-arsenic, generally used in the form of arsenious acid, and still
-more rarely other elements enter, ordinarily as oxides.</p>
-
-<p>Whatever the materials, they are commonly rather fine ground
-and very thoroughly mixed, preferably by machinery, before
-going into the furnaces. Glass furnaces are in these days commonly
-gas fired, and fall into two general classes, those in which
-the charge is melted in a huge tank above which the gas flames
-play, and those in which the charge is placed in crucibles or pots
-open or nearly closed, directly heated by the gas. In the tank
-furnaces the production is substantially continuous, the active
-melting taking place at one end, where the materials are introduced,
-while the clear molten glass flows to the cooler end of the
-tank or to a cooler compartment, whence it is withdrawn for
-working.</p>
-
-<p>The ordinary method of making optical glass is by a modification
-of the pot process, each pot being fired separately to permit
-better regulation of the temperature.</p>
-
-<p>The pots themselves are of the purest of fire clay, of moderate
-capacity, half a ton or so, and arched over to protect the contents<span class="pagenum"><a name="Page_60" id="Page_60">[Pg 60]</a></span>
-from the direct play of the gases, leaving a side opening sufficient
-for charging and stirring.</p>
-
-<p>The fundamental difference between the making of optical
-glass and the ordinary commercial varieties lies in the individual
-treatment of each charge necessary to secure uniformity and regularity,
-carried even to the extent of cooling each melting very
-slowly in its own pot, which is finally broken up to recover the
-contents. The tank furnaces are under heat week in and week
-out, may hold several hundred tons, and on this account cannot
-so readily be held to exactness of composition and quality.</p>
-
-<p>The optical glass works, too, is provided with a particularly
-efficient set of preheating and annealing kilns, for the heat treatment
-of pots and glass must be of the most careful and thorough
-kind.</p>
-
-<p>The production of a melting of optical glass begins with a very
-gradual heating of the pot to a bright red heat in one of the kilns.
-It is then transferred to its furnace which has been brought to a
-similar temperature, sealed in by slabs of firebrick, leaving its
-mouth easy of access, and then the heat is pushed up to near
-the melting temperature of the mixture in production, which
-varies over a rather wide range, from a moderate white heat
-to the utmost that a regenerative gas furnace can conveniently
-produce. After the heating comes the rather careful process of
-charging.</p>
-
-<p>The mixture is added a portion at a time, since the fused
-material tends to foam, and the raw material as a solid is more
-bulky than the fluid. The chemical reactions as the mass fuses
-are somewhat complex. In their simplest form they represent
-the formation of silicates.</p>
-
-<p>At high temperatures the silica acts as a fairly strong acid, and
-decomposes the fused carbonates of sodium and potassium with
-evolution of gas. This is the <i>rationale</i> of the fluxing action of
-such alkaline substances of rather low melting point. Other
-mixtures act somewhat analogously but in a fashion commonly
-too complex to follow.</p>
-
-<p>The final result is a thick solution, and the chief concern of
-the optical glass maker is to keep it homogeneous, free from
-bubbles, and as nearly colorless as practicable. To the first two
-ends the temperature is pushed up to gain fluidity, and frequently
-substances are added (e.g., arsenic) which by volatility or chemical
-effect tend to form large bubbles from the entrained gases, cap<span class="pagenum"><a name="Page_61" id="Page_61">[Pg 61]</a></span>able
-of clearing themselves from the fluid where fine bubbles
-would remain. For the same purpose is the stirring process.</p>
-
-<p>The stirrer is a hard baked cylinder of fire clay fastened to an
-iron bar. First heated in the mouth of the pot, the stirrer is
-plunged in the molten glass and given a steady rotating motion,
-the long bar being swivelled and furnished with a wooden handle
-for the workman. This stirring is kept up pretty steadily while
-the heat is very slowly reduced until the mass is too thick to manage,
-the process taking, for various mixtures and conditions, from
-three or four hours to the better part of a day.</p>
-
-<div class="figcenter">
-<img src="images/i_061.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 37.</span>—Testing Optical Glass in the Rough.</div>
-</div>
-
-<p>Then begins the careful and tedious process of cooling. Fairly
-rapid until the mass is solid enough to prevent the formation of
-fresh striæ, the cooling is continued more slowly, in the furnace
-or after removal to the annealing oven, until the crucible is cool
-enough for handling, the whole process generally taking a week or
-more.</p>
-
-<p>Then the real trouble begins. The crucible is broken away
-and there is found a more or less cracked mass of glass, sometimes
-badly broken up, again furnishing a clear lump weighing some
-hundreds of pounds. This glass is then carefully picked over and
-examined for flaws, striæ and other imperfections.</p>
-
-<p>These can sometimes be chipped away with more or less breaking
-up of the mass. The inspection of the glass in the raw is
-facilitated by the scheme shown in elevation Fig. 37. Here <i>A</i> is a
-tank with parallel sides of plate glass. In it is placed <i>B</i> the
-rough block of glass, and the tank is then filled with a liquid
-which can be brought to the same refractive power as the glass,
-as in Newton’s disastrous experiment. When equality is reached
-for, say, yellow light, one can see directly through the block, the<span class="pagenum"><a name="Page_62" id="Page_62">[Pg 62]</a></span>
-rays no longer being refracted at its surface, and any interior
-striæ are readily seen even in a mass a foot or more thick. Before
-adding the liquid a ray would be skewed, as <i>C</i>, <i>D</i>, <i>E</i>, <i>F</i>, afterwards
-it would go straight through; <i>C</i>, <i>D</i>, <i>G</i>, <i>H</i>.</p>
-
-<p>The fraction that passes inspection may be found to be from
-much less than a quarter to a half of the whole. This good glass
-is then ready for the next operation, forming and fine annealing.
-The final form to be reached is a disc or block, and the chunks of
-perfect glass are heated in a kiln until plastic, and then moulded
-into the required shapes, sometimes concave or convex discs
-suitable for small lenses.</p>
-
-<p>Then the blocks are transferred to a kiln and allowed to cool
-off very gradually, for several days or weeks according to the size
-of the blocks and the severity of the requirements they must
-meet. In the highest class of work the annealing oven has
-thermostatic control and close watch is kept by the pyrometer.</p>
-
-<p>It is clear that the chance of getting a large and perfect
-chunk from the crucible is far smaller than that of getting fragments
-of a few pounds, so that the production of a perfect disc
-for a large objective requires both skill and luck. Little wonder
-therefore that the price of discs for the manufacture of objectives
-increases substantially as the cube of the diameter.</p>
-
-<p>The process of optical glass making as here described is the
-customary one, used little changed since the days of Guinand.
-The great advances of the last quarter century have been in the
-production of new varieties having certain desirable qualities, and
-in a better understanding of the conditions that bring a uniform
-product of high quality. During the world war the greatly
-increased demand brought most extraordinary activity in the
-manufacture, and especially in the scientific study of the problems
-involved, both here and abroad. The result has been a long
-step toward quantity production, the discovery that modifications
-of the tank process could serve to produce certain varieties
-of optical glass of at least fair quality, and great improvements in
-the precision and rapidity of annealing.</p>
-
-<p>These last are due to the use of the electric furnace, the study
-of the strains during annealing under polarized light, and scientific
-pyrometry. It is found that cooling can be much hastened
-over certain ranges of temperature, and the total time required
-very greatly shortened. It has also been discovered, thanks to
-captured instruments, that some of the glasses commonly regarded<span class="pagenum"><a name="Page_63" id="Page_63">[Pg 63]</a></span>
-as almost impossible to free from bubbles have in fact yielded to
-improved methods of treatment.</p>
-
-<p>Conventionally optical glass is of two classes, crown and
-flint. Originally the former was a simple compound of silica
-with soda and potash, sometimes also lime or magnesia, while the
-latter was rich in lead oxide and with less of alkali. The crown
-had a low index of refraction and small dispersion, the flint a
-high index and strong dispersion. Crown glass was the material
-of general use, while the flint glass was the variety used in cut
-glass manufacture by reason of its brilliancy due to the qualities
-just noted.</p>
-
-<div class="figcenter">
-<img src="images/i_063.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 38.</span>—The Index of Refraction.</div>
-</div>
-
-<p>The refractive index is the ratio between the sine of the angle
-of incidence on a lens surface and that of the angle of refraction
-in passing the surface. Fig. 38 shows the relation of the incident
-and refracted rays in passing from air into the glass lens
-surface <i>L</i>, and the sines of the angles which determine n, the conventional
-symbol for the index of refraction. Here <i>i</i> is the angle of
-incidence and <i>r</i> the angle of refraction i.e. n = <i>s</i>/<i>s′</i>. The indices
-of refraction are usually given for specific colors representing
-certain lines in the spectrum, commonly <i>A</i>¹, the potassium line
-in the extreme red, <i>C</i> the red line due to hydrogen, <i>D</i> the sodium
-line, <i>F</i> the blue hydrogen line and <i>G′</i> the blue-violet line hydrogen
-line, and are distinguished as n<sub><i>c</i></sub>, n<sub><i>d</i></sub>, n<sub><i>f</i></sub>, etc. The standard dispersion
-(dn) for visual rays is given as between <i>C</i> and <i>F</i>, while the
-standard refractivity is taken for <i>D</i>, in the bright yellow part
-of the spectrum. (Note. For the convenience of those who are
-rusty on their trigonometry, Fig. 39 shows the simpler trigonometric
-functions of an angle. Thus the sine of the angle <i>A</i> is,
-numerically, the length of the radius divided into the length of<span class="pagenum"><a name="Page_64" id="Page_64">[Pg 64]</a></span>
-the line dropped from the end of the radius to the horizontal
-base line, i.e. <i>bc</i>/<i>Ob</i>, the tangent is <i>da</i>/<i>Ob</i>, and the cosine <i>Oc</i>/<i>Ob</i>.)</p>
-
-<p>Ordinarily the index of refraction of the crown was taken as
-about 3/2, that of the flint as about 8/5. As time has gone on
-and especially since the new glasses from the Jena works were
-introduced about 35 years ago, one cannot define crowns and
-flints in any such simple fashion, for there are crowns of high
-index and flints of low dispersion.</p>
-
-<div class="figcenter">
-<img src="images/i_064.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig.39.</span>—The Simple Trigonometric Functions of an Angle.</div>
-</div>
-
-<p>The following table gives the optical data and chemical analyses
-of a few typical optical glasses. The list includes common
-crowns and flints, a typical baryta crown and light flint, and a
-telescope crown and flint for the better achromatization of objectives,
-as developed at the Jena works.</p>
-
-<p>The thing most conspicuous here as distinguishing crowns from
-flints is that the latter have greater relative dispersion in the
-blue, the former in the red end of the spectrum, as shown by the
-bracketed ratios. This as we shall see is of serious consequence
-in making achromatic objectives. In general, too, the values of
-ν for flints are much lower than for crowns, and the indices of
-refraction themselves commonly higher.</p>
-
-<p>As we have just seen, glass comes to the optician in blocks
-or discs, for miscellaneous use the former, three or four inches
-square and an inch think, more or less; for telescope making the
-latter. The discs are commonly some ten percent greater in
-diameter than the finished objective for which they are intended,
-and in thickness from 1/8 to 1/10 the diameter. They are commonly
-well annealed and given a preliminary polish on both sides
-to facilitate close inspection.</p>
-
-<p><span class="pagenum"><a name="Page_65" id="Page_65">[Pg 65]</a></span></p>
-
-<p class="center"><a id="Characteristics_of_Optical_Glasses"></a>Characteristics of Optical Glasses</p>
-
-
-<div class="center">
-<table class="small" border="1" cellpadding="4" cellspacing="0" summary="">
-<tr>
-  <th align="center" rowspan="2">Glass</th>
-  <th align="center" rowspan="2">n<sub><i>d</i></sub></th>
-  <th align="center" rowspan="2"><span class="u">&nbsp; dn &nbsp;</span><br />(F-C)</th>
-  <th align="center" rowspan="2">ν</th>
-  <th align="center" colspan="3">Bracketed numbers are proportions of dn</th>
-</tr>
-<tr>
-  <th align="center"><span class="u">D-A´</span><br />dn</th>
-  <th align="center"><span class="u">F-D</span><br />dn</th>
-  <th align="center"><span class="u">G´-F</span><br />dn</th>
-</tr>
-<tr><td align="left" rowspan="2"> Boro-silicate crown</td>
-  <td align="right">1.5069</td>
-  <td align="right">.00813</td>
-  <td align="right">62.3</td>
-  <td align="right">.00529</td>
-  <td align="right">.00569</td>
-  <td align="right">.00457</td>
-</tr>
-<tr>
-
-  <td align="right"></td>
-  <td align="right">(.651)</td>
-  <td align="right">(.701)</td>
-  <td align="right">(.562)</td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="left" rowspan="2"> Zinco-silicate (hard) crown</td>
-  <td align="right">1.5170</td>
-  <td align="right">.00859</td>
-  <td align="right">60.2</td>
-  <td align="right">.00555</td>
-  <td align="right">.00605</td>
-  <td align="right">.00485</td>
-</tr>
-<tr>
-
-  <td align="left"></td>
-  <td align="right">(.646)</td>
-  <td align="right">(.704)</td>
-  <td align="right">(.565)</td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="left" rowspan="2"> Dense baryta crown</td>
-  <td align="right">1.5899</td>
-  <td align="right">.00970</td>
-  <td align="right">60.8</td>
-  <td align="right">.00621</td>
-  <td align="right">.00683</td>
-  <td align="right">.00546</td>
-</tr>
-<tr>
-
-  <td align="left"></td>
-  <td align="right">(.640)</td>
-  <td align="right">(.704)</td>
-  <td align="right">(.563)</td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="left" rowspan="2"> Baryta light flint</td>
-  <td align="right">1.5718</td>
-  <td align="right">.01133</td>
-  <td align="right">50.4</td>
-  <td align="right">.00706</td>
-  <td align="right">.00803</td>
-  <td align="right">.00660</td>
-</tr>
-<tr>
-
-  <td align="left"></td>
-  <td align="right">(.623)</td>
-  <td align="right">(.709)</td>
-  <td align="right">(.582)</td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="left" rowspan="2"> Common light flint</td>
-  <td align="right">1.5710</td>
-  <td align="right">.01327</td>
-  <td align="right">43.0</td>
-  <td align="right">.00819</td>
-  <td align="right">.00943</td>
-  <td align="right">.00791</td>
-</tr>
-<tr>
-
-  <td align="left"></td>
-  <td align="right">(.617)</td>
-  <td align="right">(.710)</td>
-  <td align="right">(.596)</td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="left" rowspan="2"> Common dense flint</td>
-  <td align="right">1.6116</td>
-  <td align="right">.01638</td>
-  <td align="right">37.3</td>
-  <td align="right">.00995</td>
-  <td align="right">.01170</td>
-  <td align="right">.00991</td>
-</tr>
-<tr>
-
-  <td align="left"></td>
-  <td align="right">(.607)</td>
-  <td align="right">(.714)</td>
-  <td align="right">(.607)</td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="left" rowspan="2"> Very dense flint</td>
-  <td align="right">1.6489</td>
-  <td align="right">.01919</td>
-  <td align="right">33.8</td>
-  <td align="right">.01152</td>
-  <td align="right">.01372</td>
-  <td align="right">.01180</td>
-</tr>
-<tr>
-
-  <td align="left"></td>
-  <td align="right">(.600)</td>
-  <td align="right">(.714)</td>
-  <td align="right">(.615)</td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="left" rowspan="2"> Densest flint</td>
-  <td align="right">1.7541</td>
-  <td align="right">.02743</td>
-  <td align="right">27.5</td>
-  <td align="right">.01607</td>
-  <td align="right">.01974</td>
-  <td align="right">.01730</td>
-</tr>
-<tr>
-
-  <td align="left"></td>
-  <td align="right">(.585)</td>
-  <td align="right">(.720)</td>
-  <td align="right">(.630)</td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="left" rowspan="2"> *Telescope crown</td>
-  <td align="right">1.5285</td>
-  <td align="right">.00866</td>
-  <td align="right">61.0</td>
-  <td align="right">.00557</td>
-  <td align="right">.00610</td>
-  <td align="right">.00493</td>
-</tr>
-<tr>
-
-  <td align="left"></td>
-  <td align="right">(.643)</td>
-  <td align="right">(.705)</td>
-  <td align="right">(.570)</td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="left" rowspan="2"> *Telescope flint</td>
-  <td align="right">1.5286</td>
-  <td align="right">.01025</td>
-  <td align="right">51.6</td>
-  <td align="right">.00654</td>
-  <td align="right">.00723</td>
-  <td align="right">.00591</td>
-</tr>
-<tr>
-
-  <td align="left"></td>
-  <td align="right">(.638)</td>
-  <td align="right">(.705)</td>
-  <td align="right">(.576)</td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="left" colspan="7"> &nbsp; * Optical data close approximations only.</td>
-</tr>
-</table></div>
-
-
-<div class="center">
-<table class="small" border="1" cellpadding="4" cellspacing="0" summary="">
-<tr>
-  <th align="center" colspan="15">Analysis of glasses in percentages</th></tr>
-<tr>
-  <th align="center"> Si<br />O<sub>2</sub></th>
-  <th align="center">B<sub>2</sub><br />O<sub>3</sub></th>
-  <th align="center">Zn<br />O</th>
-  <th align="center">Pb<br />O</th>
-  <th align="center">Ba<br />O</th>
-  <th align="center">K<sub>2</sub><br />O</th>
-  <th align="center">Na<sub>2</sub><br />O</th>
-  <th align="center">Ca<br />O</th>
-  <th align="center">AL<sub>2</sub><br />O<sub>3</sub></th>
-  <th align="center">As<sub>2</sub><br />O<sub>5</sub></th>
-  <th align="center">As<sub>2</sub><br />O<sub>3</sub></th>
-  <th align="center">Fe<sub>2</sub><br />O<sub>3</sub></th>
-  <th align="center">Mn<sub>2</sub><br />O<sub>3</sub></th>
-  <th align="center">Sb<sub>2</sub><br />O<sub>3</sub></th>
-  <th align="center">Mg<br />O</th>
-</tr>
-<tr>
-  <td align="right"> 74.8</td>
-  <td align="right">5.9</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="right">7.11</td>
-  <td align="right">11.3</td>
-  <td align="center">...</td>
-  <td align="right">.75</td>
-  <td align="center">...</td>
-  <td align="right">.06</td>
-  <td align="center">...</td>
-  <td align="right">.06</td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="right"> 65.4</td>
-  <td align="right">2.5</td>
-  <td align="right">2.0</td>
-  <td align="center">...</td>
-  <td align="right">9.6</td>
-  <td align="right">15.0</td>
-  <td align="right">5.0</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="right">.4</td>
-  <td align="center">...</td>
-  <td align="right">.1</td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="right"> 37.5</td>
-  <td align="right">15.0</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="right">41.0</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="right">5.0</td>
-  <td align="right">1.5</td>
-  <td></td>
-  <td></td>
-  <td></td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="right"> 51.7</td>
-  <td align="center">...</td>
-  <td align="right">7.0</td>
-  <td align="right">10.0</td>
-  <td align="right">20.0</td>
-  <td align="right">9.5</td>
-  <td align="right">1.5</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="right">.30</td>
-  <td></td>
-  <td></td>
-  <td></td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="right"> 54.3</td>
-  <td align="right">1.5</td>
-  <td align="center">...</td>
-  <td align="right">33.0</td>
-  <td align="center">...</td>
-  <td align="right">8.0</td>
-  <td align="right">3.0</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="right">.20</td>
-  <td></td>
-  <td></td>
-  <td></td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="right"> 54.8</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="right">37.0</td>
-  <td align="center">...</td>
-  <td align="right">5.8</td>
-  <td align="right">.8</td>
-  <td align="right">.60</td>
-  <td align="right">.4</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="right">.70</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="right">.20</td>
-</tr>
-<tr>
-  <td align="right"> 40.0</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="right">52.6</td>
-  <td align="center">...</td>
-  <td align="right">6.5</td>
-  <td align="right">.5</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="right">.30</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="right">.09</td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="right"> 29.3</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="right">67.5</td>
-  <td align="center">...</td>
-  <td align="right">3.0</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="right">.20</td>
-  <td align="center">...</td>
-  <td align="right">.04</td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="right"> 55.2</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="right">22.0</td>
-  <td align="right">5.7</td>
-  <td align="right">7.5</td>
-  <td align="right">5.9</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="center" colspan="2">3.7</td>
-  <td></td>
-  <td></td>
-</tr>
-<tr>
-  <td align="right"> 59.9</td>
-  <td align="right">12.7</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="right">5.1</td>
-  <td align="right">3.5</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="center">...</td>
-  <td align="center" colspan="2">2.7</td>
-  <td align="right">16.1</td>
-  <td></td>
-</tr>
-
-</table></div>
-
-
-<p><span class="pagenum"><a name="Page_66" id="Page_66">[Pg 66]</a></span></p>
-
-<p>The first step toward the telescope is the testing of these discs
-of glass, first for the presence or absence of striæ and other
-imperfections; second, for the perfection of the annealing. The
-maker has usually looked out for all the grosser imperfections
-before the discs left his works, but a much closer inspection is
-needed in order to make the best use of the glass.</p>
-
-<div class="figcenter">
-<img src="images/i_066a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 40.</span>—Testing Glass for Striæ.</div>
-</div>
-
-<p>Bad striæ are of course seen easily, as they would be in a
-window pane, but such gross imperfections are often in reality
-less damaging than the apparently slighter ones which must be
-searched for. The simplest test is to focus a good telescope on
-an artificial star, remove the eyepiece and bring the eye into its
-place.</p>
-
-<p>When the eye is in focus the whole aperture of the objective
-is uniformly filled with light, and if the disc to be tested be placed
-in front of it, any inequality in refraction will announce itself by
-an inequality of illumination. A rough judgment as to the seriousness
-of the defect may be formed from the area affected and
-the amount by which it affects the local intensity of illumination.
-Fig. 40 shows the arrangement for the test, <i>A</i> being the eye, <i>B</i> the
-objective and <i>C</i> the disc. The artificial star is conveniently
-made by setting a black bottle in the sun a hundred feet or so
-away and getting the reflection from its shoulder.</p>
-
-<div class="figcenter">
-<img src="images/i_066b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 41.</span>—The Mirror Test for Striæ.</div>
-</div>
-
-<p>A somewhat more delicate test, very commonly used, is shown
-in Fig. 41. Here <i>A</i> is a truly spherical mirror silvered on the
-front. At <i>B</i> very close to its centre of curvature is placed a lamp
-with a screen in front of it perforated with a hole 1/32 inch or so
-in diameter.</p>
-
-<p><span class="pagenum"><a name="Page_67" id="Page_67">[Pg 67]</a></span></p>
-
-<p>The rays reflected from the mirror come back quite exactly
-upon themselves and when the eye is placed at <i>C</i>, their reflected
-focus, the whole mirror <i>A</i> is uniformly lighted just as the lens
-was in Fig. 40, with the incidental advantage that it is much easier
-and cheaper to obtain a spherical mirror for testing a sizeable
-disc than an objective of similar size and quality. Now placing
-the disc <i>D</i> in front of the mirror, the light passing twice through
-it shows up the slightest stria or other imperfection as a streak
-or spot in the field. Its place is obvious and can be at once
-marked on the glass, but its exact position in the substance of the
-disc is not so obvious.</p>
-
-<p>To determine this, which may indicate that the fault can be
-ground out in shaping the lens, a modification of the first test
-serves well, as indeed it does for the general examination of large
-discs. Instead of using a distant artificial star and a telescope,
-one uses the lamp and screen, or even a candle flame ten feet or
-more away and a condensing lens of rather short focus, which
-may or may not be achromatic, so that the eye will get into its
-focus conveniently while the lens is held in the hand. Fig. 42
-shows the arrangement. Here <i>A</i> is the eye, <i>B</i> the condensing
-lens, <i>C</i> the disc and <i>D</i> the source of light. The condensing lens
-may be held on either side of the disc as convenience suggests,
-and either disc or lens may be moved. The operation is substantially
-the examination of a large disc piecemeal, instead of all at
-once by the use of a big objective or mirror.</p>
-
-<div class="figcenter">
-<img src="images/i_067.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 42.</span>—Locating Striæ in the Substance of a Disc.</div>
-</div>
-
-<p>Now when a stria has been noted mark its location as to the
-surface, and, moving the eye a little, look for parallax of the fault
-with respect to the surface mark. If it appears to shift try a
-mark on the opposite surface in the same way. Comparison of
-the two inspections will show about where the fault lies with
-respect to the surfaces, and therefore what is the chance of working
-it out. Sometimes a look edgewise of the disc will help in
-the diagnosis.</p>
-
-<p><span class="pagenum"><a name="Page_68" id="Page_68">[Pg 68]</a></span></p>
-
-<p>Numerous barely detectable striæ are usually worse than one
-or two conspicuous ones, for the latter frequently throw the light
-they transmit so wide of the focus that it does not affect the image,
-which could be greatly damaged by slight blurs of light that just
-miss focus.</p>
-
-<p>Given a disc that passes well the tests for striæ and the like
-the next step is to examine the perfection of the annealing, which
-in its larger aspect is revealed by an examination in polarized light.</p>
-
-<div class="figcenter">
-<img src="images/i_068.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 43.</span>—Testing a Disc in Polarized Light.
-</div>
-</div>
-
-<p>For this purpose the disc is set up against a frame placed on
-table or floor with a good exposure to skylight behind it, and
-inclined about 35° from the vertical. Behind it is laid a flat
-shiny surface to serve as polarizer. Black enamel cloth smoothly
-laid, a glass plate backed with black paint, or even a smooth
-board painted with asphalt paint will answer excellently. Then
-holding a Nicol prism before the eye and looking perpendicular
-to the face of the disc, rotate the prism on its axis. Fig. 43
-shows the arrangement, <i>A</i> being the eye, <i>B</i> the Nicol, <i>C</i> the disc,
-and <i>D</i> the polarizer behind it.</p>
-
-<p>If annealing has left no strain the only effect of rotating the
-Nicol will be to change the field from bright to dark and back
-again as if the disc were not there. Generally a pattern in the
-form of a somewhat hazy Maltese cross will appear, with its arms
-crossing the disc, growing darker and lighter alternately as the
-Nicol is turned.</p>
-
-<p><span class="pagenum"><a name="Page_69" id="Page_69">[Pg 69]</a></span></p>
-
-<p>If the cross is strongly marked but symmetrical and well
-centered the annealing is fair—better as the cross is fainter and
-hazier—altogether bad if colors show plainly or if the cross is
-decentered or distorted. The test is extremely sensitive, so that
-holding a finger on the surface of the disc may produce local
-strain that will show as a faint cloudy spot.</p>
-
-<p>A disc free of striæ and noticeable annealing strains is usually,
-but not invariably, good, for too frequent reheating in the moulding
-or annealing process occasionally leaves the glass slightly
-altered, the effect extending, at worst, to the crystallization or
-devitrification to which reference has been made.</p>
-
-<p>Given a good pair of discs the first step towards fashioning
-them into an objective is roughing to the approximate form
-desired. As a guide to the shaping of the necessary curves,
-templets must be made from the designed curves of the objective
-as precisely as possible. These are laid out by striking the
-necessary radii with beam compass or pivoted wire and scribing
-the curve on thin steel, brass, zinc or glass. The two last are
-the easier to work since they break closely to form.</p>
-
-<p>From these templets the roughing tools are turned up, commonly
-from cast iron, and with these, supplied with carborundum
-or even sand, and water, the discs, bearing against the revolving
-tool, are ground to the general shape required. They are then
-secured to a slowly revolving table, bearing edgewise against a
-revolving grindstone, and ground truly circular and of the proper
-final diameter.</p>
-
-<p>At this point begins the really careful work of fine grinding,
-which must bring the lens very close to its exact final shape.
-Here again tools of cast iron, or sometimes brass, are used, very
-precisely brought to shape according to the templets. They are
-grooved on the face to facilitate the even distribution of the
-abrasive, emery or fine carborundum, and the work is generally
-done on a special grinding machine, which moves the tool over
-the firmly supported disc in a complicated series of strokes
-imitating more or less closely the strokes found to be most
-effective in hand polishing.</p>
-
-<p>In general terms the operator in handwork at this task supports
-the disc on a firm vertical post, by cementing it to a suitable
-holder, and then moves the tool over it in a series of straight or
-oval strokes, meanwhile walking around the post. A skilful
-operator watches the progress of his work, varies the length and<span class="pagenum"><a name="Page_70" id="Page_70">[Pg 70]</a></span>
-position of his strokes accordingly, and, despite the unavoidable
-wear on the tool, can both keep its figure true and impart a
-true figure to the glass.</p>
-
-<div class="figcenter">
-<img src="images/i_070.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 44.</span>—Dr. Draper’s Polishing Machine.</div>
-</div>
-
-<p>The polishing machine, of which a type used by Dr. Draper is
-shown in Fig. 44, produces a similar motion, the disc slowly
-revolving and the rather small tool moving over it in oval strokes
-kept off the center. More often the tool is of approximately the
-same diameter as the disc under it. The general character of
-the motion is evident from the construction. The disc <i>a</i> is
-chucked by <i>c c′</i> on the bed, turned by the post <i>d</i> and worm wheel
-<i>e</i>. This is operated from the pulleys, <i>i</i>, <i>g</i>, which drive through <i>k</i>,
-the crank <i>m</i>, adjustable in throw by the nuts <i>n</i>, <i>n′</i>, and in position
-of tool by the clamps <i>r</i>, <i>r</i>. The motion may be considerably
-varied by adjustment of the machine, always keeping the stroke
-from repeating on the same part of the disc, by making the period
-of the revolution and of the stroke incommensurable so far as
-may be. Even in spectacle grinding machines the stroke may
-repeat only once in hundreds of times, and even this frequency
-in a big objective would, if followed in the polishing, leave tool
-marks which could be detected in the final testing.</p>
-
-<p>In the fine grinding, especially near the end of the process, the
-templets do not give sufficient precision in testing the curves, and
-recourse is had to the spherometer, by which measurements
-down to about 1/100000 inch can be consistently made.</p>
-
-<p>The next stage of operations is polishing, which transforms the
-grey translucency of the fine ground lens into the clear and
-brilliant surface which at last permits rigorous optical tests to be
-used for the final finish of the lens. This polishing is done gen<span class="pagenum"><a name="Page_71" id="Page_71">[Pg 71]</a></span>erally
-on the fine grinding machine but with a very different tool
-and with rouge of the utmost fineness.</p>
-
-<p>The polishing tool is in any case ground true and is then faced
-with a somewhat yielding material to carry the charge of rouge.
-Cheap lenses are commonly worked on a cloth polisher, a texture
-similar to billiard cloth being suitable, or sometimes on paper
-worked dry.</p>
-
-<p>With care either may produce a fairly good surface, with,
-however, a tendency to polish out the minute hollows left by
-grinding rather than to cut a true surface clear down to their
-bottoms. Hence cloth or paper is likely to leave microscopic
-inequalities apparently polished, and this may be sufficient to
-scatter over the field a very perceptible amount of light which
-should go to forming the image. All first class objectives and
-mirrors are in fact polished on optician’s pitch. This is not the
-ordinary pitch of commerce but a substance of various composition,
-sometimes an asphaltic compound, again on a base of tar,
-or of resin brought to the right consistency by turpentine.</p>
-
-<p>Whatever the exact composition, the fundamental property
-is that the material, apparently fairly hard and even brittle when
-cold, is actually somewhat plastic to continued pressure. Sealing
-wax has something of this quality, for a stick which may readily
-be broken will yet bend under its own weight if supported at the
-ends.</p>
-
-<p>If the fine grinding process has been properly carried out the
-lens has received its correct form as nearly as gauges and the
-spherometer can determine it. The next step is to polish the surface
-as brilliantly and evenly as possible. To this end advantage
-is taken of the plastic quality already mentioned, that the glass
-may form its own tool.</p>
-
-<p>The base of the tool may be anything convenient, metal, glass
-or even wood. Its working surface is made as nearly of the right
-curvature as practicable and it is then coated with warm pitch
-to a thickness of an eighth of an inch more or less, either continuously
-or in squares, and while still slightly warm the tool is placed
-against the fine ground disc, the exact shape of which it takes.</p>
-
-<p>When cold the pitch surface can easily be cut out into squares
-or symmetrically pitted with a suitable tool, at once facilitating
-the distribution of the rouge and water that serves for polishing,
-and permitting delicate adjustment of the working curvature in
-a way about to be described.</p>
-
-<p><span class="pagenum"><a name="Page_72" id="Page_72">[Pg 72]</a></span></p>
-
-<p>Fig. 45 shows the squared surface of the tool as it would be
-used for polishing a plane or very slightly convex or concave
-surface. Supplied with the thin abrasive paste, it is allowed
-to settle, cold, into its final contact with the glass, and then the
-process of polishing by hand or machine is started.</p>
-
-<p>The action of the tool must be uniform to avoid changing
-the shape of the lens. It can be regulated as it was in the grinding,
-by varying the length and character of the stroke, but even
-more delicately by varying the extent of surface covered by the
-pitch actually working on the glass.</p>
-
-<div class="figleft">
-<img src="images/i_072a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 45.</span>—Tool for Flat Surface.
-</div>
-</div>
-
-<div class="figright">
-<img src="images/i_072b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 46.</span>—Tool for Concave Surface.</div>
-</div>
-<p>This is done by channeling or boring away pitch near the rim
-or center of the tool as the case may be. Fig. 46 shows a
-tool which has been thus treated so that the squares are progressively
-smaller near the periphery. Such a spacing tends to
-produce a concave surface from a flat tool or to increase the
-concavity from a curved one. Trimming down the squares
-towards the centre produces the opposite result.</p>
-
-<p>Broadly, the principle is that the tool cuts the more in the
-areas where the contact surfaces are the greater. This is not
-wholly by reason of greater abrading surface, but also because
-where the contact is greater in area the pitch settles less, from
-the diminished pressure, thus increasing the effective contact.</p>
-
-<p>Clearly the effect of trimming away is correlated with the
-form and length of stroke, and the temper of the pitch, and in
-fact it requires the wisdom of the serpent to combine these
-various factors so as to produce the perfectly uniform and regular
-action required in polishing. Now and then, at brief intervals,<span class="pagenum"><a name="Page_73" id="Page_73">[Pg 73]</a></span>
-the operation is stopped to supply rouge and to avoid changing
-the conditions by the heat of friction. Especially must heating
-be looked out for in hand polishing of lenses which is often done
-with the glass uppermost for easier inspection of the work.</p>
-
-<p>Polishing, if the fine grinding has been judiciously done is,
-for moderate sized surfaces, a matter of only a few hours. It
-proceeds quite slowly at first while the hills are being ground down
-and then rather suddenly comes up brilliantly as the polisher
-reaches the bottoms of the valleys. Large lenses and mirrors may
-require many days.</p>
-
-<p>Now begins the final and extraordinarily delicate process of
-figuring. The lens or mirror has its appointed form as nearly
-as the most precise mechanical methods can tell—say down to one
-or two hundred-thousandths of an inch. From the optical
-standpoint the result may be thoroughly bad, for an error of a
-few millionths of an inch may be serious in the final performance.</p>
-
-<p>The periphery may be by such an amount longer or shorter in
-radius than it should be, or there may be an intermediate zone
-that has gone astray. In case of a mirror the original polishing is
-generally intended to leave a spherical surface which must be converted
-into a paraboloidal one by a change in curvature totalling
-only a few hundred-thousandths of an inch and seriously affected
-by much smaller variations.</p>
-
-<p>The figuring is done in a fashion very similar to the polishing.
-The first step is to find out by optical tests such as are described
-in Chapter IX the location of the errors existing after the polishing,
-and once found, they must be eliminated by patient and
-cautious work on the surface.</p>
-
-<p>Every optical expert has his own favorite methods of working
-out the figure. If there is a hollow zone the whole surface must
-be worked down to its level by repolishing; if, on the other hand,
-there is an annular hump, one may repolish with stroke and tool-face
-adapted to cut it down, or one may cautiously polish it out
-until it merges with the general level.</p>
-
-<p>Polishing is commonly done with tools of approximately the
-size of the work, but in figuring there is great difference of practice,
-some expert workers depending entirely on manipulation of a full
-sized tool, others working locally with small polishers, even with
-the ball of the thumb, in removing slight aberrations. In small
-work where the glass can be depended on for homogeneity and
-the tools are easily kept true the former method is the usual<span class="pagenum"><a name="Page_74" id="Page_74">[Pg 74]</a></span>
-one, but in big objectives the latter is often easier and may
-successfully reach faults otherwise very difficult to eliminate.</p>
-
-<p>Among well known makers of telescopes the Clarks and their
-equally skilled successors the Lundins, father and son, developed
-the art of local retouching to a point little short of wizardry; the
-late Dr. Brashear depended almost entirely on the adroitly
-used polishing machine; Sir Howard Grubb uses local correction
-in certain cases, and in general the cautiously modified polisher;
-while some of the Continental experts are reported to have
-developed the local method very thoroughly.</p>
-
-<p>The truth probably is that the particular error in hand should
-determine the method of attack and that its success depends
-entirely on the skill of the operator. As to the perfection of the
-objectives figured in either way, no systematic difference due to
-the method of figuring can be detected by the most delicate tests.</p>
-
-<p>In any case the figuring operation is long and tedious, especially
-in large work where problems of supporting to avoid flexure arise,
-where temperature effects on tool and glass involve long delays
-between tests and correction, and where in the last resort non-spherical
-surfaces must often be resorted to in bringing the image
-to its final perfection.</p>
-
-<p>The final test of goodness is performance, a clean round image
-without a trace of spherical or zonal aberration and the color
-correction the best the glasses will allow. Constant and rigorous
-testing must be applied all through the process of figuring, and
-the result seems to depend on a combination of experience, intuition
-and tactual expertness rarely united in any one person.</p>
-
-<p>Sir Howard Grubb, in a paper to be commended to anyone
-interested in objectives, once forcibly said: “I may safely say
-that I have never finished any objective over 10 inches diameter,
-in the working of which I did not meet with some new experience,
-some new set of conditions which I had not met before, and which
-had then to be met by special and newly devised arrangements.”</p>
-
-<p>The making of reflecting telescopes is not much easier since
-although only one surface has to be worked, that one has to be
-figured with extraordinary care, flexure has to be guarded against
-at every stage of the working, and afterwards, temperature
-change is a busy foe, while testing for correct figure, the surface
-being non-spherical, is considerably more troublesome.</p>
-
-<p>An expert can make a good mirror with far less actual labor
-than an objective of similar aperture, but when one reads Dr.<span class="pagenum"><a name="Page_75" id="Page_75">[Pg 75]</a></span>
-Henry Draper’s statement that in spite of knowing at first hand
-the methods and grinding machines of Lord Rosse and Mr. Lassell,
-he ground over a hundred mirrors, and spent three years of time,
-before he could get a correct figure with reasonable facility, one
-certainly gains a high respect for the skill acquired.</p>
-
-<p>This chapter is necessarily sketchy and not in the least intended
-to give the reader a complete account of technical glass manufacture,
-far less of the intricate and almost incommunicable art
-of making objectives and mirrors. It may however lead to a
-better understanding of the difference between the optical
-glass industry and the fabrication of commercial glass, and lead
-the reader to a fuller realization of how fine a work of art is a
-finished objective or mirror as compared with the crude efforts
-of the early makers or the hasty bungling of too many of their
-successors.</p>
-
-<p>For further details on making, properties and working of
-optical glass see:</p>
-
-<blockquote>
-
-<p><span class="smcap">Hovestadt</span>: “Jenaer Glas.”</p>
-
-<p><span class="smcap">Rosenhain</span>: “Glass Manufacture.”</p>
-
-<p><span class="smcap">Sir Howard Grubb</span>: “Telescopic Objectives and Mirrors: Their Preparation
-and Testing.” Nature <i>34</i>, 85.</p>
-
-<p><span class="smcap">Dr. Henry Draper</span>: “On the Construction of a Silvered Glass Telescope.”
-(Smithsonian Contributions to Knowledge, Vol. 34.)</p>
-
-<p><span class="smcap">G. W. Ritchey</span>: On the Modern Reflecting Telescope and the Making and
-Testing of Optical Mirrors. (Smithsonian Contributions to Knowledge,
-Vol. 34.)</p>
-
-<p><span class="smcap">Lord Rayleigh</span>: Polishing of Glass Surfaces. (Proc. Opt. Convention, 1905,
-p. 73.)</p>
-
-<p><span class="smcap">Bottone</span>: “Lens Making for Amateurs.”</p></blockquote>
-
-<hr class="chap" />
-
-<p><span class="pagenum"><a name="Page_76" id="Page_76">[Pg 76]</a></span></p>
-
-
-
-
-<div class="chapter"></div>
-<h2><a name="CHAPTER_IV" id="CHAPTER_IV">CHAPTER IV</a><br />
-
-<small>THE PROPERTIES OF OBJECTIVES AND MIRRORS</small></h2>
-
-
-<p>The path of the rays through an ordinary telescope has been
-shown in Fig. 5. In principle all the rays from a point in the
-distant object should unite precisely in a corresponding point
-in the image which is viewed by the eyepiece. Practically it
-takes very careful design and construction of the objective to
-make them meet in such orderly fashion even over an angular
-space of a single degree, and the wider the view required the more
-difficult the construction. We have spoken in the account of the
-early workers of their struggles to avoid chromatic and spherical
-aberrations, and it is chiefly these that still, in less measure,
-worry their successors.</p>
-
-<div class="figcenter">
-<img src="images/i_076.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig.</span> 47.—Chromatic Aberration of Convex Lens.</div>
-</div>
-
-<p>The first named is due to the fact that a prism does not bend
-light of all colors equally, but spreads them out into a spectrum;
-red refracted the least, violet the most. Since a lens may be
-regarded as an assemblage of prisms, of small angle near the centre
-and greater near the edge, it must on the whole and all over
-bend the blue and violet rays to meet on the axis nearer the rear
-surface than the corresponding red rays, as shown in Fig. 47.
-Here the incident ray <i>a</i> is split up by the prismatic effect of the
-lens, the red coming to a focus at <i>r</i>, the violet at <i>v</i>.</p>
-
-<p>One can readily see this chromatic aberration by covering up
-most of a common reading glass with his hand and looking through
-the edge portion at a bright light, which will be spread out into
-a colored band.</p>
-
-<p><span class="pagenum"><a name="Page_77" id="Page_77">[Pg 77]</a></span></p>
-
-<p>If the lens is concave the violet rays will still be the more
-bent, but now outwards, as shown in Fig. 48. The incident ray
-<i>a′</i> is split up and the violet is bent toward <i>v</i>, proceeding as if
-coming straight from a virtual focus <i>v′</i> in front of the lens, and
-nearer it than the corresponding red focus <i>r′</i>. Evidently if we
-could combine a convex lens, bending the violet inward too much,
-with a concave one, bending it outward too much, the two
-opposite variations might compensate each other so that red and
-violet would come to the same focus—which is the principle of
-the achromatic objective.</p>
-
-<div class="figcenter">
-<img src="images/i_077.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 48.</span>—Chromatic Aberration of Concave Lens.</div>
-</div>
-
-<p>If the refractive powers of the lenses were exactly proportional
-to their dispersive powers, as Newton erroneously thought, it is
-evident that the concave lens would pitch all the rays outwards
-to an amount which would annul both the chromatic variation
-and the total refraction of the convex lens, leaving the pair
-without power to bring anything to a focus. Fortunately flint
-glass as compared with crown glass has nearly double the dispersion
-between red and violet, and only about 20% greater
-refractive power for the intermediate yellow ray.</p>
-
-<p>Hence, the prismatic dispersive effect being proportional to
-the total curvature of the lens, the chromatic aberration of a
-crown glass lens will be cured by a concave flint lens of about half
-the total curvature, and, the refractions being about as 5 to 6, of
-⅗ the total power.</p>
-
-<p>Since the “power” of any lens is the reciprocal of its focal
-length, a crown glass convex lens of focal length 3, and a concave
-flint lens of focal length 5 (negative) will form an approximately
-achromatic combination. The power of the combination will be
-the algebraic sum of the powers of the components so that the<span class="pagenum"><a name="Page_78" id="Page_78">[Pg 78]</a></span>
-focal length of the pair will be about 5/2 that of the crown lens
-with which we started.</p>
-
-<p>To be more precise the condition of achromatism is</p>
-
-<p class="center">
-Σρδn + Σρ′δn′ = 0<br />
-</p>
-
-<p>where ρ is the reciprocal of a radius and δn, or δn′, is the difference
-in refractive index between the rays chosen to be brought to
-exact focus together, as the red and the blue or violet.</p>
-
-<p>This conventional equation simply states that the sum of the
-reciprocals of the radii of the crown lens multiplied by the dispersion
-of the crown, must equal the corresponding quantity for
-the flint lens if the two total dispersions are to annul each other,
-leaving the combination achromatic. Whatever glass is used
-the power of a lens made of it is</p>
-
-<p class="center">
-P( = 1/<i>f</i>) = Σρ(n - 1)<br />
-</p>
-
-<p>so that it will be seen that, other things being equal, a glass of
-high index of refraction tends to give moderate curves in an objective.
-Also, referring to the condition of achromatism, the greater
-the difference in dispersion between the two glasses the less
-curvatures will be required for a given focal length, a condition
-advantageous for various reasons.</p>
-
-<p>The determination of achromatism for any pair of glasses and
-focal length is greatly facilitated by employing the auxiliary
-quantity ν which is tabulated in all lists of optical glass as a
-short cut to a somewhat less manageable algebraic expression.
-Using this we can figure achromatism for unity focal length at
-once,</p>
-
-
-<p class="center">P = ν/(ν-ν′)<span class="i4">P′ = ν′/(ν-ν′)</span><span class="i4">ν = (n<sub><i>D</i></sub>-1)/δn</span></p>
-
-
-<p>being the powers of the leading and following lenses respectively.
-The combined lens will bring the rays of the two chosen colors, as
-red and blue, to focus at the same point on the axis. It does not
-necessarily give to the red and blue images of an object the same
-exact size. Failure in this respect is known as chromatic difference
-of magnification, but the fault is small and may generally be
-neglected in telescope objectives.</p>
-
-<p>We have now seen how an objective may be made achromatic
-and of determinate focal length, but the solution is in terms of the
-sums of the respective curvatures of the crown and flint lenses,<span class="pagenum"><a name="Page_79" id="Page_79">[Pg 79]</a></span>
-and gives no information about the radii of the individual surfaces.
-The relation between these is all-important in the final
-performance.</p>
-
-<div class="figcenter"><a id="Fig_49"></a>
-<img src="images/i_079a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 49.</span>—Spherical Aberration of Convex Lens.</div>
-</div>
-
-<p>For in a convex lens with spherical surfaces the rays striking
-near the edge, of whatever color, are pitched inwards too much
-compared with rays striking the more moderate curvatures near
-the axis, as shown in Fig. 49. The ray <i>a′ b′</i> thus comes to a focus
-shorter than the ray <i>a b</i>.</p>
-
-<p>This constitutes the fault of spherical aberration, which the old
-astronomers, following the suggestions of Descartes, tried ineffectually
-to cure by forming lenses with non-spherical surfaces.</p>
-
-<div class="figcenter">
-<img src="images/i_079b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 50.</span>—Spherical Aberration of Concave Lens.</div>
-</div>
-
-<p>Fig. 50 suggests the remedy, for the outer ray <i>a″</i> is pitched out
-toward <i>b″</i> as if it came from a focal point <i>c″</i>, while the ray nearer
-the center <i>a″′</i> is much less bent toward <i>b″′</i> as if it came from <i>c″′</i>.
-The spherical aberrations of a concave lens therefore, being opposite
-to those of a convex lens, the two must, at least to a certain
-extent, compensate each other as when combined in an
-achromatic objective.</p>
-
-<p><span class="pagenum"><a name="Page_80" id="Page_80">[Pg 80]</a></span></p>
-
-<p>So in fact they do, and, if the curves that go to make up the
-total curvatures of the two are properly chosen, the total spherical
-aberration can be made negligibly small, at least on and near
-the axis. Taking into account this condition, therefore, at once
-gives us a clue to the distribution of the total curvatures and
-hence to the radii of the two lenses. Spherical aberration,
-however, involves not only the curvatures but the indices of
-refraction, so that exact correction depends in part on the choice
-of glasses wherewith to obtain achromatization.</p>
-
-<p>In amount spherical aberration varies with the square of the
-aperture and inversely with the cube of the focal length i.e.
-with a²/f³. It is reckoned as + when, as in Fig. 49, the rim rays
-come to the shorter focus, as-, when they come to the longer
-focus.</p>
-
-<p>In any event, since the spherical aberration of a lens may be
-varied in above the ratio of 4:1, for the same total power, merely
-by changing the ratio of the radii, it is evident that the two lenses
-being fairly correct in total curvature might be given considerable
-variations in curvature and still mutually annul the axial spherical
-aberration.</p>
-
-<p>Such is in fact the case, so that to get determinate forms for
-the lenses one must introduce some further condition or make
-some assumption that will pin down the separate curvatures to
-some definite relations. The requirement
-may be entirely arbitrary, but
-in working out the theory of objectives
-has usually been chosen to give
-the lens some real or hypothetical
-additional advantage.</p>
-
-<p>The commonest arbitrary requirement
-is that the crown glass lens
-shall be equiconvex, merely to avoid
-making an extra tool. This fixes one
-pair of radii, and the flint lens is then given the required compensating
-aberration choosing the easiest form to make. This
-results in the objective of Fig. 51.</p>
-
-<div class="figleft">
-<img src="images/i_080.jpg" alt="" />
-<div class="caption"><span class="smcap"> Fig. 51.</span>—Objectives with Equiconvex
-Crown.</div>
-</div>
-
-<p>Probably nine tenths of all objectives are of this general form,
-equiconvex crown and nearly or quite plano-concave flint. The
-inside radii may be the same, in which case the lenses should be
-cemented, or they may differ slightly in either direction as <i>a</i>, Fig. 51<span class="pagenum"><a name="Page_81" id="Page_81">[Pg 81]</a></span>
-with the front of the flint less curved than the rear of the crown,
-and <i>b</i> where the flint has the sharper curve. The resulting
-lens if ordinary glasses are chosen gives excellent correction of the
-spherical aberration on the axis, but not much away from it,
-yielding a rather narrow sharp field. Only a few exceptional
-combinations of glasses relieve this situation materially.</p>
-
-<p>The identity of the inner radii so that the surfaces can be
-cemented is known historically as Clairault’s condition, and since
-it fixes two curvatures at identity somewhat limits the choice of
-glasses, while to get proper corrections demands quite wide
-variations in the contact radii for comparatively small variations
-in the optical constants of the glass.</p>
-
-<p>When two adjacent curves are identical they should be
-cemented, otherwise rays reflected from say the third surface of
-Fig. 51 will be reflected again from the second surface, and passing
-through the rear lens in almost the path of the original ray will
-come to nearly the same focus, producing a troublesome “ghost.”
-Hence the curvatures of the second and third surfaces when not
-cemented are varied one way or the other by two or three per
-cent, enough to throw the twice reflected rays far out of focus.</p>
-
-<div class="figright">
-<img src="images/i_081.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 52.</span>—Allied Forms of Cemented
-Objectives.</div>
-</div>
-
-<p>In this case, as in most others, the analytical expression for the
-fundamental curvature to be determined turns up in the form of
-a quadratic equation, so that the
-result takes the form a ± b and
-there are two sets of radii that
-meet the requirements. Of these
-the one presenting the gentler
-curves is ordinarily chosen. Fig.
-52 <i>a</i> and <i>c</i> shows the two cemented
-forms, thus related, for a common
-pair of crown and flint
-glasses, both cleanly corrected for chromatic and axial spherical
-aberration.</p>
-
-<p>Nearly a century ago Sir John Herschel proposed another
-defining condition, that the spherical aberration should be removed
-both for parallel incident rays and for those proceeding from a
-nearer point on the axis, say ten or more times the focal length in
-front of the objective. This condition had little practical value
-in itself, and its chief merit was that it approximated one that
-became of real importance if the second point were taken far
-enough away.</p>
-
-<p><span class="pagenum"><a name="Page_82" id="Page_82">[Pg 82]</a></span></p>
-
-<p>A little later Gauss suggested that the spherical aberration
-should be annulled for two different colors, much as the chromatic
-aberration is treated. And, being a mathematical wizard, he
-succeeded in working out the very intricate theory, which resulted
-in an objective approximately of the form shown in Fig. 53.</p>
-
-<div class="figright">
-<img src="images/i_082.jpg" alt="" />
-<div class="caption"> <span class="smcap">Fig. 53.</span>—Gaussian
-Objective.</div>
-</div>
-
-<p>It does not give a wide field but is valuable for spectroscopic
-work, where keen definition in all colors is essential.
-Troublesome to compute, and difficult to
-mount and center, the type has not been much
-used, though there are fine examples of about
-9&frac12; inches aperture at Princeton, Utrecht, and
-Copenhagen, and a few smaller ones elsewhere,
-chiefly for spectroscopic use.</p>
-
-<p>It was Fraunhofer who found and applied
-the determining condition of the highest practical
-value for most purposes. This condition was absence of <i>coma</i>,
-the comet shaped blur generally seen in the outer portions of a
-wide field.</p>
-
-<p>It is due to the fact that parallel oblique rays passing through
-the opposite rims of the lens and through points near its center
-do not commonly come to the same focus, and it practically
-is akin to a spherical aberration for oblique rays which greatly
-reduces the extent of the sharp field. It is reckoned + when
-the blur points outwards,-when it points inwards, and is directly
-proportional to the tangent of the obliquity and the square of the
-aperture, and inversely to the square of the focal length i.e. it
-varies with a²tan(u)/f².</p>
-
-<p>Just how Fraunhofer solved the problem is quite unknown, but
-solve it he did, and very completely, as he indicates in one of his
-later papers in which he speaks of his objective as reducing all the
-aberrations to a minimum, and as Seidel proved 30 years later in
-the analysis of one of Fraunhofer’s objectives. Very probably
-he worked by tracing axial and oblique rays through the objective
-form by trigonometrical computation, thus finding his way to a
-standard form for the glasses he used.<a name="FNanchor_10_10" id="FNanchor_10_10"></a><a href="#Footnote_10_10" class="fnanchor">[10]</a></p>
-<p><span class="pagenum"><a name="Page_83" id="Page_83">[Pg 83]</a></span></p>
-<p>Fraunhofer’s objective, of which Fig. 54<i>a</i> is an example
-worked by modern formulæ for the sine condition, gives very exact
-corrections over a field of 2°-3° when the glasses are suitably
-chosen and hence is invaluable for any work requiring a wide
-angle of view.</p>
-
-<p>With certain combinations of glasses the coma-free condition
-may be combined successfully with Clairault’s,
-although ordinarily the coma-free form falls
-between the two forms clear of spherical aberration,
-as in Fig. 52, <i>b</i>, which has its oblique
-rays well compensated but retains serious axial
-faults.</p>
-
-<div class="figright">
-<img src="images/i_083a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 54.</span>—The Fraunhofer
-Types.</div>
-</div>
-
-<p>Fraunhofer’s objective has for all advantageous
-combinations of glasses the front
-radius of the flint longer than the rear radius
-of the crown hence the two must be separated
-by spacers at the edge, which in small lenses in simple cells is
-slightly inconvenient. However, the common attempt to simplify
-mounting by making the front flint radius the shorter
-almost invariably violates the sine condition and reduces the
-sharp field, fortunately not a very serious matter for most astronomical
-work.</p>
-
-<p>The only material objection to the Fraunhofer type is the
-strong curvature of the rear radius of the crown which gives a
-form somewhat susceptible to flexure in large objectives. This is
-met in the flint-ahead form, developed essentially by Steinheil,
-and used in most of the objectives of his famous firm. Fig. 54<i>b</i>
-shows the flint-ahead objective corresponding to
-Fig. 54<i>a</i>. Obviously its curves are mechanically
-rather resistant to flexure.<a name="FNanchor_11_11" id="FNanchor_11_11"></a><a href="#Footnote_11_11" class="fnanchor">[11]</a></p>
-
-<div class="figleft">
-<img src="images/i_083b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 55.</span>—Clark
-Objective.</div>
-</div>
-
-<p>Mechanical considerations are not unimportant in
-large objectives, and Fig. 55, a highly useful form
-introduced by the Clarks and used in recent years
-for all their big lenses, is a case in point. Here there
-is an interval of about the proportion shown between
-the crown and flint components.</p>
-
-<p>This secures effective ventilation allowing the lenses to come
-quickly to their steady temperature, and enables the inner<span class="pagenum"><a name="Page_84" id="Page_84">[Pg 84]</a></span>
-surfaces to be cleaned readily and freed of moisture. Optically
-it lessens the deviation from the sine condition otherwise practically
-inseparable from the equiconvex crown, reduces the
-chromatic difference of spherical aberration, and gives an easy
-way of controlling the color correction by slightly varying the
-separation of the lenses.</p>
-
-<p>One further special case is worth noting, that of annulling the
-spherical aberration for rays passing through the lens in both
-directions. By proper choice of glass and curvatures this can be
-accomplished to a close approximation and the
-resulting form is shown in Fig. 56. The front of the
-crown is notably flat and the rear of the flint conspicuously
-curved, the shape in fact being intermediate
-between Figs. 52<i>b</i> and 52<i>c</i>. The type is
-useful in reading telescopes and the like, and for
-some spectroscopic applications.</p>
-
-<div class="figleft">
-<img src="images/i_084.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 56.</span>—Corrected in
-Both Directions.</div>
-</div>
-
-<p>There are two well known forms of aberration not
-yet considered; astigmatism and curvature of field.
-The former is due to the fact that when the path of
-the rays is away from the axis, as from an extended object,
-those coming from a line radial to the axis, and those from a line
-tangent to a circle about the axis, do not come to the same
-focus. The net result is that the axial and tangential elements
-are brought to focus in two coaxial surfaces touching at the axis
-and departing more and more widely from each other as they
-depart from it. Both surfaces have considerable curvature, that
-for tangential lines being the sharper.</p>
-
-<p>It is possible by suitable choice of glasses and their curvatures
-to bring both image surfaces together into an approximate plane
-for a moderate angular space about the axis without seriously
-damaging the corrections for chromatic and spherical aberration.
-To do this generally requires at least three lenses, and photographic
-objectives thus designed (<i>anastigmats</i>) may give a substantially
-flat field over a total angle of 50° to 60° with corrections
-perfect from the ordinary photographic standpoint.</p>
-
-<p>If one demands the rigorous precision of corrections called for
-in astronomical work, the possible angle is very much reduced.
-Few astrographic lenses cover more than a 10° or 15° field, and the
-wider the relative aperture the harder it is to get an anastigmatically
-flat field free of material errors. Astigmatism is rarely<span class="pagenum"><a name="Page_85" id="Page_85">[Pg 85]</a></span>
-noticeable in ordinary telescopes, but is sometimes conspicuous in
-eyepieces.</p>
-
-<p>Curvature of field results from the tendency of oblique rays in
-objectives, otherwise well corrected, to come to shorter focus
-than axial rays, from their more considerable refraction resulting
-from greatly increased angles of incidence. This applies to both
-the astigmatic image surfaces, which are concave toward the
-objective in all ordinary cases.</p>
-
-<p>Fortunately both these faults are negligible near the axis.
-They are both proportional to tan²{u}/f where u is the obliquity to
-the axis and f the focal length; turn up with serious effect in wide
-angled lenses such as are used in photography, but may generally
-be forgotten in telescopes of the ordinary <i>F</i> ratios, like <i>F</i>/12 to
-<i>F</i>/16. So also one may commonly forget a group of residual
-aberrations of higher orders, but below about <i>F</i>/8 look out for
-trouble. Objectives of wider aperture require a very careful
-choice of special glasses or the sub-division of the curvatures
-by the use of three or more lenses instead of two. Fig. 57
-shows a cemented triplet of Steinheil’s design, with a crown lens
-between two flints. Such triplets are made up to about 4 inches
-diameter and of apertures ranging from <i>F</i>/4 to <i>F</i>/5.</p>
-
-<div class="figcenter">
-<img src="images/i_085.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 57.</span>—Steinheil Triple Objective.
-&nbsp; &nbsp;  <span class="smcap">Fig. 58.</span>—Tolles Quadruple Objective.</div>
-</div>
-
-<p>In cases of demand for extreme relative aperture, objectives
-composed of four cemented elements have now and then been
-produced. An example is shown in Fig. 58, a four-part objective
-of 1 inch aperture made by Tolles years ago for a small hand
-telescope. Its performance, although it worked at <i>F</i>/4, was reported
-to be excellent even up to 75 diameters.</p>
-
-<p>The main difficulty with these objectives of high aperture is
-the relatively great curvature of field due to short focal length
-which prevents full utilization of the improved corrections off
-the axis.</p>
-
-<p><span class="pagenum"><a name="Page_86" id="Page_86">[Pg 86]</a></span></p>
-
-<p>Distortion is similarly due to the fact that magnification is
-not quite the same for rays passing at different distances
-from the axis. It varies in general with the cube of the distance
-from the axis, and is usually negligible save in photographic
-telescopes, ordinary visual fields being too small to show it
-conspicuously.</p>
-
-<p>Distortion is most readily avoided by adopting the form of a
-symmetrical doublet of at least four lenses as in common photographic
-use. No simple achromatic pair gives a field wholly free
-of distortion and also of the ordinary aberrations, except very
-near the axis, and in measuring plates taken with such simple
-objectives corrections for distortion are generally required.</p>
-
-<p>At times it becomes necessary to depart somewhat from the
-objective form which theoretically gives the least aberrations in
-order to meet some specific requirement. Luckily
-one may modify the ratios of the curves very perceptibly
-without serious results. The aberrations
-produced come on gradually and not by jumps.</p>
-
-<div class="figleft">
-<img src="images/i_086.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 59.</span>—“Bent”
-Objective.</div>
-</div>
-
-<p>A case in point is that of the so-called “bent”
-objective in which the curvatures are all changed
-symmetrically, as if one had put his fingers on the
-periphery and his thumbs on the centre of the whole
-affair, and had sprung it noticeably one way or the
-other.</p>
-
-<p>The corrections in general are slightly deteriorated
-but the field may be in effect materially flattened
-and improved. An extreme case is the photographic
-landscape lens. Figure 59 is an actual example from
-a telescope where low power and very large angular
-view were required. The objective was first designed
-from carefully chosen glass to meet accurately the sine condition.
-Even so the field, which covered an apparent angle of fully 40°,
-fell off seriously at the edge.</p>
-
-<p>Bearing in mind the rest of the system, the objective was
-then “bent” into the form given by the dotted lines, and the
-telescope then showed beautiful definition clear to the periphery
-of the field, without any visible loss in the centre.</p>
-
-<p>This spurious flattening cannot be pushed far without getting
-into trouble for it does not cure the astigmatic difference of focus,
-but it is sometimes very useful. Practically curvature of field is
-an outstanding error that cannot be remedied in objectives re<span class="pagenum"><a name="Page_87" id="Page_87">[Pg 87]</a></span>quired
-to stand high magnifying powers, except by going to the
-anastigmatic forms similar to those used in photography.<a name="FNanchor_12_12" id="FNanchor_12_12"></a><a href="#Footnote_12_12" class="fnanchor">[12]</a></p>
-
-<p>Aside from curvature the chief residual error in objectives is
-imperfection of achromatism. This arises from the fact that
-crown and flint glasses do not disperse the various colors quite in
-the same ratio. The crown gives slightly disproportionate
-importance to the red end of the spectrum, the flint to the violet
-end—the so-called “irrationality of dispersion.”</p>
-
-<p>Hence if a pair of lenses match up accurately for two chosen
-colors like those represented by the C and F lines, they will fail
-of mutual compensation elsewhere. Figure 60 shows the situation.
-Here the spectra from crown and flint glasses are brought
-to exactly the same extent between the C and F lines, which
-serve as landmarks.</p>
-
-<p>Clearly if two prisms or lenses are thus adjusted to the same
-refractions for C and F, the light passing through the combination
-will still be slightly colored in virtue of the differences elsewhere
-in the spectrum. These residual color differences produce
-what is known as the “secondary spectrum.”</p>
-
-<p>What this does in the case of an achromatic lens may be clearly
-seen from the figure; C and F having exactly the same refractions
-in the flint and crown, come to the same focus. For D, the yellow
-line of sodium, the flint lens refracts a shade the less, hence is
-not quite powerful enough to balance the crown, which therefore
-brings D to a focus a little shorter than C and F. On the other
-hand for A′ and G′, the flint refracts a bit more than the crown,
-overbalances it and brings these red and violet rays to a focus
-a little longer than the joint C and F focus.</p>
-
-<p><span class="pagenum"><a name="Page_88" id="Page_88">[Pg 88]</a></span></p>
-
-<div class="figcenter">
-<img src="images/i_088.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 60.</span>—Irrationality of Dispersion.</div>
-</div>
-
-<p>The difference for D is quite small,
-roughly about 1/2000 of the focal length,
-while the red runs long by nearly three
-times that amount, the violet by about
-four. Towards the H line the difference
-increases rapidly and in large telescopes
-the actual range of focus for the various
-colors amounts to several inches.</p>
-
-<p>This difficulty cannot be avoided by
-any choice among ordinary pairs of
-glasses, which are nearly alike in the
-matter of secondary spectrum. In the
-latter part of the last century determined
-efforts were made to produce glasses that
-would give more nearly an equal run of
-dispersion, at first by English experimenters,
-and then with final success by
-Schott and Abbé at Jena.</p>
-
-<p>Both crown and flint had to be quite
-abnormal in composition, especially the
-latter, and the pair were of very nearly
-the same refractive index and with small
-difference in the quantity ν which we have
-seen determines the general amount of
-curvature. Moreover it proved to be
-extremely hard to get the crown quite
-homogeneous and it is listed by Schott
-with the reservation that it is not free
-from bubbles and striæ.</p>
-
-<p>Nevertheless the new glasses reduce
-the secondary spectrum greatly, to about
-&frac14; of its ordinary value, in the average.
-It is difficult to get rid of the spherical
-aberration, however, from the sharp
-curves required and the small difference
-between the glasses, and it seems to be
-impracticable on this account to go to
-greater aperture than about <i>F</i>/20.</p>
-
-<p>Figure 61 shows the deeply curved
-form necessary even at half the relative
-aperture usable with common glasses. At <i>F</i>/20 the secondary<span class="pagenum"><a name="Page_89" id="Page_89">[Pg 89]</a></span>
-spectrum from the latter is not conspicuous and Roe (Pop. Ast.
-<i>18</i>, 193), testing side by side a small Steinheil of the new glasses,
-and a Clark of the old, of almost identical size and focal ratio,
-found no difference in their practical performance.</p>
-
-<p>Another attack on the same problem was more successfully
-made by H. D. Taylor. Realizing the difficulty found with a
-doublet objective of even the best matched of the new glasses, he
-adopted the plan of getting a flint of exactly the right dispersion
-by averaging the dispersions of a properly selected pair of flints
-formed into lenses of the appropriate relative curvatures.</p>
-
-<div class="figcenter">
-<img src="images/i_089.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 61.</span>—Apochromatic Doublet.
-&nbsp; &nbsp; <span class="smcap">Fig. 62.</span>—Apochromatic Triplet.</div>
-</div>
-
-
-<p>The resulting form of objective is made, especially, by Cooke of
-York, and also by Continental makers, and carries the name of
-“photo-visual” since the exactness of corrections is carried well
-into the violet, so that one can see and photograph at the same
-focus. The residual chromatic error is very small, not above 1/8
-to 1/10 the ordinary secondary spectrum.</p>
-
-<p>By this construction it is practicable to increase the aperture
-to <i>F</i>/12 or <i>F</i>/10 while still retaining moderate curvatures and
-reducing the residual spherical aberration. There are a round
-dozen triplet forms possible, of which the best, adopted by Taylor,
-is shown in Fig. 62. It has the duplex flint ahead—first a baryta
-light flint, then a borosilicate flint, and to the rear a special light
-crown. The two latter glasses have been under some suspicion
-as to permanence, but the difficulty has of late years been reported
-as remedied. Be that as it may, neither doublets nor triplets
-with reduced secondary spectrum have come into any large<span class="pagenum"><a name="Page_90" id="Page_90">[Pg 90]</a></span>
-use for astronomical purposes. Their increased cost is considerable,<a name="FNanchor_13_13" id="FNanchor_13_13"></a><a href="#Footnote_13_13" class="fnanchor">[13]</a>
-their aperture even in the triplet, rather small for
-astrophotography, and their achromatism is still lacking the
-perfection reached by a mirror.</p>
-
-<p>The matter of achromatism is further complicated by the fact
-that objectives are usually over-achromatized to compensate for
-the chromatic errors in the eyepiece, and especially in the eye.
-As a general rule an outstanding error in any part of an optical
-system can be more or less perfectly balanced by an opposite error
-anywhere else in the system—the particular point chosen being a
-matter of convenience with respect to other corrections.</p>
-
-<p>The eye being quite uncorrected for color the image produced
-even by a reflector is likely to show a colored fringe if at all bright,
-the more conspicuous as the relative aperture of the pupil
-increases. For low power eyepieces the emerging ray may quite
-fill a wide pupil and then the chromatic error is troublesome.
-Hence it has been the custom of skilled opticians, from the time
-of Fraunhofer, who probably started the practice, to overdo the
-correction of the objective just a little to balance the fault of
-the eye.</p>
-
-<p>What actually happens is shown in Fig. 63, which gives the
-results of achromatization as practiced by some of the world’s
-adepts. The shortest focus is in the yellow green, not far from
-the line D. The longest is in the violet, and F, instead of coinciding
-in focus with C as it is conventionally supposed to do,
-actually coincides with the deep and faint red near the line marked
-B. Hence the visible effect is to lengthen the focus for blue
-enough to make up for the tendency of the eye in the other
-direction. The resulting image then should show no conspicuous
-rim of red or blue. The actual adjustment of the color correction
-is almost wholly a matter of skilled judgment but Fig. 63
-shows that of the great makers to be quite uniform. The smallest
-overcorrection is found in the Grubb objective, the largest in the
-Fraunhofer. The differences seem to be due mainly to individual
-variations of opinion as to what diameter of pupil should be
-taken as typical for the eye.</p>
-
-<p>The common practice is to get the best possible adjustment for
-a fairly high power, corresponding to a beam hardly 1/64 inch in
-diameter entering the pupil.</p>
-
-<p><span class="pagenum"><a name="Page_91" id="Page_91">[Pg 91]</a></span></p>
-
-<p>In any case the bigger the pencil of rays utilized by the eye,
-i.e., the lower the power, the more overcorrection must be provided,
-so that telescopes intended, like comet seekers, for regular
-use with low powers must be designed accordingly, either as
-respects objective or ocular.</p>
-
-<div class="figcenter">
-<img src="images/i_091.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 63.</span>—Achromatization Curves by Various Makers.</div>
-</div>
-
-<p>The differences concerned in this chromatic correction for power
-are by no means negligible in observing, and an objective actually
-conforming to the C to F correction assumed in tables of optical
-glass would produce a decidedly unpleasant impression when<span class="pagenum"><a name="Page_92" id="Page_92">[Pg 92]</a></span>
-used with various powers on bright objects. And the values for
-ν implied in the actual color correction are not immaterial in
-computing the best form for a proposed objective.</p>
-
-<p>1 is from Franunhofer’s own hands, the instrument of 9.6 inches
-aperture and 170 inches focus in the Berlin Observatory.</p>
-
-<p>2 The Clark refractor of the Lowell Observatory, 24 inches
-aperture and 386 inches focal length. This is of the usual Clark
-form, crown ahead, with lenses separated by about ⅙ of their
-diameter.</p>
-
-<p>3 is a Steinheil refractor at Potsdam of 5.3 inches aperture, and
-85 inches focus.</p>
-
-<p>4 is from the fine equatorial at Johns Hopkins University,
-designed by Professor Hastings and executed by Brashear.</p>
-
-<p>The objective was designed with special reference to minimizing
-the spherical aberration not only for one chosen wave length
-but for all others, has the flint lens ahead, aperture 9.4 inches,
-focal length 142 inches, and the lenses separated by &frac14; inch in the
-final adjustment of the corrections.</p>
-
-<p>5 is from the Potsdam equatorial by Grubb, 8.5 inches aperture
-124 inches focus.</p>
-
-<p>The great similarity of the color curves is evident at a glance,
-the differences due to variations in the glass being on the whole
-much less significant than those resulting from the adjustment
-for power.</p>
-
-<p>Really very little can be done to the color correction without
-going to the new special glasses, the use of which involves other
-difficulties, and leaves the matter of adjustment for power quite
-in the air, to be brought down by special eye pieces. Now and
-then a melting of glass has a run of dispersion somewhat more
-favorable than usual, but there is small chance of getting large
-discs of special characteristics, and the maker has to take his
-chance, minute differences in chromatic quality being far less
-important than uniformity and good annealing.</p>
-
-<p>Regarding the aberrations of mirrors something has been said
-in Chap. I, but it may be well here to show the practical side
-of the matter by a few simple illustrations.</p>
-
-<p>Figure 64 shows the simplest form of concave mirror—a
-spherical surface, in this instance of 90° aperture, the better to
-show its properties. If light proceeded radially outward from <i>C</i>,
-the center of curvature of the surface, evidently any ray would
-strike the surface perpendicularly as at <i>a</i> and would be turned<span class="pagenum"><a name="Page_93" id="Page_93">[Pg 93]</a></span>
-squarely back upon itself, passing again through the center of
-curvature as indicated in the figure.</p>
-
-<p>A ray, however, proceeding parallel to the axis and striking
-the surface as at <i>bb</i> will be deflected by twice the angle of incidence
-as is the case with all reflected rays. But this angle is
-measured by the radius <i>Cb</i> from the center of curvature and the
-reflected ray makes an angle <i>CbF</i> with the radius, equal to <i>FCb</i>.
-For points very near the axis <i>bF</i>, therefore, equals <i>FC</i>, and substantially
-also equals <i>cF</i>. Thus rays near the axis and parallel
-to it meet at <i>F</i> the focus half, way from <i>c</i> to <i>C</i>. The equivalent
-focal length of a spherical concave mirror of small aperture is
-therefore half its radius of curvature.</p>
-
-<div class="figcenter">
-<img src="images/i_093.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 64.</span>—Reflection from Concave Spherical Mirror.</div>
-</div>
-
-<p>But obviously for large angles of incidence these convenient
-equalities do not hold. As the upper half of the figure shows, the
-ray parallel to the axis and incident on the mirror 45° away at <i>e</i>
-is turned straight down, for it falls upon a surface inclined to it by
-45° and is therefore deflected by 90°, cutting the axis far inside the
-nominal focus, at <i>d</i>. Following up other rays nearer the axis it
-appears that there is no longer a focal point but a cusp-like focal
-surface, known to geometrical optics as a caustic and permitting
-no well defined image.</p>
-
-<p>A paraboloidal reflecting surface as in Fig. 65 has the property
-of bringing to a single point focus all rays parallel to its axis while<span class="pagenum"><a name="Page_94" id="Page_94">[Pg 94]</a></span>
-quite failing of uniting rays proceeding from any point on its
-axis, since its curvature is changing all the way out from vertex to
-periphery. Here the parallel rays <i>a</i>, <i>a</i>, <i>a</i>, <i>a</i> meeting the surface
-are reflected to the focus <i>F</i>, while in a
-perfectly symmetrical way the prolongation
-of these rays <i>a′</i>, <i>a′</i>, <i>a′</i>, <i>a′</i> if incident on the
-convex surface of the paraboloid would be
-reflected in <i>R</i>, <i>R′</i>, <i>R″</i> <i>R″′</i> just as if they
-proceeded from the same focus <i>F</i>.</p>
-
-<div class="figleft">
-<img src="images/i_094a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 65.</span>—Reflection
-from Paraboloid.</div>
-</div>
-
-<p>The difference between the spherical and
-parabolic curves is well shown in Fig. 66.
-Here are sections of the former, and in
-dotted lines of the latter. The difference
-points the moral. The parabola falls away
-toward the periphery and hence pushes
-outward the marginal rays. But it is of relatively sharper
-curvature near the center and pulls in the central to meet the
-marginal portion. In the actual construction of parabolic
-mirrors one always starts with a sphere which is easy to test
-for precision of figure at its center of curvature. Then the
-surface may be modified into a paraboloid lessening the curvature
-towards the periphery, or by increasing the curvature toward
-the center starting in this case with a sphere of a bit longer radius
-as in Fig. 66a.</p>
-
-<div class="figcenter">
-<img src="images/i_094b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 66</span><i>a</i>. and
-<span class="smcap">Fig. 66</span><i>b</i>.<br />
-Variation of Paraboloid from Sphere.</div>
-</div>
-
-<p>Practice differs in this respect, either process leading to the
-same result. In any case the departure from the spherical
-curve is very slight—a few hundred thousandths or at most ten
-thousandths of an inch depending on the size and relative focus
-of the mirror.</p>
-
-<p>Yet this small variation makes all the difference between
-admirable and hopelessly bad definition. However the work is
-done it is guided by frequent testing, until the performance shows
-that a truly parabolic figure has been reached. Its attainment is
-a matter of skilled judgment and experience.</p>
-
-<p>The weak point of the parabolic mirror is in dealing with rays<span class="pagenum"><a name="Page_95" id="Page_95">[Pg 95]</a></span>
-coming in parallel but oblique to the axis. Figure 67 shows the
-situation plainly enough. The reflected rays <i>a′</i>, <i>a″</i> no longer meet
-in a point at the focus <i>F</i> but inside the focus for parallel rays, at <i>f</i>
-forming a surface of aberration. The practical effect is that the
-image rapidly deteriorates as the star passes away from the axis,
-taking on an oval character that suggests a bad case of astigmatism
-with serious complications from coma, which in fact is substantially
-the case.</p>
-
-<div class="figcenter">
-<img src="images/i_095.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 67.</span>—Aberration of Parabolic Mirror.</div>
-</div>
-
-<p>Even when the angular aperture is very small the focal surface
-is nevertheless a sphere of radius equal to one half the focal length,
-and the aberrations off the axis increase approximately as the
-square of the relative aperture, and directly as the angular
-distance from the axis.</p>
-
-<p>The even tolerably sharp field of the mirror is therefore
-generally small, rarely over 30′ of arc as mirrors are customarily
-proportioned. At the relative aperture usual with refractors, say
-F/15, the sharp fields of the two are quite comparable in extent.
-The most effective help for the usual aberrations<a name="FNanchor_14_14" id="FNanchor_14_14"></a><a href="#Footnote_14_14" class="fnanchor">[14]</a> of the</p>
-<p><span class="pagenum"><a name="Page_96" id="Page_96">[Pg 96]</a></span></p>
-<p>mirror is the adoption of the Cassegrain form, by all odds the
-most convenient for large instruments, with a hyperboloidal
-secondary mirror.</p>
-
-<p>The hyperboloid is a curve of very interesting optical properties.
-Just as a spherical mirror returns again rays proceeding from its
-center of curvature without aberration, and the paraboloid sends
-from its focus a parallel axial beam free of aberration, or returns
-such a beam to an exact focus again, so a hyperboloid, Fig. 68,
-sends out a divergent beam free from aberration or brings it,
-returning, to an exact focus.</p>
-
-<p>Such a beam <i>a</i>, <i>a</i>, <i>a</i>, in fact behaves as if it came from and
-returned to a virtual conjugate focus <i>F′</i> on the other side of the
-hyperbolic surface. And if the convex side be reflecting, converging
-rays <i>R</i>, <i>R</i>′, <i>R″</i>, falling upon it at <i>P</i>, <i>P′</i>, <i>P″</i>, as if headed
-for the virtual focus <i>F</i>, will actually
-be reflected to <i>F′</i>, now a real focus.</p>
-
-<div class="figleft">
-<img src="images/i_096.jpg" alt="" />
-<div class="caption"> <span class="smcap">Fig. 68.</span>—Reflection from
-Hyperboloid.</div>
-</div>
-
-<p>This surface being convex its aberrations
-off the axis are of opposite
-sign to those due to a concave surface,
-and can in part at least, be made to
-compensate the aberrations of a parabolic
-main mirror. The rationale of
-the operation appears from comparison
-of Figs. 67 and 68.</p>
-
-<p>In the former the oblique rays <i>a</i>,
-<i>a′</i> are pitched too sharply down.
-When reflected from the convex surface of Fig. 68 as a converging
-beam along <i>R</i>, <i>R′</i>, <i>R″</i>, they can nevertheless, if the hyperbola be
-properly proportioned, be brought down to focus at <i>F′</i> conjugate
-to <i>F</i>, their approximate mutual point of convergence.</p>
-
-<p>Evidently, however, this compensation cannot be complete over
-a wide angle, when <i>F′</i> spreads into a surface, and the net result is
-that while the total aberrations are materially reduced there is
-some residual coma together with some increase of curvature of
-field, and distortion. Here just as in the parabolizing of the large
-speculum the construction is substantially empirical, guided in
-the case of a skilled operator by a sort of insight derived from
-experience.</p>
-
-<p>Starting from a substantially spherical convexity of very
-nearly the required curvature the figure is gradually modified
-as in the earlier example until test with the truly parabolic mirror<span class="pagenum"><a name="Page_97" id="Page_97">[Pg 97]</a></span>
-shows a flawless image for the combination. The truth is that
-no conic surface of revolution save the sphere can be ground to
-true figure by any rigorous geometrical method. The result
-must depend on the skill with which one by machine or hand
-can gauge minute departures from the sphere.</p>
-
-<p>Attempts have been made by the late Professor Schwarzchild
-and others to improve the corrections of reflectors so as to increase
-the field but they demand either very difficult curvatures imposed
-on both mirrors, or the interposition of lenses, and have thus far
-reached no practical result.</p>
-
-
-<p class="center"><span class="smcap">References</span></p>
-
-<blockquote>
-<ul><li><span class="smcap">Schwarzchild</span>: Untersuchungen 2, Geom., Opt. II.</li>
-<li><span class="smcap">Sampson</span> <i>Observatory 36</i>, 248.</li>
-<li><span class="smcap">Coddington</span>: “Reflexion and Refraction of Light.”</li>
-<li><span class="smcap">Herschel</span>: “Light.”</li>
-<li><span class="smcap">Taylor</span>: “Applied Optics.”</li>
-<li><span class="smcap">Southall</span>: “Geometrical Optics.”</li>
-<li><span class="smcap">Martin</span>: <i>Ann. Sci. de l’Ecole Normale</i>, 1877, Supplement.</li>
-<li><span class="smcap">Moser</span>: <i>Zeit. f.</i> Instrumentenkunde, 1887.</li>
-<li><span class="smcap">Harting</span>: <i>Zeit. f. Inst.</i>, 1899.</li>
-<li><span class="smcap">Harting</span>: <i>Zeit. f. Inst.</i>, 1898.</li>
-<li><span class="smcap">Von Hoegh</span>: <i>Zeit. f. Inst.</i>, 1899.</li>
-<li><span class="smcap">Steinheil &amp; Voit</span>: “Applied Optics.”</li>
-<li><span class="smcap">Collected Researches</span>, National Physical Laboratory, Vol. 14.</li>
-<li><span class="smcap">Gleichen</span>: “Lehrbuch d. Geometrische Optik.”</li>
-</ul>
-</blockquote>
-
-<p><span class="smcap">Note.</span>—In dealing with optical formulæ look out for the algebraic
-signs. Writers vary in their conventions regarding them and
-it sometimes is as difficult to learn how to apply a formula as
-to derive it from the start. Also, especially in optical patents,
-look out for camouflage, as omitting to specify an optical constant,
-giving examples involving glasses not produced by any manufacturer,
-and even specifying curves leading to absurd properties.
-It is a good idea to check up the achromatization and focal length
-before getting too trustful of a numerical design.</p>
-
-<hr class="chap" />
-
-<p><span class="pagenum"><a name="Page_98" id="Page_98">[Pg 98]</a></span></p>
-
-
-
-
-<div class="chapter"></div>
-<h2><a name="CHAPTER_V" id="CHAPTER_V">CHAPTER V</a><br />
-
-<small>MOUNTINGS</small></h2>
-
-
-<p>A steady and convenient mounting is just as necessary to the
-successful use of the telescope as is a good objective. No satisfactory
-observations for any purpose can be made with a telescope
-unsteadily mounted and not provided with adjustments
-enabling it to be moved smoothly and easily in following a
-celestial object.</p>
-
-<p>Broadly, telescope mounts may be divided into two general
-classes, alt-azimuth and equatorial. The former class is, as its
-name suggests, arranged to be turned in azimuth about a vertical
-axis, and in altitude about a horizontal axis. Such a mounting
-may be made of extreme simplicity, but obviously it requires two
-motions in order to follow up any object in the field, for the
-apparent motion of the heavenly bodies is in circles about the
-celestial pole as an axis, and consequently inclined from the
-vertical by the latitude of the place of observation.</p>
-
-<p>Pointing a telescope with motions about a vertical and horizontal
-axis only, therefore means that, as a star moves in its
-apparent path, it will drift away from the telescope both in
-azimuth and in altitude, and require to be followed by a double
-motion.</p>
-
-<p>Alt-azimuth mounts may be divided into three general groups
-according to their construction. The first and simplest of them
-is the pillar-and-claw stand shown in Figure 69. This consists
-of a vertical pillar supported on a strong tripod, usually of brass
-or iron, and provided at its top with a long conical bearing
-carrying at its upper extremity a hinged joint, bearing a bar to
-which the telescope is screwed as shown in the illustration.</p>
-
-<p>If properly made the upper joint comprises a circular plate
-carrying the bar and held between two cheek pieces with means
-for taking up wear, and providing just enough friction to permit
-of easy adjustment of the telescope, which can be swung in
-altitude from near the zenith to the horizon or below, and turned
-around its vertical axis in any direction.</p>
-
-<p><span class="pagenum"><a name="Page_99" id="Page_99">[Pg 99]</a></span></p>
-
-<p>When well made a stand of this kind is steady and smooth
-working, readily capable of carrying a telescope up to about 3
-inches aperture. It needs for its proper use a firm sub-support
-for the three strong hinged legs of the pillar. This is conveniently
-made as a very solid stool with spreading legs, or a plank of
-sufficient size may be firmly bolted to a well set post.</p>
-
-<div class="figcenter">
-<img src="images/i_099.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 69.</span>—Table Mount with Slow Motion.</div>
-</div>
-
-<p>Thus arranged the mount is a very serviceable one for small
-instruments. Its stability, however, depends on the base upon
-which it is set. The writer once unwisely attempted to gain
-convenience by removing the legs of the stand and screwing its
-body firmly upon a very substantial tripod. The result was a
-complete failure in steadiness, owing to the rather long lever arm
-furnished by the height of the pillar; and the instrument, which
-had been admirably steady originally, vibrated abominably
-when touched for focussing.</p>
-
-<p><span class="pagenum"><a name="Page_100" id="Page_100">[Pg 100]</a></span></p>
-
-<p>The particular stand here shown is furnished with a rack
-motion in altitude which is a considerable convenience in following.
-More rarely adjustable steadying rods attached to the
-objective end of the instrument are brought down to its base,
-but for a telescope large enough to require this a better mount is
-generally desirable.</p>
-
-<p>Now and then an alt-azimuth head of just the sort used in the
-pillar-and-claw stand is actually fitted on a tall tripod, but such
-an arrangement is usually found only in cheap instruments and
-for such tripod mountings other fittings are desirable.</p>
-
-<div class="figcenter">
-<img src="images/i_100.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 70.</span>—Alt-azimuth Mount, Clark Type T.</div>
-</div>
-
-<p>The second form of alt-azimuth mount, is altogether of more
-substantial construction. The vertical axis, usually tapered and
-carefully ground in its bearings, carries an oblique fork in
-which the telescope tube is carried on trunnions for its vertical
-motion. The inclination of the forked head enables the telescope
-to be pointed directly toward the zenith and the whole
-mount forms the head of a well made tripod.</p>
-
-<p>Figure 70 shows an excellent type of this form of mount as<span class="pagenum"><a name="Page_101" id="Page_101">[Pg 101]</a></span>
-used for the Clark Type T telescope, designed for both terrestrial
-and astronomical observation. In this particular arrangement
-the telescope lies in an aluminum cradle carried on the trunnions,
-from which it can be readily removed by loosening the thumb
-screws and opening the cradle.</p>
-
-<div class="figcenter">
-<img src="images/i_101.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 71.</span>—Alt-azimuth with Full Slow Motions.</div>
-</div>
-
-<p>It can also be set longitudinally for balance in the cradle if any
-attachments are to be placed upon either end. Here the adjustment
-for the height of the instrument is provided both in the<span class="pagenum"><a name="Page_102" id="Page_102">[Pg 102]</a></span>
-spread of the tripod and in the adjustable legs. So mounted a
-telescope of 3 or 4 inches aperture is easily handled and capable
-of rendering very good service either for terrestrial or celestial
-work.</p>
-
-<p>Indeed the Clarks have made instruments up to 6 inches
-aperture, mounted for special service in this simple manner.
-For celestial use where fairly high powers may be required this
-or any similar mount can be readily furnished with slow motions
-either in azimuth or altitude or both.</p>
-
-<p>Figure 71 shows a 4&frac14; inch telescope and mount by Zeiss thus
-equipped. Some alt-azimuth mounts are also provided with a
-vertical rack motion to bring the telescope to a convenient height
-without disturbing the tripod. A good alt-azimuth mount such
-as is shown in Figs. 70 and 71 is by no means to be despised
-for use with telescopes of 3 or 4 inch aperture.</p>
-
-<p>The sole inconvenience to be considered is that of the two
-motions required in following. With well fitted slow motions
-this is not really serious for ordinary observing with moderate
-powers, for one can work very comfortably up to powers of
-150 or 200 diameters keeping the object easily in view; but with
-the higher powers in which the field is very small, only a few
-minutes of arc, the double motion becomes rather a nuisance and
-it is extremely inconvenient even with low powers in sweeping
-for an object the place of which is not exactly known.</p>
-
-<p>There are in fact two distinct kinds of following necessary
-in astronomical observations. First, the mere keeping of the
-object somewhere in the field, and second, holding it somewhat
-rigorously in position, as in making close observations of detail
-or micrometrical measurements. When this finer following
-is necessary the sooner one gets away from alt-azimuth mounts
-the better.</p>
-
-<p>Still another form of alt-azimuth mount is shown in Fig. 72
-applied for a Newtonian reflector of 6 or 8 inches aperture.
-Here the overhung fork carrying the tube on trunnions is supported
-on a stout fixed tripod, to which it is pivoted at the front,
-and it is provided at the rear with a firm bearing on a sector borne
-by the tripod.</p>
-
-<p>At the front a rod with sliding coarse, and screw fine, adjustment
-provides the necessary motion in altitude. The whole fork
-is swung about its pivot over the sector bearing by a cross screw
-turned by a rod with a universal joint.</p>
-
-<p><span class="pagenum"><a name="Page_103" id="Page_103">[Pg 103]</a></span></p>
-
-<p>This mount strongly suggests the original one of Hadley, Fig.
-16, and is most firm and serviceable. A reflector thus mounted is
-remarkably convenient in that the eyepiece is always in a most
-accessible position, the view always horizontal, and the adjustments
-always within easy reach of the observer.</p>
-
-<div class="figcenter">
-<img src="images/i_103.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 72.</span>—Alt-azimuth Newtonian Reflector.</div>
-</div>
-
-<p>Whenever it is necessary to follow an object closely, as in
-using a micrometer and some other auxiliaries, the alt-azimuth
-mount is troublesome and some modification adjustable by a
-single motion, preferably made automatic by clockwork, becomes
-necessary.</p>
-
-<p>The first step in this direction is a very simple one indeed.<span class="pagenum"><a name="Page_104" id="Page_104">[Pg 104]</a></span>
-Suppose one were to tilt the azimuth axis so that it pointed to the
-celestial pole, about which all the stars appear to revolve. Then
-evidently the telescope being once pointed, a star could be followed
-merely by turning the tube about this tilted axis. Of
-course one could not easily reach some objects near the pole
-without, perhaps, fouling the mount, but in general the sky is
-within reach and a single
-motion follows the star, very
-easily if the original mount
-had a slow motion in azimuth.</p>
-
-<div class="figleft">
-<img src="images/i_104.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 73.</span>—Parallactic Mount for Reflector.</div>
-</div>
-
-<p>This is in fact the simplest
-form of equatorial mount,
-sometimes called parallactic.
-Figure 73 shows the principle
-applied to a small reflector.
-An oblique block with its angle
-adjusted to the co-latitude of
-the place drops the vertical
-axis into line with the pole,
-and the major part of the celestial
-vault is then within
-easy reach.</p>
-
-<p>It may be regarded as the
-transition step from the alt-azimuth
-to the true equatorial.
-It is rarely used for
-refractors, and the first attempt
-at a real equatorial
-mount was in fact made by
-James Short F. R. S. in
-mounting some of his small
-Gregorians.<a name="FNanchor_15_15" id="FNanchor_15_15"></a><a href="#Footnote_15_15" class="fnanchor">[15]</a> As a matter of
-record this is shown, from Short’s own paper before the Royal
-Society in 1749, in Fig. 74.</p>
-
-<p>A glance shows a stand apparently most complicated, but
-closer examination discloses that it is merely an equatorial
-on a table stand with a sweep in declination over a very wide arc,<span class="pagenum"><a name="Page_105" id="Page_105">[Pg 105]</a></span>
-and quite complete arrangements for setting to the exact latitude
-and azimuth. The particular instrument shown was of 4 inches
-aperture and about 18 inches long and was one of several
-produced by Short at about this epoch.</p>
-
-<div class="figcenter">
-<img src="images/i_105.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 74.</span>—Short’s Equatorial Mount.</div>
-</div>
-
-<p>In the instrument as shown there is first an azimuth circle
-<i>A A</i> supported on a base <i>B B B B</i> having levelling screws in the
-feet. Immediately under the azimuth circle is mounted a compass
-needle for approximate orientation, and the circle is adjustable
-by a tangent screw <i>C</i>.</p>
-
-<p><span class="pagenum"><a name="Page_106" id="Page_106">[Pg 106]</a></span></p>
-
-<p>Carried by the azimuth circle on a bearing supported by four
-pillars is a latitude circle <i>D D</i> for the adjustment of the polar
-axis, with a slow motion screw <i>E</i>. The latitude circle carries a
-right ascension circle <i>F F</i>, with a slow motion <i>G</i>, and this in turn
-carries on four pillars the declination circle <i>H H</i>, and its axis
-adjustable by the slow motion <i>K</i>.</p>
-
-<p>To this declination circle is secured the Gregorian reflector
-<i>L L</i> which serves as the observing telescope. All the circles are
-provided with verniers as well as slow motions. And the
-instrument is, so to speak, a universal one for all the purposes of
-an equatorial, and when the polar axis is set vertical equally
-adapted for use as a transit instrument, theodolite, azimuth
-instrument, or level, since the circles are provided with suitable
-levels.</p>
-
-<p>This mount was really a very neat and complete piece of work
-for the purpose intended, although scarcely suitable for mounting
-any but a small instrument. A very similar construction was
-used later by Ramsden for a small refractor.</p>
-
-<p>It is obvious that the reach of the telescope when used as an
-equatorial is somewhat limited in the mount just described.
-In modern constructions the telescope is so mounted that it may
-be turned readily to any part of the sky, although often the
-polar axis must be swung through 180° in order to pass freely
-from the extreme southern to the extreme northern heavens.</p>
-
-<p>The two motions necessary are those in right ascension to
-follow the heavenly bodies in their apparent course, and in
-declination to reach an object at any particular angular distance
-from the pole.</p>
-
-<p>There are always provided adjustments in azimuth and for
-latitude over at least a small arc, but these adjustments are
-altogether rudimentary as compared with the wide sweep given
-by Short.</p>
-
-<p>The fundamental construction of the equatorial involves
-two axes working at right angles positioned like a capital T.</p>
-
-<p>The upright of the T is the polar axis, fitted to a sleeve and
-bearing the cross of the T, which is hollow and provides the
-bearing for the declination axis, which again carries at right
-angles to itself the tube of the telescope.</p>
-
-<p>When the sleeve which carries the upright of the T points to
-the pole the telescope tube can evidently be swung to cover an
-object at any altitude, and can then be turned on its polar axis<span class="pagenum"><a name="Page_107" id="Page_107">[Pg 107]</a></span>
-so as to follow that object in its apparent diurnal motion. The
-front fork of a bicycle set at the proper angle with a cross axis
-replacing the handle bars has more than once done good service
-in an emergency. Figure 75 shows in section a modern equatorial
-mount for a medium sized telescope.</p>
-
-<div class="figcenter">
-<img src="images/i_107.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 75.</span>—Section of Modern Equatorial.</div>
-</div>
-
-<p>The mounting shown in Fig. 75, by Zeiss, is thoroughly typical
-of recent practice in instruments of moderate size. The general
-form of this equatorial comes straight down to us from Fraun<span class="pagenum"><a name="Page_108" id="Page_108">[Pg 108]</a></span>hofer’s
-mounting of the Dorpat instrument. It consists essentially
-of two axes crossed exactly at right angles.</p>
-
-<p>P, the polar axis, is aligned exactly with the pole, and is supported
-on a hollow iron pier provided at its top with the latitude
-block L to which the bearings of P are bolted. D the declination
-axis supports the telescope tube T.</p>
-
-<p>The tube is counterpoised as regards the polar axis by the
-weight a, and as regards the declination axis by the weights b b.
-At A, the upper section of the pier can be set in exact azimuth
-by adjusting screws, and at the base of the lower section the
-screws at B. B. allow some adjustment in latitude. To such
-mere rudiments are the azimuth and altitude circles of Short’s
-mount reduced.</p>
-
-<p>At the upper end of the polar axis is fitted the gear wheel g,
-driven by a worm from the clockwork at C to follow the stars
-in their course. At the lower end of the same axis is the hour
-circle h, graduated for right ascension, and a hand wheel for
-quick adjustment in R. A.</p>
-
-<p>At d is the declination circle, which is read, and set, by the telescope
-t with a right angled prism at its upper end, which saves
-the observer from leaving the eye piece for small changes.</p>
-
-<p>F is the usual finder, which should be applied to every telescope
-of 3 inches aperture and above. It should be of low power, with
-the largest practicable field, and has commonly an aperture &frac14; or
-⅕ that of the main objective, big enough to pick up readily
-objects to be examined and by its coarse cross wires to bring
-them neatly into the field. At m and n are the clamping screws
-for the right ascension and declination axes respectively, while
-o and p control the respective tangent screws for fine adjustment
-in R. A. and Dec. after the axes are clamped. This mount has
-really all the mechanical refinements needed in much larger
-instruments and represents the class of permanently mounted
-telescopes used in a fixed observatory.</p>
-
-<p>The ordinary small telescope is provided with a mount of
-the same general type but much simpler and, since it is not in a
-fixed observatory, has more liberal adjustments in azimuth and
-altitude to provide for changes of location. Figure 76 shows in
-some detail the admirable portable equatorial mounting used
-by the Clarks for instruments up to about 5 or 6 inches aperture.</p>
-
-<p>Five inches is practically the dividing line between portable
-and fixed telescopes. In fact a 5 inch telescope of standard con<span class="pagenum"><a name="Page_109" id="Page_109">[Pg 109]</a></span>struction
-with equatorial mounting is actually too heavy for
-practical portability on a tripod stand. The Clarks have turned
-out really portable instruments of this aperture, of relatively
-short focus and with aluminum tube fitted to the mounting
-standard for a 4 inch telescope, but the ordinary 5 inch equipment
-of the usual focal length deserves a permanent placement.</p>
-
-<p>In this mount the short tapered polar axis P is socketed between
-the cheeks A, and tightened in any required position by the hand
-screws B. The stout declination axis D bears the telescope
-and the counterweight C. Setting circles in R. A. and Dec., p
-and d respectively, are carried on the two axes, and each axis
-has a worm wheel and tangent screw operated by a universal
-joint to give the necessary slow motion.</p>
-
-<div class="figcenter">
-<img src="images/i_109.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 76.</span>—Clark Adjustable Equatorial Mount.</div>
-</div>
-
-<p>The worm wheels carry their respective axes through friction
-bearings and the counter poising is so exact that the instrument
-can be quickly swung to any part of the sky and the slow motion
-picked up on the instant. The wide sweep of the polar axis
-allows immediate conversion into an alt-azimuth for terrestrial<span class="pagenum"><a name="Page_110" id="Page_110">[Pg 110]</a></span>
-use, or adjustment for any latitude. A graduated latitude arc is
-customarily engraved on one of the check pieces to facilitate
-this adjustment.</p>
-
-<p>Ordinarily portable equatorials on tripod mounts are not
-provided with circles, and have only a single slow motion, that
-in R. A. A declination circle, however, facilitates setting up
-the instrument accurately and is convenient for locating an
-object to be swept for in R. A. which must often be done if one
-has not sidereal time at hand. In Fig. 76 a thumb screw underneath
-the tripod head unclamps the mount so that it may be at
-once adjusted in azimuth without shifting the tripod.</p>
-
-<p>As a rule American stands for fixed equatorials have the clock
-drive enclosed in the hollow pillar which carries the equatorial
-head as shown in the reflector of Fig. 35, and in the Clark
-mount for refractors of medium size shown in Fig. 77. Here a
-neat quadrangular pillar carries an equatorial mounting in
-principle very much like Fig. 76, but big enough to carry telescopes
-of 8 to 10 inches aperture. It has universal adjustment in
-latitude, so that it can be used in either hemisphere, the clock
-and its driving weight are enclosed in the pillar and slow motions
-are provided for finding in R. A. and Dec. The adjustment in
-azimuth is made by moving the pillar on its base-plate, which is
-bolted to the pier. The convenient connections for accurate
-following and the powerful clock make the mount especially
-good for photographic telescopes of moderate size and the whole
-equipment is most convenient and workmanlike. It is worth
-noting that the circles are provided with graduations that are
-plain rather than minute, in accordance with modern practice.
-In these days of celestial photography equatorials are seldom
-used for determining positions except with the micrometer, and
-graduated circles therefore, primarily used merely for finding,
-should be, above all things, easy to read.</p>
-
-<p>All portable mounts are merely simplifications of the observatory
-type of Fig. 75, which, with the addition of various labor
-saving devices is applied to nearly all large refractors and to many
-reflectors as well.</p>
-
-<p>There is a modified equatorial mount sometimes known as
-the “English” equatorial in which the polar axis is long and
-supported on two piers differing enough in height to give the
-proper latitude angle, the declination axis being about midway
-of the polar axis. A bit of the sky is cut off by the taller pier,<span class="pagenum"><a name="Page_111" id="Page_111">[Pg 111]</a></span>
-and the type is not especially advantageous unless in supporting
-a very heavy instrument, too heavy to be readily overhung in
-the usual way.</p>
-
-<div class="figcenter">
-<img src="images/i_111.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 77.</span>—Universal Observatory Mount (Clark 9-inch).</div>
-</div>
-
-<p>In such case some form of the “English” mounting is very
-important to securing freedom from flexure and thereby the<span class="pagenum"><a name="Page_112" id="Page_112">[Pg 112]</a></span>
-perfection of driving in R. A. so important to photographic work.
-The 72 inch Dominion Observatory reflector and the 100 inch
-Hooker telescope at Mt. Wilson are thus mounted, the former
-on a counterpoised declination axis crosswise the polar axis, the
-original “English” type; the latter on trunnions within a long
-closed fork which carries the polar bearings at its ends.</p>
-
-<div class="figcenter">
-<img src="images/i_112.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 78.</span>—English Equatorial Mount (Hooker 100-inch Telescope).</div>
-</div>
-
-<p><span class="pagenum"><a name="Page_113" id="Page_113">[Pg 113]</a></span></p>
-
-<p>Figure 78 shows the latter instrument, of 100 inches clear aperture
-and of 42 feet principal focal length, increased to 135 feet
-when used as a Cassegrainian. It is the immense stability of this
-mount that has enabled it to carry the long cross girder bearing
-the interferometer recently used in measuring the diameters of
-the stars. Note the mercury-flotation drum at each end of the
-polar axis. The mirrors were figured by the skillful hands of
-Mr. Ritchey.</p>
-
-<div class="figcenter">
-<img src="images/i_113.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 79.</span>—English Equatorial Mount (72-inch Dominion Observatory Telescope).</div>
-</div>
-
-<p>Figure 79 gives in outline the proportions and mounting of
-the beautiful instrument in service at the Dominion Observatory,
-near Victoria, B. C. The mirror and its auxiliaries were figured
-by Brashear and the very elegant mounting was by Warner and
-Swasey. The main mirror is of 30 feet principal focus. The 20
-inch hyperboloidal mirror extends the focus as a Cassagrainian to
-108 feet. The mechanical stability of these English mounts
-for very large instruments has been amply demonstrated by<span class="pagenum"><a name="Page_114" id="Page_114">[Pg 114]</a></span>
-this, as by the Hooker 100 inch reflector. They suffer less from
-flexure than the Fraunhofer mount where great weights are to be
-carried, although the latter is more convenient and generally
-useful for instruments of moderate size. It is hard to say too
-much of the mechanical skill that has made these two colossal
-telescopes so completely successful as instruments of research.</p>
-
-<div class="figcenter">
-<img src="images/i_114.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 80.</span>—Astrographic Mount with Bent Pier.</div>
-</div>
-
-<p>The inconvenience of having to swing the telescope tube to
-clear the pier at certain points in the R. A. following is often a
-serious nuisance in photographic work requiring long exposures,
-and may waste valuable time in visual work. Several recent<span class="pagenum"><a name="Page_115" id="Page_115">[Pg 115]</a></span>
-forms of equatorial mount have therefore been devised to allow
-the telescope complete freedom of revolution in R. A., swinging
-clear of everything.</p>
-
-<p>One such form is shown in Fig. 80 which is a standard astrographic
-mount for a Brashear doublet and guiding telescope.
-The pier is strongly overhung in the direction of the polar axis
-far enough to allow the instrument to follow through for any
-required period, even to resuming operations on another night
-without a shift of working position.</p>
-
-<div class="figcenter">
-<img src="images/i_115.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 81.</span>—Open Fork Mounting.</div>
-</div>
-
-<p>Another form, even simpler and found to be extremely satisfactory
-even for rather large instruments, is the open polar fork
-mount. Here the polar axis of an ordinary form is continued by
-a wide and stiff casting in the form of a fork within which the
-tube is carried on substantial trunnions, giving it complete
-freedom of motion.</p>
-
-<p>The open fork mount in its simplest form, carrying a heliostat
-mirror, is shown in Fig. 81. Here <i>A</i> is the fork, <i>B</i> the polar
-axis, carried on an adjustable sector for variation in latitude, <i>C</i>
-the declination axis carrying the mirror <i>D</i> in its cell, <i>E</i> the slow<span class="pagenum"><a name="Page_116" id="Page_116">[Pg 116]</a></span>
-motion in declination, and <i>F</i> that in R. A. Both axes can be
-unclamped for quick motion and the R. A. axis can readily be
-driven by clock or electric motor.</p>
-
-<p>The resemblance to the fully developed English equatorial
-mount of Fig. 78 is obvious, but the present arrangement gives
-entirely free swing to a short instrument, is conveniently adjustable,
-and altogether workmanlike. It can easily carry a short
-focus celestial camera up to 6 or 8 inches aperture or a reflector of
-4 or 5 feet focal length.</p>
-
-<p>In Fig. 173, Chap. X a pair of these same mounts are shown
-at Harvard Observatory. The nearer one, carrying a celestial
-camera, is exposed to view. It is provided with a slow motion
-and clamp in declination, and with an electric drive in R. A.,
-quickly unclamped for swinging the camera. It works very
-smoothly, its weight is taken by a very simple self adjusting
-thrust bearing at the lower end of the polar axis, and altogether
-it is about the simplest and cheapest equatorial mount of first
-class quality that can be devised for carrying instruments of
-moderate length.</p>
-
-<p>Several others are in use at the Harvard Observatory and very
-similar ones of a larger growth carry the 24 inch Newtonian
-reflector there used for stellar photography and the 16 inch
-Metcalf photographic doublet.</p>
-
-<div class="figcenter">
-<img src="images/i_116a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 82.</span>—Mounting of Mt. Wilson 60-inch
-Reflector.</div>
-</div>
-<div class="figcenter">
-<img src="images/i_116b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 83.</span>—The 60-inch as Cassegrainian,
-F = 100′.</div>
-</div>
-
-<p>In fact the open fork mount, which was developed by the late<span class="pagenum"><a name="Page_117" id="Page_117">[Pg 117]</a></span>
-Dr. Common, is very well suited to the mounting of big reflectors.
-It was first adapted by him to his 3 ft. reflector and later used for
-his two 5 ft. mirrors, and more recently for the 5 ft. instrument at
-Mt. Wilson, and a good many others of recent make. Dr.
-Common in order to secure the easiest possible motion in R. A.
-devised the plan of floating most of the weight assumed by the
-polar axis in mercury.</p>
-
-<p>Figure 82 is, diagrammatically, this fork mount as worked out
-by Ritchey for the 5′ Mt. Wilson reflector. Here A is the lattice
-tube, B the polar axis, C the fork and D the hollow steel drum
-which floats the axis in the mercury trough E. The great mirror
-is here shown worked as a simple Newtonian of 25 ft. focal length.
-As a matter of fact it is used much of the time as a Cassegranian.</p>
-
-<p>To this end the upper section of tube carrying the oblique
-mirror is removed and a shorter tube carrying any one of three
-hyperboloidal mirrors is put in its place. Fig. 83 is the normal
-arrangement for visual or photographic work on the long focus,
-100 ft. The dotted lines show the path of the rays and it will be
-noticed that the great mirror is not perforated as in the usual
-Cassegrainian construction, but that the rays are brought out by
-a diagonal flat.</p>
-
-<p>Figure 84 is a similar arrangement used for stellar spectroscopy
-with a small flat and an equivalent focus of 80 ft. In Fig.
-85 a radically different scheme is carried out. The hyperboloidal<span class="pagenum"><a name="Page_118" id="Page_118">[Pg 118]</a></span>
-mirror now used gives an equivalent focus of 150 ft., and the auxiliary
-flat is arranged to turn on an axis parallel to the declination
-axis so as to send the reflected beam down the hollow polar axis
-into a spectrograph vault below the southern end of the axis.
-Obviously one cannot work near the pole with this arrangement
-but only through some 75° as indicated by the dotted lines. The
-fork mount is not at all universal for reflectors, as has already been
-seen, and Cassegrainian of moderate size are very commonly
-mounted exactly like refractors.</p>
-
-<div class="figleft">
-<img src="images/i_117a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 84.</span>—The 60-inch as Cassegrainian,
-F = 80′.</div>
-</div>
-<div class="figcenter">
-<img src="images/i_117b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 85.</span>—The 60-inch as Polar
- Cassegrainian, F = 150′.</div>
-</div>
-
-<p>We now come to a group of mounts which have in common the
-fundamental idea of a fixed eyepiece, and incidentally better
-protection of the observer against the rigors of long winter nights
-when the seeing may be at its best but the efficiency of the
-observer is greatly diminished by discomfort. Some of the
-arrangements are also of value in facilitating the use of long focus
-objectives and mirrors and escaping the cost of the large domes
-which otherwise would be required.</p>
-
-<p>Perhaps the earliest example of the class is found in Caroline
-Herschel’s comet seeker, shown in Fig. 86. This was a Newtonian
-reflector of about 6 inches aperture mounted in a fashion
-that is almost self explanatory. It was, like all Herschel’s
-telescopes, an alt-azimuth but instead of being pivoted in altitude
-about the mirror or the center of gravity of the whole tube, it
-was pivoted on the eyepiece location and the tube was counterbalanced
-as shown so that it could be very easily adjusted in
-altitude while the whole frame turned in azimuth about a
-vertical post.</p>
-
-<p>Thus the observer could stand or sit at ease sweeping in a
-vertical circle, and merely had to move around the post as the
-azimuth was changed. The arrangement is not without advantages,
-and was many years later adopted with modifications
-of detail by Dr. J. W. Draper for the famous instrument with
-which he advanced so notably the art of celestial photography.</p>
-
-<p>The same fundamental idea of freeing the observer from continual
-climbing about to reach the eyepiece has been carried out
-in various equatorially mounted comet seekers. A very good
-example of the type is a big comet seeker by Zeiss, shown in
-Fig. 87. The fundamental principle is that the ocular is at the
-intersection of the polar and declination axis, the telescope tube
-being overhung well beyond the north end of the former and
-counterbalanced on the latter. The observer can therefore sit<span class="pagenum"><a name="Page_119" id="Page_119">[Pg 119]</a></span>
-in his swivel chair and without stirring from it sweep rapidly
-over a very wide expanse of sky.</p>
-
-<p>This particular instrument is probably the largest of regular
-comet seekers, 8 inches in clear aperture and 52&frac12; inches focal
-length with a triple objective to ensure the necessary corrections
-in using so great a relative aperture. In
-this figure 1 is the base with corrections
-in altitude and azimuth, 2 the counterpoise
-of the whole telescope on its base,
-3 the polar axis and R. A. circle, 4 the
-overhung declination axis and its circle,
-5 the counterpoise in declination, 6 the
-polar counterpoise, and 7 the main telescope
-tube. The handwheel shown
-merely operates the gear for revolving
-the dome without leaving the observing
-chair.</p>
-
-<p>The next step beyond the eyepiece
-fixed in general position is so to locate
-it that the observer can be thoroughly
-protected without including the optical
-parts of the telescope in such wise as to
-injure their performance.</p>
-
-<p>One cannot successfully observe through an open window on
-account of the air currents due to temperature differences, and
-in an observatory dome, unheated as it is, must wait after the
-shutter is opened until the temperature is fairly steadied.</p>
-
-<p>Except for these comet seekers practically all of the class
-make use of one or two auxiliary reflections to bring the image
-into the required direction, and in general the field of possible
-view is somewhat curtailed by the mounting. This is less of a
-disadvantage than it would appear at first thought, for, to begin
-with, observations within 20° of the horizon or thereabouts are
-generally unsatisfactory, and the advantages of a stable and
-convenient long focus instrument are so notable as for many
-purposes quite to outweigh some loss of sky-space.</p>
-
-<div class="figleft">
-<img src="images/i_119.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 86.</span>—Caroline Herschel’s
-Comet Seeker.</div>
-</div>
-
-<p>The simplest of the fixed eyepiece group is the polar telescope
-of which the rudiments are well shown in Fig. 88, a mount
-described by Sir Howard Grubb in 1880, and an example of which
-was installed a little later in the Crawford Observatory in Cork.
-Here the polar axis A is the main tube of the telescope, and in<span class="pagenum"><a name="Page_120" id="Page_120">[Pg 120]</a></span>
-front of the objective B, is held in a fork the declination cradle
-and mirror C, by which any object within a wide sweep of declination
-can be brought into the field and held there by hand or
-clockwork through rotating the polar tube.</p>
-
-<p>Looked at from another slant it is a polar heliostat, of which the
-telescope forms the driving axis in R. A. The whole mount was
-a substantial casting on wheels which ran on a pair of rails.
-For use the instrument was rolled to a specially arranged window
-and through it until over its regular bearings on a pier just
-outside.</p>
-
-<div class="figcenter">
-<img src="images/i_120.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 87.</span>—Mounting of Large Comet Seeker.</div>
-</div>
-
-<p>A few turns of the wheel D lowered it upon these, and the back
-of the frame then closed the opening in the wall leaving the
-instrument in the open, and the eye end inside the room. The
-example first built was of only 4 inches aperture but proved its
-case admirably as a most useful and convenient instrument.</p>
-
-<p>This mount with various others of the fixed eyepiece class
-may be regarded as derived from the horizontal photoheliographs<span class="pagenum"><a name="Page_121" id="Page_121">[Pg 121]</a></span>
-used at the 1874 transit of Venus and subsequently at many
-total solar eclipses. Given an equatorially mounted heliostat
-like Fig. 81 and it is evident that the beam from it may be turned
-into a horizontal telescope placed in the meridian, (or for that
-matter in any convenient direction) and held there by rotation of
-the mirror in R. A., but also in declination, save in the case
-where the beam travels along the extension of the polar axis.</p>
-
-<div class="figcenter">
-<img src="images/i_121.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 88.</span>—Grubb’s Original Polar Telescope.</div>
-</div>
-
-<p>For the brief exposure periods originally needed and the slow
-variation of the sun in declination this heliostatic telescope was
-easily kept in adjustment. The original instruments were of
-5 inches aperture and 40 ft. focal length, and the 7 inch heliostat
-mirror was provided with ordinary equatorial clockwork. Set up
-with the telescope pointing along the polar axis no continuous
-variation in declination is needed and the clock drive holds the
-field steadily, as in any other equatorial.</p>
-
-<p><span class="pagenum"><a name="Page_122" id="Page_122">[Pg 122]</a></span></p>
-
-<p>Figure 89 shows diagrammatically the 12 inch polar telescope
-used for more than twenty years past at the Harvard Observatory.
-The mount was designed by Mr. W. P. Gerrish of the Harvard
-staff and contains many ingenious features. Unlike Fig. 88 this
-is a fixed mount, with the eye-end comfortably housed in a room
-on the second floor of the main observatory building, and the
-lower bearing on a substantial pier to the southward.</p>
-
-<div class="figcenter">
-<img src="images/i_122.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 89.</span>—Diagram of Gerrish Polar Telescope.</div>
-</div>
-
-<p>In the figure, <i>A</i> is the eye end, <i>B</i> the main tube with the
-objective at its lower end and prolonged by a fork supported by
-the bearing <i>C</i> and <i>D</i> is the declination mirror sending the beam
-upward. The whole is rotated in R. A. by an electric clock drive,
-and all the necessary adjustments are made from the eye end.</p>
-
-<p>A view of the exterior is shown in Fig. 90, with the mirror and
-objective uncovered. The rocking arm at the objective end,
-operated by a small winch beside the ocular, swings clear both
-mirror and objective caps in a few seconds, and the telescope is
-then ready for use. Its focal length is 16 ft. 10 inches and it gives
-a sweep in declination of approximately 80°. It gives excellent
-definition and has proved a most useful instrument.</p>
-
-<p>A second polar telescope was set up at the Harvard Observatory
-station in Mandeville, Jamaica, in the autumn of 1900.<span class="pagenum"><a name="Page_123" id="Page_123">[Pg 123]</a></span>
-This was intended primarily for lunar photography and was
-provided with a 12 inch objective of 135 ft. 4 inches focal length
-and an 18 inch heliostat with electric clock drive.</p>
-
-<div class="figcenter">
-<img src="images/i_123.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 90.</span>—Gerrish Polar Telescope, Harvard Observatory.</div>
-</div>
-
-<p>Inasmuch as all instruments of this class necessarily rotate
-the image as the mirror turns, the tail-piece of this telescope is
-also mounted for rotation by a similar drive so that the image is
-stationary on the plate both in position and orientation. As
-Mandeville is in N. lat. 18° 01′ the telescope is conveniently near
-the horizontal. The observatory of Yale University has a large
-instrument of this class, of 50 feet focal length, with a 15-inch
-photographic objective and a 10-inch visual guiding objective
-working together from the same heliostat.</p>
-
-<p><span class="pagenum"><a name="Page_124" id="Page_124">[Pg 124]</a></span></p>
-
-<p>Despite its simplicity and convenience the polar telescope
-has an obvious defect in its very modest sweep in declination,
-only to be increased by the use of an exceptionally large mirror.
-It is not therefore remarkable that the first serious attempt at a
-fixed eyepiece instrument for general use turned to a different
-construction even at the cost of an additional reflection.</p>
-
-<div class="figleft">
-<img src="images/i_124.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 91.</span>—Diagram of Equatorial Coudé.</div>
-</div>
-
-<p>This was the <i>equatorial coudé</i> devised by M. Loewy of the
-Paris Observatory in 1882. (Fig. 91.) In the diagram A is
-the main tube which forms
-the polar axis, and B the eye
-end under shelter, with all
-accessories at the observer’s
-hand. But the tube is broken
-by the box casing C containing
-a mirror rigidly supported
-at 45° to the axis of
-the main tube and of the side
-tube D, which is counterbalanced
-and is in effect a hollow
-declination axis carrying the
-objective E at its outer end.</p>
-
-<p>In lieu of the telescope tube
-usually carried on this declination
-axis we have the 45° mirror, F, turning in a sleeve concentric
-with the objective, which, having a lateral aperture, virtually
-gives the objectives a full sweep in declination, save as the upper
-pier cuts it off. The whole instrument is clock driven in R. A.,
-and has the usual circles and slow motions all handily manipulated
-from the eye end.</p>
-
-<p>The <i>equatorial coudé</i> is undeniably complicated and costly,
-but as constructed by Henry Frères it actually performs admirably
-even under severe tests, and has been several times duplicated
-in French observatories. The first <i>coudé</i> erected was of
-10&frac12; inches aperture and was soon followed by one of 23.6 inches
-aperture and 59 ft. focus, which is the largest yet built.</p>
-
-<p>Still another mounting suggestive of both the polar telescope
-and the <i>coudé</i> is due to Sir Howard Grubb, Fig. 92. Here as in
-the <i>coudé</i> the upper part of the polar axis, <i>A</i>, is the telescope tube
-which leads into a solid casing <i>B</i>, about which a substantial
-fork, <i>C</i>, is pivoted. This fork is the extension of the side tube <i>D</i>,
-which carries the objective, and thus has free swing in declina<span class="pagenum"><a name="Page_125" id="Page_125">[Pg 125]</a></span>tion
-through an angle limited by the roof of the observing room
-above, and the proximity of the horizon below.</p>
-
-<p>Its useful swing, as in the polar telescope, is limited by the
-dimensions of the mirror <i>E</i>, which receives the cone of rays from
-the objective and turns it up the polar tube to the eyepiece. This
-mirror is geared to turn at half the rate of the tube <i>D</i> so that the
-angle <i>D E A</i> is continually bisected.</p>
-
-<div class="figcenter">
-<img src="images/i_125.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 92.</span>—Grubb Modified Coudé.</div>
-</div>
-
-<p>In point of fact the sole gain in this construction is the reduction
-in the size of mirror required, by reason of the diminished
-size of the cone of rays when it reaches the mirror. The plan
-has been very successfully worked out in the fine astrographic
-telescope of the Cambridge Observatory of 12&frac12; inches aperture
-and 19.3 ft. focal length.</p>
-
-<p>As in the other instruments of this general class the adjustments
-are all conveniently made from the eye end. The Cambridge
-instrument has a triple photo-visual objective of the form
-designed by Mr. H. D. Taylor and the side tube, when not in use,
-is turned down to the horizontal and covered in by a low wheeled
-housing carried on a track. The sky space covered is from 15°
-above the pole to near the horizontal.</p>
-
-<p>It is obvious that various polar and <i>coudé</i> forms of reflector are<span class="pagenum"><a name="Page_126" id="Page_126">[Pg 126]</a></span>
-quite practicable and indeed one such arrangement is shown in
-connection with the 60 inch Mt. Wilson reflector, but we are here
-concerned only with the chief types of mounting which have
-actually proved their usefulness. None of the arrangements
-which require the use of additional large reflecting surfaces are
-exempt from danger of impaired definition. Only superlatively
-fine workmanship and skill in mounting can save them from distortion
-and astigmatism due to flexure and warping of the mirrors,
-and such troubles have not infrequently been encountered.</p>
-
-<p>To a somewhat variant type belong several valuable constructions
-which utilize in the auxiliary reflecting system the cœlostat
-rather than the polar heliostat or its equivalent. The cœlostat
-is simply a plane mirror mounted with its plane fixed in that of a
-polar axis which rotates once in 48 hours, i.e., at half the apparent
-rate of the stars.</p>
-
-<div class="figcenter">
-<img src="images/i_126.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 93.</span>—Diagram of Snow Horizontal Telescope.</div>
-</div>
-<p>A telescope pointed at such a mirror will hold the stars motionless
-in its field as if the firmament were halted à la Joshua. But
-if a change of view is wanted the telescope must be shifted in
-altitude or azimuth or both. This is altogether inconvenient,
-so that as a matter of practice a second plane mirror is used to
-turn the steady beam from the cœlostat into any desired
-direction.</p>
-
-<p>By thus shifting the mirror instead of the telescope, the latter
-can be permanently fixed in the most convenient location, at the
-cost of some added expense and loss of light. Further, the image
-does not rotate as in case of the polar heliostat, which is often an
-advantage.</p>
-
-<p>An admirable type of the fixed telescope thus constituted is
-the Snow telescope at Mt. Wilson (Cont. from the Solar Obs.<span class="pagenum"><a name="Page_127" id="Page_127">[Pg 127]</a></span>
-#2, Hale). Fig. 93 from this paper shows the equipment in
-plan and elevation. The topography of the mountain top made
-it desirable to lay out the axis of the building 15° E. of N. and
-sloping downward 5° toward the N.</p>
-
-<p>At the right hand end of the figure is shown the cœlostat
-pier, 29 ft. high at its S end. This pier carries the cœlostat mirror
-proper, 30 inches in diameter, on rails <i>a a</i> accurately E. and W. to
-allow for sliding the instrument so that its field may clear the
-secondary mirror of 24 inches diameter which is on an alt-azimuth
-fork mounting and also slides on rails <i>b b</i>.</p>
-
-<p>The telescope here is a pair of parabolic mirrors each of 24 inches
-aperture and of 60 ft. and 145 ft. focus respectively. The beam
-from the secondary cœlostat mirror passes first through the
-spectrographic laboratory shown to the left of the main pier, and
-in through a long and narrow shelter house to one of these mirrors;
-the one of longest focus on longitudinal focussing rails <i>e e</i>, the
-other on similar rails <i>c c</i>, with provision for sliding sidewise at <i>d</i>
-to clear the way for the longer beam.</p>
-
-<p>The ocular end of this remarkable telescope is the spectrographic
-laboratory where the beam can be turned into the
-permanently mounted instruments, for the details of which the
-original paper should be consulted. The purpose of this brief
-description is merely to show the beautiful facility with which
-a cœlostatic telescope may be adapted to astrophysical work.
-Obviously an objective could be put in the cœlostat beam for any
-purpose for which it might be desirable.</p>
-
-<p>Such in fact is the arrangement of the tower telescopes at
-the Mt. Wilson Observatory. In these instruments we have the
-ordinary cœlostat arrangement turned on end for the sake of
-getting the chief optical parts well above the ground where,
-removed from the heated surface, the definition is generally
-improved. To be sure the focus is at or near the ground level, but
-the upward air currents cause much less disturbance than the
-crosswise ones in the Snow telescope.</p>
-
-<p>The head of the first tower telescope is shown in Fig. 94.<a name="FNanchor_16_16" id="FNanchor_16_16"></a><a href="#Footnote_16_16" class="fnanchor">[16]</a>
-A is the cœlostat mirror proper 17 inches in diameter and 12
-inches thick, B the secondary mirror 12&frac34; inches in the shorter
-axis of the ellipse, 22&frac14; inches in the longer, and also 12 inches<span class="pagenum"><a name="Page_128" id="Page_128">[Pg 128]</a></span>
-thick. C is the 12 inch objective of 60 ft. focus, and D the focussing
-gear worked by a steel ribbon from below.</p>
-
-<div class="figcenter">
-<img src="images/i_128.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 94.</span>—Head of 60-inch Tower Telescope.</div>
-</div>
-
-<p>This instrument being for solar research the mirrors are
-arranged for convenient working with the sun fairly low on either
-horizon where the definition is at its best, and can be shifted
-accordingly, to the same end as in the Snow telescope. There
-is also provision for shifting the objective laterally at a uniform<span class="pagenum"><a name="Page_129" id="Page_129">[Pg 129]</a></span>
-rate from below, to provide for the use of the apparatus as
-spectro-heliograph.</p>
-
-<p>The tower is of the windmill type and proved to be fairly
-steady in spite of its height, high winds being rare on Mt. Wilson.
-The great thickness of the mirrors in the effort to escape
-distortion deserves notice. They actually proved to be too
-thick to give thermal conductivity sufficient to prevent distortion.</p>
-
-<div class="figcenter">
-<img src="images/i_129.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 95.</span>—Porter’s Polar Reflector.</div>
-</div>
-
-<p>In the later 150′ tower telescope the mirrors are relatively less
-thick, and a very interesting modification has been introduced
-in the tower, in that it consists of a lattice member for member
-within another exterior lattice, so that the open structure is
-retained, while each member that supports the optical parts is<span class="pagenum"><a name="Page_130" id="Page_130">[Pg 130]</a></span>
-shielded from the wind and sudden temperature change by its
-corresponding outer sheath.</p>
-
-<p>Still another form of mounting to give the observer access
-to a fixed eyepiece under shelter is found in the ingenious polar
-reflector by Mr. Russell W. Porter of which an example with main
-mirror of 16 inches diameter and 15 ft. 6 inches focal length was
-erected by him a few years ago. Fig. 95 is entirely descriptive
-of the arrangement which from Mr. Porter’s account seems to
-have worked extremely well. The chief difficulty encountered
-was condensation of moisture on the mirrors, which in some
-climates is very difficult to prevent.</p>
-
-<div class="figcenter">
-<img src="images/i_130.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 96.</span>—Diagram of Hartness Turret Telescope.</div>
-</div>
-
-<p>It is interesting to note that Mr. Porter’s first plan was to use
-the instrument as a Herschelian with its focus thrown below the
-siderostat at <i>F′</i>, but the tilting of the mirror, which was worked
-at F/11.6, produced excessive astigmatism of the images, and the
-plan was abandoned in favor of the Newtonian form shown in
-the figure. At F/25 or thereabouts the earlier scheme would
-probably have succeeded well.</p>
-
-<p>Still another fixed eyepiece telescope of daring and successful
-design is the turret telescope of the Hon. J. E. Hartness of which
-the inventor erected a fine example of 10 inch aperture at Springfield,
-Vermont. The telescope is in this case a refractor, and the
-feature of the mount is that the polar axis is expanded into a
-turret within which the observer sits comfortably, looking into
-the ocular which lies in the divided declination axis and is supplied
-from a reflecting prism in the main beam from the objective</p>
-
-<p><span class="pagenum"><a name="Page_131" id="Page_131">[Pg 131]</a></span></p>
-
-<p>Figure 96 shows a diagram of the mount and observatory.
-Here <i>a</i> is the polar turret, <i>bb</i> the bearings of the declination
-axis, <i>c</i> the main tube, d its support, and <i>e</i> the ocular end. Optically
-the telescope is merely an ordinary refractor used with a
-right angled prism a little larger and further up the tube than
-usual. The turret is entered in this instance from below, through
-a tunnel from the inventor’s residence. The telescope as shown
-in Fig. 96 has a 10 inch Brashear objective of fine optical quality,
-and the light is turned into the ocular tube by a right angled
-prism only 2&frac34; inches in the face. This is an entirely practicable
-size for a reflecting prism and the light lost is not materially
-in excess of that lost in the ordinary “star diagonal” so necessary
-for the observation of stars near the zenith in an ordinary equatorial.
-The only obvious difficulty of the construction is the
-support of the very large polar axis. Being an accomplished
-mechanical engineer, Mr. Hartness worked out the details of
-this design very successfully although the moving parts weighed
-some 2 tons. The ocular is not absolutely fixed with reference
-to the observer but is always conveniently placed, and the performance
-of the instrument is reported as excellent in every
-respect, while the sheltering of the observer from the rigors of
-a Vermont winter is altogether admirable. Figure 97 shows the
-complete observatory as it stands. Obviously the higher the
-latitude the easier is this particular construction, which lends
-itself readily to large instruments and has the additional advantage
-of freeing the observer from the insect pests which are
-extremely troublesome in warm weather over a large part of
-the world.</p>
-
-<p>This running account of mountings makes no claim at completeness.
-It merely shows the devices in common use and some
-which point the way to further progress. The main requirements
-in a mount are steadiness, and smoothness of motion.
-Even an alt-azimuth mount with its need of two motions, if
-smooth working and steady, is preferable to a shaky and jerky
-equatorial.</p>
-
-<p>Remember that the Herschels did immortal work without
-equatorial mountings, and used high powers at that. A clock
-driven equatorial is a great convenience and practically indispensable
-for the photographic work that makes so large a part of
-modern astronomy, but for eye observations one gets on very
-fairly without the clock.</p>
-
-<p><span class="pagenum"><a name="Page_132" id="Page_132">[Pg 132]</a></span></p>
-
-<div class="figcenter">
-<img src="images/i_132.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 97.</span>—Hartness Turret Observatory from the N. E.</div>
-</div>
-
-<p>Circles arc a necessity in all but the small telescopes used on
-portable tripods, otherwise much time will be wasted in finding.
-In any event do not skimp on the finder, which should be of
-ample aperture and wide field, say &frac14; the aperture of the main<span class="pagenum"><a name="Page_133" id="Page_133">[Pg 133]</a></span>
-objective, and 3° to 5° in field. Superior definition is needless,
-light, and sky room enough to locate objects quickly being the
-fundamental requisites.</p>
-
-<p>As a final word see that all the adjustments are within easy
-reach from the eyepiece, since an object once lost from a high
-power ocular often proves troublesome to locate again.</p>
-
-
-<p class="center">REFERENCES</p>
-
-<blockquote>
-<ul><li><span class="smcap">Chambers’</span> Astronomy, Vol. II.</li>
-<li><span class="smcap">F. L. O. Wadsworth</span>: <i>Ap. J.</i>, <b>5</b>, 132. Ranyard’s mounts for reflectors.</li>
-<li><span class="smcap">G. W. Ritchey</span>: <i>Ap. J.</i>, <b>5</b>, 143. Supporting large specula.</li>
-<li><span class="smcap">G. E. Hale</span>: Cont. Solar Obs. # 2. The “Snow” horizontal telescope.</li>
-<li><span class="smcap">G. E. Hale</span>: Cont. Solar Obs. # 23. The 60 ft. tower telescope.</li>
-<li><span class="smcap">J. W. Draper</span>: Smithsonian Contrib. <b>34</b>. Mounting of his large reflector.</li>
-<li><span class="smcap">G. W. Ritchey</span>: Smithsonian Contrib. <b>35</b>. Mounting of the Mt. Wilson 60 inch reflector.</li>
-<li><span class="smcap">Sir H. Grubb</span>: Tr. Roy. Dublin Soc. Ser. 2. <b>3</b>. Polar Telescopes.</li>
-<li><span class="smcap">Sir R. S. Ball</span>: <i>M. N.</i> <b>59</b>, 152. Photographic polar telescope.</li>
-<li><span class="smcap">A. A. Common</span>: Mem. R. A. S., <b>46</b>, 173. Mounting of his 3 ft. reflector.</li>
-<li><span class="smcap">R. W. Porter</span>: <i>Pop. Ast.</i>, <b>24</b>, 308. Polar reflecting telescope.</li>
-<li><span class="smcap">James Hartness</span>: <i>Trans. A. S. M. E.</i>, 1911, Turret Telescope.</li>
-<li><span class="smcap">Sir David Gill</span>: Enc. Brit., 11th Ed. Telescope. Admirable summary of mounts.</li>
-</ul>
-</blockquote>
-
-<hr class="chap" />
-
-<p><span class="pagenum"><a name="Page_134" id="Page_134">[Pg 134]</a></span></p>
-
-
-
-
-<div class="chapter"></div>
-<h2><a name="CHAPTER_VI" id="CHAPTER_VI">CHAPTER VI</a><br />
-
-<small>EYE PIECES</small></h2>
-
-
-<p>The eyepiece of a telescope is merely an instrument for
-magnifying the image produced by the objective or mirror. If
-one looks through a telescope without its eyepiece, drawing the
-eye back from the focus to its ordinary distance of distinct
-vision, the image is clearly seen as if suspended in air, or it can be
-received on a bit of ground glass.</p>
-
-<p>It appears larger or smaller than the object seen by the naked
-eye, in proportion as the focal length of the objective is larger
-or smaller than the distance to which the eye has to drop back
-to see the image clearly.</p>
-
-<p>This real image, the quality of which depends on the
-exactness of correction of the objective or mirror, is then to be
-magnified so much as may be desirable, by the eyepiece of the
-instrument. In broad terms, then, the eyepiece is a simple
-microscope applied to the image of an object instead of the
-object itself.</p>
-
-<p>And looking at the matter in the simplest way the magnifying
-power of any simple lens depends on the focal length of that lens
-compared with the ordinary seeing distance of the eye. If this
-be taken at 10 inches as it often conventionally is, then a lens of
-1 inch focus brings clear vision down to an inch from the object,
-increases the apparent angle covered by the object 10 times and
-hence gives a magnifying power of 10.</p>
-
-<p>But if the objective has a focal length of 100 inches the image,
-as we have just seen, is already magnified 10 times as the naked
-eye sees it, hence with an objective of 100 inches focus and a 1
-inch eyepiece the total magnification is 100 diameters. And this
-expresses the general law, for if we took the normal seeing distance
-of the naked eye at some other value than 10 inches, say 12&frac12;
-inches then we should have to reckon the image as magnified by
-8 times so far as the objective inches is concerned, but 12&frac12;
-times due to the 1 inch eyepiece, and so forth. Thus the
-magnifying power of any eyepiece is F/f where F is the focal<span class="pagenum"><a name="Page_135" id="Page_135">[Pg 135]</a></span>
-length of the objective or mirror and f that of the eyepiece.
-The focal distance of the eye quite drops out of the reckoning.</p>
-
-<p>All these facts appear very quickly if one explores the image
-from an objective with a slip of ground glass and a pocket lens.
-An ordinary camera tells the same story. A distant object which
-covers 1° will cover on the ground glass 1° reckoned on a radius
-equal to the focal length of the lens. If this is equal to the ordinary
-distance of clear vision, an eye at the same distance will see
-the image (or the distant object) covering the same 1°.</p>
-
-<p>The geometry of the situation is as follows: Let <i>o</i> Fig. 5, Chap.
-1, be the objective. This lens, as in an ordinary camera, forms an
-inverted image of an object A B at its focus, as at <i>a b</i>, and for
-any point, as <i>a</i>, of the image there is a corresponding point of the
-object lying on the straight line from A to that point through the
-center, <i>c</i>, of the objective.</p>
-
-<p>A pair of rays 1, 2, diverging from the object point A pass
-through rim and center of <i>o</i> respectively and meet in A. After
-crossing at this point they fall on the eye lens <i>e</i>, and if <i>a</i> is nearly
-in the principal focus of <i>e</i>, the rays 1 and 2 will emerge substantially
-parallel so that the eye will unite them to form a clear
-image.</p>
-
-<p>Now if F is the focal length of <i>o</i>, and f that of <i>a</i>, the object
-forming the image subtends at the center of the objective, o, an
-angle <i>A c B</i>, and for a distant object this will be sensibly the angle
-under which the eye sees the same object.</p>
-
-<p>If L is the half linear dimension of the image, the eye sees half
-the object covering the angle whose tangent is L/F. Similarly
-half the image <i>ab</i> is seen through the eye lens <i>e</i> as covering a half
-angle whose tangent is L/f. Since the magnifying power of the
-combination, m, is directly as the ratio of increase in this tangent
-of the visual angle, which measures the image dimension</p>
-
-<p class="center">
-m = F/f, as before
-</p>
-
-<p>Further, as all the light which comes in parallel through the
-whole opening of the objective forms a single conical beam concentrating
-into a focus and then diverging to enter the eye lens,
-the diameter of the cone coming through the eye lens must bear
-the same relation to the diameter of <i>o</i>, that f does to F.</p>
-
-<p>Any less diameter of <i>e</i> will cut off part of the emerging light;
-any more will show an emergent beam smaller than the eye lens,<span class="pagenum"><a name="Page_136" id="Page_136">[Pg 136]</a></span>
-which is generally the case. Hence if we call p the diameter of
-the bright pencil of light which we see coming through the eye
-lens then for that particular eye lens,</p>
-
-<p class="center">m = <i>o</i>/p</p>
-
-<p>That is, f = pF/<i>o</i> which is quite the easiest way of measuring the
-focal length of an eyepiece.</p>
-
-<p>Point the telescope toward the clear sky, focusing for a distant
-object so that the emergent pencil is sharply defined at the
-ocular, and then measure its diameter by the help of a fine scale
-and a pocket lens, taking care that scale and emergent pencil are
-simultaneously in sharp focus and show no parallax as the eye is
-shifted a bit. This bright circle of the emerging beam is actually
-the projection by the eye lens of the focal image of the objective
-aperture.</p>
-
-<p>This method of measuring power is easy and rather accurate.
-But it leads to trouble if the measured diameter of the objective
-is in fact contracted by a stop anywhere along the path of the
-beam, as occasionally happens. Examine the telescope carefully
-with reference to this point before thus testing the power.<a name="FNanchor_17_17" id="FNanchor_17_17"></a><a href="#Footnote_17_17" class="fnanchor">[17]</a></p>
-
-<p>The eye lens of Fig. 5 is a simple double convex one, such as
-was used by Christopher Scheiner and his contemporaries.
-With a first class objective or mirror the simple eye lens such
-as is shown in Fig. 98a is by no means to be despised even now.
-Sir William Herschel always preferred it for high powers, and
-speaks with evident contempt of observers who sacrificed its
-advantages to gain a bigger field of view. Let us try to fathom
-the reason for his vigorously expressed opinion, strongly backed
-up by experienced observers like the late T. W. Webb and Mr.
-W. F. Denning.</p>
-
-<p>First of all a single lens saves about 10% of the light. Each
-surface of glass through which light passes transmits 95 to 96%
-of that light, so that a single lens transmits approximately 90%,
-two lenses 81% and so on. This loss may be enough to determine
-the visibility of an object. Sir Wm. Herschel found that
-faint objects invisible with the ordinary two lens eyepiece came
-to view with the single lens.</p>
-
-<p><span class="pagenum"><a name="Page_137" id="Page_137">[Pg 137]</a></span></p>
-
-<p>Probably the actual loss is less serious than its effect on seeing
-conditions. The loss is due substantially to reflection at the
-surfaces, and the light thus reflected is scattered close to, or
-into, the eye and produces stray light in the field which injures
-the contrast by which faint objects become visible.</p>
-
-<p>In some eyepieces the form of the surfaces is such that reflected
-light is strongly concentrated where the eye sees it, forming
-a “ghost” quite bright enough greatly to interfere with the vision
-of delicate contrasts.</p>
-
-<p>The single lens has a very small sharp field, hardly 10° in
-angular extent, the image falling off rapidly in quality as it
-departs from the axis. If plano-convex, as is the eye lens of
-common two-lens oculars, it works best with the curved side to
-the eye, i.e., reversed from its usual position, the spherical
-aberration being much less in this position.</p>
-
-<div class="figcenter">
-<img src="images/i_137.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 98.</span>—Simple Oculars.</div>
-</div>
-
-<p>Herschel’s report of better definition with a single lens than
-with an ordinary two lens ocular speaks ill for the quality of
-the latter then available. Of course the single lens gives some
-chromatic aberration, generally of small account with the narrow
-pencils of light used in high powers.</p>
-
-<p>A somewhat better form of eye lens occasionally used is the
-so-called Coddington lens, really devised by Sir David Brewster.
-This, Fig. 98b, is derived from a glass sphere with a thick equatorial
-belt removed and a groove cut down centrally leaving a diameter
-of less than half the radius of the sphere. The focus is, for ordinary
-crown glass, 3/2 the radius of the sphere, and the field is a
-little improved over the simple lens, but it falls off rather rapidly,
-with considerable color toward the edge.</p>
-
-<p>The obvious step toward fuller correction of the aberrations
-while retaining the advantages of the simple lens is to make the
-ocular achromatic, like a minute objective, thus correcting at
-once the chromatic and spherical aberrations over a reasonably
-large field. As the components are cemented the loss of light at
-their common surface is negligible. Figure 98c shows such a<span class="pagenum"><a name="Page_138" id="Page_138">[Pg 138]</a></span>
-lens. If correctly designed it gives an admirably sharp field of
-15° to 20°, colorless and with very little distortion, and is well
-adapted for high powers.</p>
-
-<div class="figcenter">
-<img src="images/i_138a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 99.</span>—Triple Cemented Oculars.</div>
-</div>
-
-<p>Still better results in field and orthoscopy can be attained
-by going to a triple cemented lens, similar to the objective of
-Fig. 57. Triplets thus constituted are made abroad by Zeiss,
-Steinheil and others, while in this country an admirable triplet
-designed by Professor Hastings is made by Bausch &amp; Lomb.</p>
-
-<div class="figcenter">
-<img src="images/i_138.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 100.</span>—Path of Rays Through Huygenian Ocular.</div>
-</div>
-
-<p>Such lenses give a beautifully flat and sharp field over an angle
-of 20° to 30°, quite colorless and orthoscopic. Fig. 99<i>a</i>, a form
-used by Steinheil, is an excellent example of the construction
-and a most useful ocular. The late R. B. Tolles made such
-triplets, even down to ⅛ inch focus, which gave admirable
-results.</p>
-
-<p>A highly specialized form of triplet is the so-called monocentric
-of Steinheil Fig. 99<i>b</i>. Its peculiarity is less in the fact
-that all the curves are struck from the same center than in the
-great thickness of the front flint and the crown, which, as in some<span class="pagenum"><a name="Page_139" id="Page_139">[Pg 139]</a></span>
-photographic lenses, give added facilities for flattening the field
-and eliminating distortion.</p>
-
-<p>The monocentric eyepiece has a high reputation for keen
-definition and is admirably achromatic and orthoscopic. The
-sharp field is about 32°, rather the largest given by any of the
-cemented combinations. All these optically single lenses are
-quite free of ghosts, reduce scattered light to a minimum, and
-leave little to be desired in precise definition. The weak point
-of the whole tribe is the small field, which, despite Herschel’s
-opinion, is a real disadvantage for certain kinds of work and
-wastes the observer’s time unless his facilities for close setting
-are more than usually good.</p>
-
-<p>Hence the general use of oculars of the two lens types, all
-of them giving relatively wide fields, some of them faultless also
-in definition and orthoscopy. The earliest form, Fig. 100, is
-the very useful and common one used by Huygens and bearing
-his name, though perhaps independently devised by Campani of
-Rome. Probably four out of five astronomical eyepieces belong
-to this class.</p>
-
-<p>The Huygenian ocular accomplishes two useful results—first,
-it gives a wider sharp field than any single lens, and second
-it compensates the chromatic aberration, which otherwise must
-be removed by a composite lens. It usually consists of a plano-convex
-lens, convex side toward the objective, which is brought
-inside the objective focus and forms an image in the plane of a
-rear diaphragm, and a similar eye lens of shorter focus by which
-this image is examined.</p>
-
-<p>Fig. 100 shows the course of the rays—<i>A</i> being the field lens,
-<i>B</i> the diaphragm and <i>C</i> the eye lens. Let <i>1</i>, <i>2</i>, be rays which are
-incident near the margin of <i>A</i>. Each, in passing through
-the lens, is dispersed, the blue being more refracted than the
-red. Both rays come to a general focus at <i>B</i>, and, crossing,
-diverge slightly towards <i>C</i>.</p>
-
-<p>But, on reaching <i>C</i>, ray <i>1</i>, that was nearer the margin and
-the more refracted because in a zone of greater pitch, now falls on
-<i>C</i> the nearer its center, and is less refracted than ray <i>2</i> which
-strikes <i>C</i> nearer the rim. If the curvatures of <i>A</i> and <i>C</i> are
-properly related <i>1</i> and <i>2</i> emerge from <i>C</i> parallel to each other
-and thus unite in forming a distinct image.</p>
-
-<p>Now follow through the two branches of <i>l</i> marked <i>l_r</i>, and <i>l_v</i>,
-the red and violet components. Ray <i>l_v</i>, the more refrangible,<span class="pagenum"><a name="Page_140" id="Page_140">[Pg 140]</a></span>
-strikes <i>C</i> nearer the center, and is the less refracted, emerging
-from <i>C</i> substantially parallel with its mate <i>l_r</i>, hence blending
-the red and violet images, if, being of the same glass, <i>A</i> and <i>C</i>
-have suitably related focal lengths and separation.</p>
-
-<p>As a matter of fact the condition for this chromatic compensation
-is</p>
-
-<p class="center">d = (f + f′)/2</p>
-
-<p>where d is the distance between the lenses and f, f′, their respective
-focal lengths. If this condition of achromatism be combined
-with that of equal refraction at <i>A</i> and <i>C</i>, favorable to minimizing
-the spherical aberration, we find f = 3f′ and d = 2f′. This is
-the conventional Huygenian ocular with an eye lens ⅓ the focus
-of the field lens, spaced at double the focus of the eye lens, with
-the diaphragm midway.</p>
-
-<div class="figleft">
-<img src="images/i_140.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 101</span><i>a</i>.—Airy and
-Mittenzuey Oculars.</div>
-</div>
-
-<p>In practice the ratio of foci varies from 1:3 to 1:2 or even
-1:1.5, the exact figure varying with the
-amount of overcorrection in the objective
-and under-correction in the eye that has to
-be dealt with, while the value of d should
-be adjusted by actual trial on the telescope
-to obtain the best color correction practicable.
-One cannot use any chance ocular
-and expect the finest results.</p>
-
-<p>The Huygenian eyepieces are often referred to as “negative”
-inasmuch as they cannot be used directly as magnifiers, although
-dealing effectively with an image rather than an object. The
-statement is also often made that they cannot be used with
-cross wires. This is incorrect, for while there is noticeable distortion
-toward the edge of the wide field, to say nothing of astigmatism,
-in and near the center of the field the situation is a
-good deal better.</p>
-
-<p>Central cross wires in the plane of the diaphragm are entirely
-suitable for alignment of the instrument, and over a moderate
-extent of field the distortion is so small that a micrometer scale
-in the plane of the diaphragm gives very good approximate
-measurements, and indeed is widely used in microscopy.</p>
-
-<p>It should be noted that the achromatism of this type of eyepiece
-is compensatory rather than real. One cannot at the same<span class="pagenum"><a name="Page_141" id="Page_141">[Pg 141]</a></span>
-time bring the images of various colors to the same size, and also
-to the same plane. As failure in the latter respect is comparatively
-unimportant, the Huygenian eyepiece is adjusted so far
-to compensate the paths of the various rays as to bring the
-colored images to the same size, and in point of fact the result
-is very good.</p>
-
-<p>The field of the conventional form of Huygenian ocular is
-fully 40°, and the definition, particularly centrally, is very
-excellent. There are no perceptible ghosts produced, and while
-some 10% of light is lost by reflection in the extra lens it is
-diffused in the general field and is damaging only as it injures
-the contrast of faint objects. The theory of the Huygenian eyepiece
-was elaborately given by Littrow, (Memoirs R. A. S. Vol. 4,
-p. 599), wherein the somewhat intricate geometry of the situation
-is fully discussed.</p>
-
-<div class="figright">
-<img src="images/i_141.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 101</span><i>b</i>.—Airy
- and Mittenzwey Oculars.</div>
-</div>
-
-<p>Various modifications of the Huygenian type have been devised
-and used. Figure 101<i>a</i> is the Airy form devised as a result of a
-somewhat full mathematical investigation by
-Sir George Airy, later Astronomer Royal.
-Its peculiarity lies in the form of the lenses
-which preserve the usual 3:1 ratio of focal
-lengths. The field lens is a positive meniscus
-with a noticeable amount of concavity in the
-rear face while the eye lens is a “crossed”
-lens, the outer curvature being about ⅙ of
-the inner curvature. The marginal field in this ocular is a little
-better than in the conventional Huygenian.</p>
-
-<p>A commoner modification now-a-days is the Mittenzwey
-form, Fig. 101<i>b</i>. This is usually made with 2:1 ratio of focal
-lengths, and the field lens still a meniscus, but less conspicuously
-concave than in the Airy form. The eye lens is the usual plano-convex.
-It is widely used, especially abroad, and gives perhaps
-as large available field as any ocular yet devised, approximately
-50°, with pretty good definition out to the margin.</p>
-
-<p>Finally, we come to the solid eyepiece Fig. 102<i>a</i>, devised by
-the late R. B. Tolies nearly three quarters of a century ago, and
-and often made by him both for telescopes and microscopes.
-It is practically a Huygenian eyepiece made out of a single
-cylinder of glass with a curvature ratio of 1&frac12;:1 between the eye
-and the field lens. A groove is cut around the long lens at about
-⅓ its length from the vertex of the field end. This serves as a<span class="pagenum"><a name="Page_142" id="Page_142">[Pg 142]</a></span>
-stop, reducing the diameter of the lens to about one-half its
-focal length.</p>
-
-<p>It is in fact a Huygenian eyepiece free from the loss of light
-in the usual construction. It gives a wide field, more extensive
-than in the ordinary form, with exquisite definition. It is really
-a most admirable form of eyepiece which should be used far
-more than is now the case. The late Dr. Brashear is on record
-as believing that all negative eyepieces less than &frac34; inch focus
-should be made in this form.</p>
-
-<div class="figcenter">
-<img src="images/i_142.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 102.</span>—Tolles’ Solid and Compensated Oculars.</div>
-</div>
-
-<p>So far as the writer can ascertain the only reason that it is not
-more used is that it is somewhat more difficult to construct than
-the two lens form, for its curvatures and length must be very
-accurately adjusted. It is consequently unpopular with the constructing
-optician in spite of its conspicuous merits. It gives no
-ghosts, and the faint reflection at the eye end is widely spread so
-that if the exterior of the cylinder is well blackened, as it should
-be, it gives exceptional freedom from stray light. Still another
-variety of the Huygenian ocular sometimes useful is analogous to
-the compensating eyepiece used in microscopy. If, as commonly
-is the case, a telescope objective is over-corrected for color to correct
-for the chromatism of the eye in low powers, the high powers
-show strong over correction, the blue focus being longer than the
-red, and the blue image therefore the larger.</p>
-
-<p>If now the field lens of the ocular be made of heavy flint glass
-and the separation of the lenses suitably adjusted, the stronger
-refraction of the field lens for the blue pulls up the blue focus and
-brings its image to substantially the dimensions of the red, so
-that the eye lens performs as if there were no overcorrection
-of the objective.</p>
-
-<p>The writer has experimented with an ocular of this sort as
-shown in Fig. 102<i>b</i> and finds that the color correction is, as
-might be expected, greatly improved over a Mittenzwey ocular<span class="pagenum"><a name="Page_143" id="Page_143">[Pg 143]</a></span>
-of the same focus (⅕ inch). There would be material advantage
-in thus varying the ocular color correction to suit the power.</p>
-
-<p>In the Huyghenian eyepiece the equivalent focal length F is
-given by,</p>
-
-<p class="center">F = 2ff′/(f + f′)</p>
-
-<p>where f and f′ are the focal lengths of the field and eye lenses
-respectively. This assumes the normal spacing, d, of half the
-sum of the focal lengths, not always adhered to by constructors.
-The perfectly general case, as for any two combined lenses is,</p>
-
-<p class="center">F = ff<sub>1</sub>/(f + f<sub>1</sub>-d)</p>
-
-<div class="figcenter">
-<img src="images/i_143.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 103.</span>—Path of Rays Through Ramsden Ocular.</div>
-</div>
-
-<p>To obtain a flatter field, and particularly one free from distortion
-the construction devised by Ramsden is commonly used.
-This consists, Fig. 103, of two plano convex lenses of equal focal
-length, placed with their plane faces outward, at a distance equal
-to, or somewhat less than, their common focal length. The
-former spacing is the one which gives the best achromatic compensation
-since as before the condition for achromatism is</p>
-
-<p class="center">d = &frac12;(f + f′)</p>
-
-<p>When thus spaced the plane surface of the field lens is exactly
-in the focus of the eye lens, the combined focus F is the same as
-that of either lens, since as just shown in any additive combination
-of two lenses</p>
-
-<p class="center">F = ff′/(f + f′-d)</p>
-
-<p>and while the field is flat and colorless, every speck of dust on the
-field lens is offensively in view.</p>
-
-<p><span class="pagenum"><a name="Page_144" id="Page_144">[Pg 144]</a></span></p>
-
-<p>It is therefore usual to make this ocular in the form suggested
-by Airy, in which something of the achromatic correction
-is sacrificed to obviate this difficulty, and to obtain a better
-balance of the residual aberrations. The path of the rays is
-shown in Fig. 103. The lenses <i>A</i> and <i>B</i> are of the same focal
-length but are now spaced at ⅔ of this length apart.</p>
-
-<p>The two neighboring rays <i>1</i>, <i>2</i>, coming through the objective
-from the distant object meet at the objective focus in a point, <i>a</i>,
-of the image plane <i>a b</i>. Thence, diverging, they are so refracted
-by <i>A</i> and <i>B</i> as to leave the latter substantially parallel so that
-both appear to proceed from the point c, of the image plane <i>c</i>, <i>d</i>,
-in the principal focus of <i>B</i>.</p>
-
-<p>From the ordinary equation for the combination, F = &frac34; f.
-The combination focusses &frac14; f back of the principal focus of the
-objective, and the position of the eye is &frac14; F back of the eye
-lens, which is another reason for shortening the lens spacing.
-At longer spacing the eye distance is inconveniently reduced.</p>
-
-<p>Thus constituted, the Ramsden ocular, known as “positive”
-from its capability for use as a magnifier of actual objects, gives
-a good flat field free from distortion over a field of nearly 35° and
-at some loss of definition a little more. It is the form most
-commonly used for micrometer work.</p>
-
-<p>In all optical instruments the aberrations increase as one
-departs from the axis, so that angular field is rather a loose term
-depending on the maximum aberrations that can be tolerated.<a name="FNanchor_18_18" id="FNanchor_18_18"></a><a href="#Footnote_18_18" class="fnanchor">[18]</a></p>
-
-<p>Of the Ramsden ocular there are many modifications. Sometimes
-f and f′ are made unequal or there is departure from the
-simple plano-convex form. More often the lenses are made
-achromatic, thus getting rid of the very perceptible color in the
-simpler form and materially helping the definition. Figure 104<i>a</i>
-shows such an achromatic ocular as made by Steinheil. The
-general arrangement is as in the ordinary Ramsden, but the
-sharp field is slightly enlarged, a good 36°, and the definition is
-improved quite noticeably.</p>
-
-<p>A somewhat analogous form, but considerably modified in<span class="pagenum"><a name="Page_145" id="Page_145">[Pg 145]</a></span>
-detail, is the Kellner ocular, Fig. 104<i>b</i>. It was devised by an
-optician of that name, of Wetzlar, who exploited it some three
-quarters of a century since in a little brochure entitled “Das
-orthoskopische Okular,” as notable a blast of “hot air” as ever
-came from a modern publicity agent.</p>
-
-<p>As made today the Kellner ocular consists of a field lens which
-is commonly plano-convex, plano side out, but sometimes crossed
-or even equiconvex, combined with a considerably smaller eye
-lens which is an over-corrected achromatic. The focal length
-of the field lens is approximately 7/4 F, that of the eye lens 4/3 F,
-separated by about &frac34; F.</p>
-
-<p>This ocular has its front focal plane very near the field lens,
-sometimes even within its substance, and a rather short eye
-distance, but it gives admirable definition and a usable field of
-very great extent, colorless and orthoscopic to the edge. The
-writer has one of 2⅝″ focus, with an achromatic triplet as eye
-lens, which gives an admirable field of quite 50°.</p>
-
-<div class="figcenter">
-<img src="images/i_145.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 104.</span>—Achromatic and Kellner Oculars.</div>
-</div>
-
-<p>The Kellner is decidedly valuable as a wide field positive
-ocular, but it has in common with the two just previously
-described a sometimes unpleasant ghost of bright objects.
-This arises from light reflected from the inner surface of the field
-lens, and back again by the front surface to a focus. This focus
-commonly lies not far back of the field lens and quite too near
-to the focus of the eye lens for comfort. It should be watched
-for in going after faint objects with oculars of the types noted.</p>
-
-<p>A decidedly better form of positive ocular is the modern
-orthoscopic as made by Steinheil and Zeiss, Fig. 105<i>a</i>. It
-consists of a triple achromatic field lens, a dense flint between
-two crowns, with a plano-convex eye lens of much shorter focus
-(⅓ to &frac12;) almost in contact on its convex side.</p>
-
-<p>The field triplet is heavily over-corrected for color, the front
-focal plane is nearly &frac12; F ahead of the front vertex of the field
-lens, and the eye distance is notably greater than in the Kellner.
-The field is above 40°, beautifully flat, sharp, and orthoscopic,<span class="pagenum"><a name="Page_146" id="Page_146">[Pg 146]</a></span>
-free of troublesome ghosts. On the whole the writer is inclined
-to rate it as the best of two-lens oculars.</p>
-
-<p>There should also here be mentioned a very useful long relief
-ocular, often used for artillery sights, and shown in Fig. 105<i>b</i>.
-It consists like Fig. 104<i>a</i>, of a pair of achromatic lenses, but they
-are placed with the crowns almost in contact and are frequently
-used with a simple plano convex field lens of much longer focus,
-to render the combination more fully orthoscopic.</p>
-
-<p>The field, especially with the field lens, is wide, quite 40° as
-apparent angle for the whole instrument, and the eye distance is
-roughly equal to the focal length. It is a form of ocular that
-might be very advantageously used in finders, where one often
-has to assume uncomfortable angles of view, and long relief is
-valuable.</p>
-
-<div class="figcenter">
-<img src="images/i_146.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 105.</span>—Orthoscopic and Long Relief Oculars.</div>
-</div>
-
-<p>Whatever the apparent angular field of an ocular may be,
-the real angular field of view is obtained by dividing the apparent
-field by the magnifying power. Thus the author’s big Kellner,
-just mentioned, gives a power of 20 with the objective for which
-it was designed, hence a real field of 2&frac12;°, while a second, power
-65, gives a real field of hardly 0°40′, the apparent field in this case
-being a trifle over 40°. There is no escaping this relation, so that
-high power always implies small field.</p>
-
-<p>The limit of apparent field is due to increasing errors away
-from the axis, strong curvature of the field, and particularly
-astigmatism in the outer zones. The eye itself can take in only
-about 40° so that more than this, while attainable, can only be
-utilized by peering around the marginal field.</p>
-
-<p>For low powers the usable field is helped out by the accommodation
-of the eye, but in oculars of short focus the curvature
-of field is the limiting factor. The radius of curvature of the
-image is, in a single lens approximately 3/2 F, and in the common
-two lens forms about &frac34; F.</p>
-
-<p>In considering this matter Conrady has shown (M. N. <i>78</i>
-445) that for a total field of 40° the sharpness of field fails at a<span class="pagenum"><a name="Page_147" id="Page_147">[Pg 147]</a></span>
-focal length of about 1 inch for normal power of accommodation.
-The best achromatic combinations reduce this limit to about
-&frac12; inch.</p>
-
-<p>At focal lengths below this the sharpest field is obtainable
-only with reduced aperture. There is an interesting possibility
-of building an anastigmatic ocular on the lines of the modern
-photographic lens, which Conrady suggests, but the need of
-wide field in high powers is hardly pressing enough to stimulate
-research.</p>
-
-<div class="figcenter">
-<img src="images/i_147.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 106.</span>—Ordinary Terrestrial Ocular.</div>
-</div>
-
-<p>Finally we may pass to the very simple adjunct of most
-small telescopes, the terrestrial ocular which inverts the image
-and shows the landscape right side up. Whatever its exact
-form it consists of an inverting system which erects the inverted
-image produced by the objective alone, and an eyepiece for viewing
-this erected image. In its common form it is composed of
-four plano-convex lenses arranged as in Fig. 106. Here A and B
-for the inverting pair and C and D a modified Huygenian ocular.
-The image from the objective is formed in the front focus of AB
-which is practically an inverted ocular, and the erected image is
-formed in the usual way between C and D.</p>
-
-<p>The apparent field is fairly good, about 35°, and while slightly
-better corrections can be gained by using lenses of specially
-adjusted curvatures, as Airy has shown, these are seldom applied.
-The chief objection to this erecting system is its length, some ten
-times its equivalent focus. Now and then to save light and gain
-field, the erector is a single cemented combination and the ocular
-like Fig. 99<i>a</i> or Fig. 102<i>a</i>. Fig. 107 shows a terrestrial eyepiece so
-arranged, from an example by the late R. B. Tolles. When carefully
-designed an apparent field of 40° or more can be secured,
-with great brilliancy, and the length of the erecting system is
-moderate.</p>
-
-<p>Very much akin in principle is the eyepiece microscope, such
-as is made by Zeiss to give variable power and a convenient
-position of the eye in connection with filar micrometers, Fig. 108.<span class="pagenum"><a name="Page_148" id="Page_148">[Pg 148]</a></span>
-It is provided with a focussing collar and its draw tube allows
-varying power just as in case of an ordinary microscope. In fact
-eyepiece microscopes have long been now and then used to
-advantage for high powers. They are easier on the eye, and give
-greater eye distance than the exceedingly small eye lenses of
-short focus oculars, and using a solid eyepiece and single lens
-objective lose no more light than an ordinary Huygenian ocular.
-The erect resultant image is occasionally a convenience in
-astronomical use.</p>
-
-<div class="figcenter">
-<img src="images/i_148a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 107.</span>—Tolles Triplet Inverting System.</div>
-</div>
-
-<div class="figcenter">
-<img src="images/i_148b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 108.</span>—Microscope as Ocular.</div>
-</div>
-
-<div class="figcenter">
-<img src="images/i_148.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 109.</span>—“Davon” Instrument.</div>
-</div>
-
-<p>Quite analogous to the eyepiece microscope is the so-called
-“Davon” micro-telescope. Originally developed as an attachment
-for the substage of a microscope to give large images
-of objects at a little distance it has grown also into a separate
-hand telescope, monocular or binocular, for general purposes.
-The attachment thus developed is shown complete in Fig. 109.
-D is merely a well corrected objective set in a mount provided
-with ample stops. The image is viewed by an ordinary microscope
-or special eyepiece microscope A, as the case may be,
-furnished with rack focussing at A′ and assembled with the objective
-by means of the carefully centered coupling C.</p>
-
-<p><span class="pagenum"><a name="Page_149" id="Page_149">[Pg 149]</a></span></p>
-
-<p>It furnishes a compact and powerful instrument, very suitable
-for terrestrial or minor astronomical uses, like the Tolles’ short-focus
-hand telescopes already mentioned. When properly
-designed telescopes of this sort give nearly the field of prism
-glasses, weigh much less and lose far less light for the same effective
-power and aperture. They also have under fairly high
-powers rather the advantage in the matter of definition, other
-things being equal.</p>
-
-<hr class="chap" />
-
-<p><span class="pagenum"><a name="Page_150" id="Page_150">[Pg 150]</a></span></p>
-
-
-
-
-<div class="chapter"></div>
-<h2><a name="CHAPTER_VII" id="CHAPTER_VII">CHAPTER VII</a><br />
-
-<small>HAND TELESCOPES AND BINOCULARS</small></h2>
-
-
-<p>The hand telescope finds comparatively little use in observing
-celestial bodies. It is usually quite too small for any except
-very limited applications, and cannot be given sufficient power
-without being difficult to keep steady except by the aid of a
-fixed mounting. Still, for certain work, especially the observation
-of variable stars, it finds useful purpose if sufficiently
-compact and of good light-gathering power.</p>
-
-<p>There is most decidedly a limit to the magnifying power which
-can be given to an instrument held in the hand without making
-the outfit too unsteady to be serviceable. Anything beyond 8 to
-10 diameters is highly troublesome, and requires a rudimentary
-mount or at least steadying the hand against something in order
-to observe with comfort.</p>
-
-<p>The longer the instrument the more difficult it is to manage,
-and the best results with hand telescopes are to be obtained with
-short instruments of relatively large diameter and low power.
-The ordinary field glass of Galilean type comes immediately
-to mind and in fact the field glass is and has been much used. As
-ordinarily constructed it is optically rather crude for astronomical
-purposes. The objectives are rarely well figured or accurately
-centered and a bright star usually appears as a wobbly flare
-rather than a point.</p>
-
-<p>Furthermore the field is generally small, and of quite uneven
-illumination from centre to periphery, so that great caution has
-to be exercised in judging the brightness of a star, according to its
-position in the field. The lens diameter possible with a field
-glass of ordinary construction is limited by the limited distance
-between the eyes, which must be well centered on the eyepieces
-to obtain clear vision.</p>
-
-<p>The inter-pupillary distance is generally a scant 2&frac12; inches so
-that the clear aperture of one of the objectives of a field glass is
-rarely carried up to 2 inches. The best field glasses have each
-objective a triple cemented lens, and the concave lenses also<span class="pagenum"><a name="Page_151" id="Page_151">[Pg 151]</a></span>
-triplets, the arrangement of parts being that shown in Fig. 110.
-Glasses of this sort rarely have a magnifying power above 5.</p>
-
-<p>In selecting a field glass with the idea of using it on the sky
-try it on a bright star, real or artificial, and if the image with
-careful focussing does not pull down to a pretty small and uniform
-point take no further interest in the instrument.</p>
-
-<div class="figcenter">
-<img src="images/i_151.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 110.</span>—Optical Parts of Field Glass.</div>
-</div>
-
-<p>The advantage of a binocular instrument is popularly much
-exaggerated. It gives a somewhat delusive appearance of
-brilliancy and clearness which is psychological rather than
-physical. During the late war a very careful research was made
-at the instance of the United States Government to determine
-the actual value of a binocular field glass against a monocular
-one of exactly the same type, the latter being cheaper, lighter, and
-in many respects much handier.</p>
-
-<p>The difference found in point of actual seeing all sorts of objects
-under varying conditions of illumination was so small as to be
-practically negligible. An increase of less than 5 per cent in
-magnifying power enabled one to see with the monocular instrument
-everything that could be seen with the binocular, equally
-well, and it is altogether probable that in the matter of seeing
-fine detail the difference would be even less than in general use,
-since it is not altogether easy to get the two sides of a binocular
-working together efficiently or to keep them so afterwards.</p>
-
-<p>There has been, therefore, a definite field for monocular hand
-telescopes of good quality and moderate power and such are
-manufactured by some of the best Continental makers. Such<span class="pagenum"><a name="Page_152" id="Page_152">[Pg 152]</a></span>
-instruments have sometimes been shortened by building them on
-the exact principle of the telephoto lens, which gives a relatively
-large image with a short camera extension.</p>
-
-<div class="figcenter">
-<img src="images/i_152.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 111.</span>—Steinheil Shortened Telescope.</div>
-</div>
-
-<p>A much shortened telescope, as made by Steinheil for solar
-photographic purposes, is shown in Fig. 111. This instrument
-with a total length of about 2 feet and a clear aperture of 2⅜
-inches gives a solar image of &frac12; inch diameter, corresponding to an
-ordinary glass of more than double that total length. Quite the
-same principle has been applied to terrestrial telescopes by the
-same maker, giving again an equivalent focus of about double the
-length of the whole instrument. This identical principle has
-often been used in the so-called Barlow lens, a negative lens
-placed between objective and eyepiece and giving increased
-magnification with small increase of length; also photographic
-enlargers of substantially similar function have found considerable
-use.</p>
-
-<p>A highly efficient hand telescope for astronomical purposes
-might be constructed along this line, the great shortening of the
-instrument making it possible to use somewhat higher powers
-than the ordinary without too much loss of steadiness. There is
-also constructed a binocular for strictly astronomical use consisting
-of a pair of small hand comet-seekers.</p>
-
-<p>One of these little instruments is shown in Fig. 112. It has
-a clear diameter of objectives of 1⅜ inch, magnification of 5, and
-a brilliant and even field of 7&frac12;° aperture. The objectives are
-triplets like Fig. 57, already referred to, the oculars achromatic
-doublets of the type of Fig. 104<i>a</i>.</p>
-
-<p>With the exception of these specialized astronomical field
-glasses the most useful and generally available hand instrument
-is the prism glass now in very general use. It is based on reversal
-of the image by internal total reflection in two prisms having
-their reflecting surfaces perpendicular each to the other. The<span class="pagenum"><a name="Page_153" id="Page_153">[Pg 153]</a></span>
-rudiments of the process lie in the simple reversion prism shown
-in diagram in Fig. 113.</p>
-
-<div class="figright">
-<img src="images/i_153a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 112.</span>—Astronomical
-Binocular.</div>
-</div>
-
-<p>This is nothing more nor less than a right angled glass prism
-set with its hypothenuse face parallel and with its sides at 45° to
-the optical axis of the instrument.
-Rays falling upon one of its refracting
-faces at an angle of 45° are refracted
-upon the hypothenuse face, are there
-totally reflected and emerge from the
-second face of the prism parallel to
-their original course.</p>
-
-<p>Inspection of Fig. 113 shows that
-an element like A B perpendicular to
-the plane of the hypothenuse face is
-inverted by the total reflection so that
-it takes the position A′ B′. It is
-equally clear that an element exactly
-perpendicular to A B will be reflected
-from the hypothenuse face flatwise
-as it were, and will emerge without its ends being reversed so
-that the net effect of this single reflection is to invert the image
-without reversing it laterally at the same time.</p>
-
-<p>On the other hand if a second prism be placed behind the
-first, flat upon its side, with its hypothenuse face occupying a
-plane exactly perpendicular to that of the first prism, the line
-A′B′ will be refracted, totally reflected and refracted again out of
-the prism without a second inversion, while a line perpendicular
-to A′B′ will be refracted endwise on the hypothenuse face of
-the second prism and will be
-inverted as was the line A B
-at the start.</p>
-
-<div class="figleft">
-<img src="images/i_153b.jpg" alt="" />
-<div class="caption"> <span class="smcap">Fig. 113.</span>—Reversion Prism.</div>
-</div>
-
-<p>Consequently two prisms
-thus placed will completely
-invert the image, producing
-exactly the same effect as the
-ordinary inverting system Fig. 106. The simple reversion prism
-is useful as furnishing a means, when placed over an eye lens, and
-rotated, of revolving the image on itself, a procedure occasionally
-convenient, especially in stellar photometry. The two prisms
-together constitute a true inverting system and have been utilized
-in that function, but they give a rather small angular field and<span class="pagenum"><a name="Page_154" id="Page_154">[Pg 154]</a></span>
-have never come into a material amount of use. The exact
-effect of this combination, known historically as Dove’s prisms,
-is shown plainly in Fig. 114.</p>
-
-<div class="figcenter">
-<img src="images/i_154a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 114.</span>—Dove’s Prisms.</div>
-</div>
-
-<p>The first actual prismatic inverting system was due to M.
-Porro, who invented it about the middle of the last century, and
-later brought it out commercially under the name of “Lunette à
-Napoleon Troisiéme,” as a glass for military purposes.</p>
-
-<div class="figcenter">
-<img src="images/i_154b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 115.</span>—Porro’s Prism System.</div>
-</div>
-
-<p>The prism system of this striking form of instrument is shown
-in Fig. 115. It was composed of three right angle prisms <i>A</i>, <i>B</i>,
-and <i>C</i>. <i>A</i> presented a cathetus face to the objective and <i>B</i> a
-cathetus face to the ocular. Obviously a vertical element
-brought in along <i>a</i> from the objective would be reflected at the
-hypothenuse face <i>b</i>, to a position at right angles to the original
-one, would enter the hypothenuse face of <i>C</i> and thence after
-two reflections at <i>c</i> and <i>d</i> flatwise and without change of direction
-would emerge, enter the lower cathetus face of <i>B</i> and by reflection
-at the hypothenuse face <i>e</i> of <i>B</i> would be turned another
-90° making a complete reversion as regards up and down at the
-eye placed at <i>f</i>. An element initially at right angles to the one
-just considered would enter <i>A</i>, be reflected flatwise, in the faces
-of <i>C</i> be twice reflected endwise, thereby completely inverting it,<span class="pagenum"><a name="Page_155" id="Page_155">[Pg 155]</a></span>
-and would again be reflected flatwise from the hypothenuse
-face of <i>C</i>, thereby effecting, as the path of the rays indicated
-plainly shows, a complete inversion of the image. Focussing was
-very simply attained by a screw
-motion affecting the prism <i>C</i> and
-the whole affair was in a small
-flat case, the external appearance
-and size of which is indicated in
-Fig. 116.</p>
-
-<div class="figright">
-<img src="images/i_155a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 116.</span>—Lunette à Napoleon
-Troisiéme.</div>
-</div>
-
-<p>From ocular to objective the
-length was about an inch and a
-half. It was of 10 power and took
-in a field of 45 yards at a distance
-of 1000 yards. Here for the first
-time we find a prismatic inverting
-system of strictly modern type.
-And it is interesting to note that
-if one had wished to make a
-binocular “Lunette à Napoleon
-Troisiéme” he would inevitably
-have produced an instrument with
-enhanced stereoscopic effect like
-the modern prism field glass by the mere effort to dodge the
-observer’s nose. Somewhat earlier M. Porro had arranged his
-prisms in the present conventional form of Fig. 117, where two
-right angle prisms have their faces positioned in parallel planes,
-but turned around by 90° as in Fig. 114. The ray traced through
-this conventional system shows that exactly the same inversion
-occurs here as in the original Porro construction, and this form
-is the one which has been most commonly used for prismatic
-inversion and is conveniently known as Porro’s first form, it
-actually having been antecedent in principle and practice to the<span class="pagenum"><a name="Page_156" id="Page_156">[Pg 156]</a></span>
-“Lunette à Napoleon Troisiéme.” The original published
-description of Porro’s work, translated from “Cosmos” Vol. 2,
-p. 222 (1852) et seq. is here annexed as it sets forth the origin
-of the modern prism glass in unmistakable terms.</p>
-
-<div class="figcenter">
-<img src="images/i_155b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 117.</span>—Porro’s First Form of Prisms.</div>
-</div>
-
-<p><i>Cosmos, Vol. 2</i>, p. 222.—“We have wished for some time to make
-known to our readers the precious advantages of the “longue-vue
-cornet” or télémetre of M. Porro. Ordinary spyglasses or terrestrial
-telescopes of small dimensions are at least 30 or 40 cm.
-long when extended to give distinct vision of distant objects.
-The length is considerably reduced by substituting for a fixed
-tube multiple tubes sliding into each other. But the drawing
-out which this substitution necessitates is a somewhat grave
-inconvenience; one cannot point the telescope without arranging
-it and losing time.</p>
-
-<p>For a long time we have wished it were possible to have the
-power of viewing distant objects, with telescopes very short and
-without draw. M. Porro’s “longue-vue cornet” seems to us to
-solve completely this difficult and important problem. Its construction
-rests upon an exceedingly ingenious artifice which literally
-folds triply the axis of the telescope and the luminous ray so
-that by this fact alone the length of the instrument is reduced by
-two-thirds.</p>
-
-<p>Let us try to give an idea of this construction: Behind the
-telescope objective M. Porro places a rectangular isosceles
-prism of which the hypothenuse is perpendicular to the optic
-axis. The luminous rays from the object fall upon the rectangular
-faces of this prism, are twice totally reflected, and return upon
-themselves parallel to their original direction: half way to the
-point where they would form the image of the object, they are
-arrested by a second prism entirely similar to the first, which
-returns them to their original direction and sends them to the
-eyepiece through which we observe the real image. If the rectangular
-faces of the second prism were parallel to the faces of the
-first, this real image would be inverted—the telescope would be
-an astronomical and not a terrestrial telescope. But M. Porro
-being an optician eminently dextrous, well divined that to
-effect the reinversion it sufficed to place the rectangular faces of
-the second prism perpendicular to the corresponding faces of the
-first by turning them a quarter revolution upon themselves.</p>
-
-<p>In effect, a quarter revolution of a reflecting surface is a half
-revolution for the image, and a half revolution of the image<span class="pagenum"><a name="Page_157" id="Page_157">[Pg 157]</a></span>
-evidently carries the bottom to the top and the right to the left,
-effecting a complete inversion. As the image is thus <i>redressed</i>
-independently of the eyepiece one can evidently view it with a
-simple two-lens ocular which decreases still further the length
-of the telescope so that it is finally reduced to about a quarter
-of that of a telescope of equal magnifying power, field and
-clearness.</p>
-
-<p>The new telescope is then a true pocket telescope even with
-a magnifying power of 10 or 15. Its dimensions in length and
-bulk are those of a field glass usually magnifying only 4 to 6
-times. The more draws, the more bother,—it here suffices to
-turn a little thumbscrew to find in an instant the point of
-sharpest vision.</p>
-
-<p>In brilliancy necessarily cut down a little, not by the double
-total reflection, which as is well known does not lose light, but
-by the quadruple passage across the substance of the two prisms,
-the cornet in sharpness and amplification of the images can
-compare with the best hunting telescopes of the celebrated
-optician Ploessl of Vienna. M. Porro has constructed upon the
-same principles a marine telescope only 15 c.m. long with an
-objective of 40 m.m. aperture which replaces an ordinary marine
-glass 70 c.m. long. He has done still better,—a telescope only
-30 c.m. long carries a 60 m.m. objective and can be made by turns
-a day and a night glass, by substituting by a simple movement of
-the hand and without dismounting anything, one ocular for the
-other. Its brilliancy and magnification of a dozen times with
-the night ocular, of twenty-five times with the day ocular,
-permits observing without difficulty the eclipses of the satellites
-of Jupiter.</p>
-
-<p>This is evidently immense progress. One of the most illustrious
-of German physicists, M. Dove of Berlin, gave in 1851 the
-name of reversion prism to the combination of two prisms placed
-normally one behind the other so that their corresponding faces
-were perpendicular. He presented this disposition as an important
-new discovery made by himself. He doubtless did not
-know that M. Porro, who deserves all the honor of this charming
-application, had realized it long before him.”</p>
-
-<div class="figleft">
-<img src="images/i_158a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 118.</span>—Porro’s
-Second Form.</div>
-</div>
-
-<p>A little later M. Porro produced what is commonly referred to
-as Porro’s second form, which is derived directly from annexing <i>A</i>
-Fig. 115 to the corresponding half of <i>C</i> as a single prism, the
-other half of <i>B</i> being similarly annexed to the prism <i>C</i>, thus form<span class="pagenum"><a name="Page_158" id="Page_158">[Pg 158]</a></span>ing
-two sphenoid prisms, such as are shown in Fig. 118
-which may be mounted separately or may have their faces
-cemented together to save loss of light by
-reflections. The sphenoid prisms have
-had the reputation of being much more
-difficult to construct than the plain right
-angled prisms of the other forms shown.
-In point of fact they are not particularly
-difficult to make and the best inverting
-eye pieces for telescopes are now constructed
-with sphenoid prisms like those
-just described.</p>
-
-<div class="figcenter">
-<img src="images/i_158b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 119.</span>—Clark Prismatic Eyepiece.</div>
-</div>
-
-<p>This particular arrangement lends itself very readily to a fairly
-compact and symmetrical mounting, as is well shown in Fig. 119
-which is the terrestrial prismatic eyepiece as constructed by the
-Alvan Clark corporation for application to various astronomical
-telescopes of their manufacture. A glance at the cut shows the
-compactness of the arrangement, which actually shortens the
-linear distance between objective and ocular by the amount of<span class="pagenum"><a name="Page_159" id="Page_159">[Pg 159]</a></span>
-the path of the ray through the prisms instead of lengthening the
-distance as in the common terrestrial eyepiece.</p>
-
-<p>The field moreover is much larger than that attainable by a
-construction like Fig. 110, extending to something over 40°,
-and there is no strong tendency for the illumination or definition
-to fall off near the edge of the field.</p>
-
-<p>In the practical construction of prism field glasses the two right
-angled prisms are usually separated by a moderate space as in
-Porro’s original instruments so as to shorten the actual length
-of the prism telescope by folding the ray upon itself as in Fig. 120,
-which is a typical modern binocular of this class.</p>
-
-<div class="figcenter">
-<img src="images/i_159a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 120.</span>—Section of Prism Binocular.</div>
-</div>
-
-<p>The path of the rays is plainly shown and the manner in which
-the prisms fold up the total focal length of the objective is quite
-obvious. The added stereoscopic effect obtained by the arrangement
-of the two sides of the instrument is practically a very
-material gain. It gives admirable modelling of the visible field,
-a perception of distance which is at least very noticeable and a
-certain power of penetration, as through a mass of underbrush,
-which results from the objectives to a certain extent seeing around
-small objects so that one or the other of them gives an image of
-something beyond. For near objects there is some exaggeration
-of stereoscopic effect but on the whole for terrestrial use the net
-gain is decidedly in evidence.</p>
-
-<p>A well made prism binocular is an extremely useful instrument
-for observation of the heavens, provided the objectives are of fair<span class="pagenum"><a name="Page_160" id="Page_160">[Pg 160]</a></span>
-size, and the prisms big enough to receive the whole beam from
-the objective, and well executed enough to give a thoroughly
-good image with a flat field.</p>
-
-<p>The weak points of the prism glass are great loss of light
-through reflection at the usual 10 air-glass surfaces and the
-general presence of annoying ghosts of bright objects in the
-field. Most such binoculars have Kellner eyepieces which are
-peculiarly bad, as we have seen, with respect to reflected images,
-and present the plane surface of the last prism to the plane
-front of the field lens. Recently some constructors have utilized
-the orthoscopic eyepiece, Figure 105<i>a</i>, as a substitute with great
-advantage in the matter of reflections.</p>
-
-<p>The loss of light in the prism glass is really a serious matter,
-between reflection at the surfaces and absorption in the thick
-masses of glass necessary in the prisms. If of any size the transmitted
-light is not much over one-half of that received, very
-seldom above 60%. If the instrument is properly designed the
-apparent field is in the neighborhood of 45°, substantially flat
-and fairly evenly illuminated. Warning should here be given
-however that many binoculars are on the market in which the
-field is far from flat and equally far from being uniform.</p>
-
-<p>In many instances the prisms are too small to take the whole
-bundle of rays from the objective back to the image plane without
-cutting down the marginal light considerably. Even when
-the field is apparently quite flat this fault of uneven illumination
-may exist, and in a glass for astronomical uses it is highly
-objectionable.</p>
-
-<p>Before picking out a binocular for a study of the sky make very
-careful trial of the field with respect to flatness and clean definition
-of objects up to the very edge. Then judge as accurately
-as you may of the uniformity of illumination, if possible by observation
-on two stars about the radius of the field apart. It should
-be possible to observe them in any part of the field without
-detectable change in their apparent brilliancy.</p>
-
-<p>If the objectives are easily removable unscrew one of them to
-obtain a clear idea as to the actual size of the prisms.<a name="FNanchor_19_19" id="FNanchor_19_19"></a><a href="#Footnote_19_19" class="fnanchor">[19]</a> Look out,
-too, for ghosts of bright stars.</p>
-<p><span class="pagenum"><a name="Page_161" id="Page_161">[Pg 161]</a></span></p>
-<p>The objectives of prism glasses usually run from &frac34; inch to 1&frac12;
-inch in diameter, and the powers from 6 to 12. The bigger the
-objectives the better, provided the prisms are of ample size, while
-higher power than 6 or 8 is generally unnecessary and disadvantageous.
-Occasional glasses of magnifying power 12 to 20 or
-more are to be found but such powers are inconveniently great
-for an instrument used without support. Do not forget that a
-first class monocular prism glass is extremely convenient and
-satisfactory in use, to say nothing of being considerably less in
-price than the instrument for two eyes. A monocular prism
-glass, by the way, makes an admirable finder when fitted with
-coarse cross lines in the eyepiece. It is particularly well suited
-to small telescopes without circles.</p>
-
-<div class="figcenter">
-<img src="images/i_161.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 121.</span>—Binocular with Extreme Stereoscopic Effect.</div>
-</div>
-
-<p>Numerous modifications of Porro’s inverting prisms have been
-made adapting them to different specific purposes. Of these a
-single familiar example will suffice as showing the way in which
-the Porro prism system can be treated by mere rearrangement of
-the prismatic elements. In Fig. 121 is shown a special Zeiss
-binocular capable of extreme stereoscopic effect. It is formed of
-two Porro prism telescopes with the rays brought into the objectives
-at right angles to the axis of the instrument by a right angled
-prism external to the objective.</p>
-
-<p>The apertures of these prisms appear pointing forward in the
-cut. As shown they are in a position of maximum stereoscopic
-effect.</p>
-
-<p>Being hinged the tubes can be swung up from the horizontal
-position, in which latter the objectives are separated by something
-like eight times the interocular distance. The stereoscopic
-effect with the tubes horizontal is of course greatly exaggerated
-so that it enables one to form a fair judgment as to the relative
-position of somewhat distant objects, a feature useful in locating
-shell bursts.</p>
-
-<p>The optical structure of one of the pair of telescopes is shown in
-Fig. 122 in which the course of the entering ray can be traced<span class="pagenum"><a name="Page_162" id="Page_162">[Pg 162]</a></span>
-through the exterior prism of the objective and the remainder of
-the reversing train and thence through the eyepiece. This
-prism erecting system is obviously
-derived from the “Lunette à
-Napoleon Troisiéme” by bringing
-down the prism <i>B</i> upon the corresponding
-half <i>A</i> and cementing it
-thereto, meanwhile placing the
-objective immediately under <i>A</i>.</p>
-
-<div class="figleft">
-<img src="images/i_162a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 122.</span>—Path of Ray in Fig. 121.</div>
-</div>
-
-<p>One occasionally meets prismatic
-inverting systems differing considerably
-from the Porro forms. Perhaps the best known of
-these is the so called roof prism due to Prof. Abbé, Fig. 123, and
-occasionally useful in that the entering and emerging rays lie in
-the same straight line, thus forming a direct vision system.
-Looking at it as we did at the Porro system a vertical element in
-front of the prism is reversed in reflection from the two surfaces
-a and b, while a corresponding horizontal element is reflected
-flatwise so far as these are concerned, but is turned end for end by
-reflection at the roof surfaces c and d, thus giving complete
-inversion.</p>
-
-<p>In practice the prism is made as shown, in three parts, two of
-them right angled prisms, the third containing the roof surfaces.
-The extreme precision required in figuring the roof forms a considerable
-obstacle to the production of such prisms in quantity
-and while they have found convenient use in certain special
-instruments like gunsights, where direct vision is useful, they are
-not extensively employed for general purposes, although both
-monocular and binocular instruments have been constructed
-by their aid.</p>
-
-<div class="figcenter">
-<img src="images/i_162.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 123.</span>—Abbé Roof Prism.</div>
-</div>
-
-<p>One other variety of prism involving the roof principle has
-found some application in field glasses manufactured by the firm<span class="pagenum"><a name="Page_163" id="Page_163">[Pg 163]</a></span>
-of Hensoldt. The prism form used is shown in Fig. 124. This
-like other forms of roof prism is less easy to make than the conventional
-Porro type. Numerous inverting and laterally reflecting
-prisms are in use for specific purposes. Some of them are highly
-ingenious and remarkably well adapted
-for their use, but hardly can be said to
-form a material portion of telescope
-practice. They belong rather to the
-technique of special instruments like
-gunsights and periscopes, while some of
-them have been devised chiefly as ingenious
-substitutes for the simpler Porro
-forms.</p>
-
-<p>Most prism telescopes both monocular
-and binocular are generally made
-on one or the other of the Porro forms.
-This is particularly true of the large
-binoculars which are occasionally constructed. Porro’s second
-form with the sphenoid prisms seems to be best adapted to
-cases where shortening of the instrument is not a paramount
-consideration. For example, some Zeiss short focus telescopes
-are regularly made in binocular form, and supplied with inverting
-systems composed of two sphenoid prisms, and with oculars constructed
-on the exact principle of the triple nose-piece of a
-microscope, so that three powers are immediately available
-to the observer.</p>
-
-<div class="figright">
-<img src="images/i_163.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 124.</span>—Hensoldt Prism.</div>
-</div>
-
-<p>Still less commonly binocular telescopes of considerable
-aperture are constructed, primarily for astronomical use, being
-provided with prismatic inversion for terrestrial employment,
-but more particularly in order to gain by the lateral displacement
-of a Porro system the space necessary for two objectives of
-considerable size. As we have already seen, the practical
-diameter of objectives in a binocular is limited to a trifle over
-2 inches unless space is so gained. The largest prismatic binocular
-as yet constructed is one made years ago by the Clarks, of 6&frac14;
-inches objective aperture and 92&frac14; inches focal length. So big and
-powerful an instrument obviously would give admirable binocular
-views of the heavens and so accurately was it constructed that the
-reports of its performance were exceedingly good. The same
-firm has made a good many similar binoculars of 3 inch and
-above, of which a typical example of 4 inch aperture and 60<span class="pagenum"><a name="Page_164" id="Page_164">[Pg 164]</a></span>
-inch focal length is shown in Fig. 125. In this case the erecting
-systems were of Porro’s first form, and were provided with Kellner
-oculars of very wide field. These binoculars constructions in
-instruments of such size, however well made and agreeable for
-terrestrial observation, hardly justify the expense for purely
-astronomical use.</p>
-
-<div class="figcenter">
-<img src="images/i_164.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 125.</span>—Clark 4″ Binocular Telescope.</div>
-</div>
-
-<hr class="chap" />
-
-<p><span class="pagenum"><a name="Page_165" id="Page_165">[Pg 165]</a></span></p>
-
-
-
-
-<div class="chapter"></div>
-<h2><a name="CHAPTER_VIII" id="CHAPTER_VIII">CHAPTER VIII</a><br />
-
-<small>ACCESSORIES</small></h2>
-
-
-<p>Aside from the ordinary equipment of oculars various accessories
-form an important part of the observer’s equipment, their
-number and character depending on the instrument in use and
-the purposes to which it is devoted.</p>
-
-<div class="figcenter">
-<img src="images/i_165.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 126.</span>—Star Diagonal.</div>
-</div>
-
-<p>First in general usefulness are several special forms of eyepiece
-equipment supplementary to the usual oculars. At the head of
-the list is the ordinary star diagonal for the easier viewing of
-objects near the zenith here shown in Fig. 126. It is merely a
-tube, <i>A</i>, fitting the draw tube of the telescope, with a slotted side
-tube <i>B</i>, at a right angle, into which the ordinary ocular fits, and a
-right angled prism <i>C</i> with its two faces perpendicular respectively
-to the axes of the main and side tubes, and the hypothenuse face
-at 45° to each. The beam coming down the tube is totally
-reflected at this face and brought to focus at the ocular. The
-lower end of the tube is closed by a cap to exclude dust.</p>
-
-<p>One looks, by help of this, horizontally at zenith stars, or, if
-observing objects at rather high altitude, views them at a
-comfortable angle downward. The prism must be very accu<span class="pagenum"><a name="Page_166" id="Page_166">[Pg 166]</a></span>rately
-made to avoid injury to the definition, but loses only
-about 10% of the light, and adds greatly to the comfort of
-observing.</p>
-
-<p>Of almost equal importance is the solar diagonal devised by
-Sir John Herschel, Fig. 127. Here the tube structure <i>A</i>, <i>B</i>, is
-quite the same as in Fig. 126 but the right angled prism is
-replaced by a simple elliptical prism <i>C</i> of small angle, 10° or less,
-with its upper face accurately plane and at 45° to the axes of the
-tubes, resting on a lining tube <i>D</i> cut off as shown. In viewing
-the sun only about 5% of the light (and heat) is reflected at
-this upper surface to form the image at the eye piece.</p>
-
-<div class="figcenter">
-<img src="images/i_166.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 127.</span>—Solar Diagonal.</div>
-</div>
-
-<p>Any reflection from the lower polished surface is turned aside
-out of the field, while the remainder of the radiation passes
-through the prism <i>C</i> and is concentrated below it. To prevent
-scorching the observer the lower end of the tube is capped at <i>E</i>,
-but the cap has side perforations to provide circulation for the
-heated air. Using such a prism, the remnant of light reflected
-can be readily toned down by a neutral tinted glass over the
-ocular.</p>
-
-<p>In the telescopes of 3 inches and less aperture, and ordinary focal
-ratio, a plane parallel disc of very dark glass over the ocular gives
-sufficient protection to the eye. This glass is preferably of
-neutral tint, and commonly is a scant 1/16 inch thick. Some
-observers prefer other tints than neutral. A green and a red glass
-superimposed give good results and so does a disc of the deepest
-shade of the so-called Noviweld glass, which is similar in effect.</p>
-
-<p>With an aperture as large as 3 inches a pair of superimposed dark<span class="pagenum"><a name="Page_167" id="Page_167">[Pg 167]</a></span>
-glasses is worth while, for the two will not break simultaneously
-from the heat and there will be time to get the eye away in
-safety. A broken sunshade is likely to cost the observer a
-permanent scotoma, blindness in a small area of the retina which
-will neither get better nor worse as time goes on.</p>
-
-<div class="figright">
-<img src="images/i_167.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 128.</span>—Diagram of Polarizing
-Eyepiece.</div>
-</div>
-
-<p>Above 3 inches aperture the solar prism should be used or, if one
-cares to go to fully double the cost, there is nothing more comfortable
-to employ in solar observation
-than the polarizing eye piece,
-Fig. 128. This shows schematically
-the arrangement of the device. It
-depends on the fact that a ray of light
-falling on a surface of common glass
-at an angle of incidence of approximately
-57° is polarized by the reflection
-so that while it is freely reflected
-if it falls again on a surface parallel to
-the first, it is absorbed if it falls at the
-same incidence on a surface at right
-angles to the first.</p>
-
-<p>Thus in Fig. 128 the incident beam
-from the telescope falls on the black
-glass surface <i>a</i> at 57° incidence, is
-again reflected from the parallel mirror
-<i>b</i>, and then passed on, parallel to its
-original path, to the lower pair of
-mirrors <i>c</i>, <i>d</i>. The purpose of the second reflection is to polarize
-the residual light which through the convergence of the rays
-was incompletely polarized at the first.</p>
-
-<p>The lower pair of mirrors <i>c</i>, <i>d</i>, again twice reflect the light at the
-polarizing angle, and, in the position shown, pass it on to the
-ocular diminished only by the four reflections. But if the second
-pair of mirrors be rotated together about a line parallel to <i>b c</i> as an
-axis the transmitted light begins to fade out, and when they have
-been turned 90°, so that their planes are inclined 90° to <i>a</i> and <i>b</i>
-(= 33° to the plane of the paper), the light is substantially
-extinguished.</p>
-
-<p>Thus by merely turning the second pair of mirrors the solar
-image can be reduced in brilliancy to any extent whatever,
-without modifying its color in any way. The typical form given
-to the polarizing eyepiece is similar to Fig. 129. Here <i>t</i>_2 is the<span class="pagenum"><a name="Page_168" id="Page_168">[Pg 168]</a></span>
-box containing the polarizing mirrors, <i>a b</i>, fitted to the draw
-tube, but for obvious reasons eccentric with it, <i>t</i>_1 is the rotating
-box containing the “analysing” mirrors <i>c</i>, <i>d</i>, and <i>a</i> is the ocular
-turning with it.</p>
-
-<p>Sometimes the polarizing mirrors are actually a pair of Herschel
-prisms as in Fig. 126, facing each other, thus getting rid of much
-of the heat. Otherwise the whole set of mirrors is of black glass
-to avoid back reflections. In simpler constructions single mirrors
-are used as polarizer and analyser, and in fact there are many
-variations on the polarizing solar eyepiece involving about the
-same principles.</p>
-
-<div class="figcenter">
-<img src="images/i_168.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 129.</span>—Polarizing Solar Eyepiece.</div>
-</div>
-
-<p>In any solar eyepiece a set of small diaphragms with holes
-from perhaps 1/64 inch up are useful in cutting down the general
-glare from the surface outside of that under scrutiny. These
-may be dropped upon the regular diaphragm of the ocular or
-conveniently arranged in a revolving diaphragm like that used
-with the older photographic lenses.</p>
-
-<p>The measurement of celestial objects has developed a large
-group of important auxiliaries in the micrometers of very varied
-forms. The simplest needs little description, since it consists
-merely of a plane parallel disc of glass fitting in the focus of a
-positive ocular, and etched with a network of uniform squares,<span class="pagenum"><a name="Page_169" id="Page_169">[Pg 169]</a></span>
-forming a reticulated micrometer by which the distance of
-one object from another can be estimated.</p>
-
-<p>It can be readily calibrated by measuring a known distance
-or noting the time required for an equatorial star to drift across
-the squares parallel to one set of lines. It gives merely a useful
-approximation, and accurate measures must be turned over to
-more precise instruments.</p>
-
-<div class="figcenter">
-<img src="images/i_169.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 130.</span>—Diagram of Ring Micrometer.</div>
-</div>
-
-<p>The ring micrometer due, like so much other valuable apparatus,
-to Fraunhofer, is convenient and widely used for determining
-positions. It consists, as shown in Fig. 130, of an accurately
-turned opaque ring, generally of thin steel, cemented to a plane
-parallel glass or otherwise suspended in the center of the eyepiece
-field. The whole ring is generally half to two thirds the width of
-the field and has a moderate radial width so that both the ingress
-and the egress of a star can be conveniently timed.</p>
-
-<p>It depends wholly on the measurement of time as the stars
-to be compared drift across the ring while the telescope is fixed,
-and while a clock or chronometer operating a sounder is a
-desirable adjunct one can do pretty well with a couple of stop
-watches since only differential times are required.</p>
-
-<p>For full directions as to its use consult Loomis’ Practical
-Astronomy, a book which should be in the library of every one
-who has the least interest in celestial observations. Suffice it to<span class="pagenum"><a name="Page_170" id="Page_170">[Pg 170]</a></span>
-say here that the ring micrometer is very simple in use, and the
-computation of the results is quite easy. In Fig. 130 F is the
-edge of the field, R the ring, and <i>a b</i>, <i>a′b′</i>, the paths of the stars
-<i>s</i> and <i>s′</i>, the former well into the field, the latter just within the
-ring. The necessary data comprise the time taken by each star
-to transverse the ring, and the radius of the ring in angular
-measure, whence the difference in R. A. or Dec, can be obtained.<a name="FNanchor_20_20" id="FNanchor_20_20"></a><a href="#Footnote_20_20" class="fnanchor">[20]</a></p>
-
-<p>Difference of R. A. = &frac12; (t′-t)&frac12; (T′-T) where (T′-T)
-is the time taken for transit of second star. To obtain
-differences of declination one declination should be known at
-least approximately, and the second estimated from its relative
-position in the ring or otherwise. Then with these tentative
-values proceed as follows.</p>
-
-<div class="figcenter">
-<img src="images/i_170.jpg" alt="" />
-<div class="caption">
-<span class="smcap">Fig. 131.</span>—Double Image Micrometer. (<i>Courtesy of The Clarendon Press.</i>)</div>
-</div>
-
-<p>
-Put x = angle <i>aob</i> and <i>x</i>′ = angle <i>a′o′b′</i><br />
-<br />
-Also let d  = approximate declination of <i>s</i> and<br />
-<span style="margin-left: 4em;">d′ = approximate declination of <i>s′</i></span><br />
-</p>
-
-<p>Then sin x = (15/2r) cos d (T′-T)</p>
-
-<p><span style="margin-left: 2.4em;">sin x′ = (15/2r) cos d′ (t′-t) and finally</span><br /><span class="pagenum"><a name="Page_171" id="Page_171">[Pg 171]</a></span>
-Difference of Dec. = r (cos x′-cos x), when both arcs are on
-the same side of center of ring. If on opposite sides, Diff. = r
-(cos x′ + cos x).</p>
-
-<p>There is also now and then used a square bar micrometer,
-consisting of an opaque square set with a diagonal in the line of
-diurnal motion. It is used in much the same way as the ring,
-and the reductions are substantially the same. It has some
-points of convenience but is little used, probably on account of
-the great difficulty of accurate construction and the requirement,
-for advantageous use, that the telescope should be on a well
-adjusted equatorial stand.<a name="FNanchor_21_21" id="FNanchor_21_21"></a><a href="#Footnote_21_21" class="fnanchor">[21]</a> The ring micrometer works reasonably
-well on any kind of steady mount, requires no illumination
-of the field and is in permanent working adjustment.</p>
-
-<p>Still another type of micrometer capable of use without a
-clock-drive is the double image instrument. In its usual form
-it is based on the principle that if a lens is cut in two along a
-diameter and the halves are slightly displaced along the cut all
-objects will be seen double, each half of the lens forming its
-own set of images.</p>
-
-<p>Conversely, if one choses two objects in the united field these
-can be brought together by sliding the halves of the lens as before,
-and the extent of the movement needed measures the distance
-between them. Any lens in the optical system can be thus used,
-from the objective to the eyepiece. Fig. 131 shows a very
-simple double image micrometer devised by Browning many
-years ago. Here the lens divided is a so-called Barlow lens, a
-weak achromatic negative lens sometimes used like a telephoto
-lens to lengthen the focus and hence vary the power of a telescope.</p>
-
-<p>This lens is shown at A with the halves widely separated by the
-double threaded micrometer screw B, which carries them apart
-symmetrically. The ocular proper is shown at C.</p>
-
-<p>Double image micrometers are now mainly of historical
-interest, and the principle survives chiefly in the heliometer, a
-telescope with the objective divided, and provided with sliding
-mechanism of the highest refinement. The special function of
-the heliometer is the direct micrometric measurement of stellar
-distances too great to be within the practicable range of a filar
-micrometer—distances for example up to 1&frac12;° or even more.</p>
-
-<p>The observations with the heliometer are somewhat laborious<span class="pagenum"><a name="Page_172" id="Page_172">[Pg 172]</a></span>
-and demand rather intricate corrections, but are capable of great
-precision. (See Sir David Gill’s article “Heliometer” in the
-Enc. Brit. 11th Ed.). At the present day celestial photography,
-with micrometric measurement of the resulting plates, has gone
-far in rendering needless visual measurements of distances
-above a very few minutes of arc, so that it is somewhat doubtful
-whether a large heliometer would again be constructed.</p>
-
-<div class="figcenter">
-<img src="images/i_172.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 132.</span>—Filar Micrometer. (<i>Courtesy of J. B. Lippincott Co.</i>)</div>
-</div>
-
-<p>The astronomer’s real arm of precision is the filar micrometer.
-This is shown in outline in Fig. 132, the ocular and the plate that
-carries it being removed so as to display the working parts. It
-consists of a main frame aa, carrying a slide bb, which is moved
-by the screws and milled head B. The slide bb carries the vertical
-spider line mm, and usually one or more horizontal spider lines,
-line mm is the so-called fixed thread of the micrometer, movable
-only as a convenience to avoid shifting the telescope.</p>
-
-<p>On bb moves the micrometer slide cc, carrying the movable
-spider line nn and the comb which records, with mm as reference
-line, the whole revolutions of the micrometer screw C. The
-ocular sometimes has a sliding motion of its own on cc, to get it
-positioned to the best advantage. In use one star is set upon
-mm by the screw B and then C is turned until nn bisects the
-other star.</p>
-
-<p>Then the exact turns and fraction of a turn can be read off
-on the comb and divided head of C, and reduced to angular
-measure by the known constant of the micrometer, usually
-determined by the time of passage of a nearly equatorial star
-along the horizontal thread when mm, nn, are at a definite setting</p>
-
-<p>apart. (Then r = (15(t′-t) cos d)/N where r is the value of a
-revolution in seconds of arc, N the revolutions apart of mm, nn,
-and t and d as heretofore.)</p>
-
-<p><span class="pagenum"><a name="Page_173" id="Page_173">[Pg 173]</a></span></p>
-
-<p>Very generally the whole system of slides is fitted to a
-graduated circle, to which the fixed horizontal thread is diametral.
-Then by turning the micrometer until the horizontal threads cut
-the two objects under comparison, their position angle with
-reference to a graduated circle can be read off. This angle is
-conventionally counted from 0° to 360° from north around
-through east.</p>
-
-<div class="figcenter">
-<img src="images/i_173.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 133.</span>—Filar Position Micrometer.</div>
-</div>
-
-<p>Figure 133 shows the micrometer constructed by the Clarks for
-their 24 inch equatorial of the Lowell Observatory. Here A is the
-head of the main micrometer screw of which the whole turns are
-reckoned on the counter H in lieu of the comb of Fig. 132. B is
-the traversing screw for the fixed wire system, C the clamping
-screw of the position circle, D its setting pinion, E the rack
-motion for shifting the ocular, F the reading glass for the position
-circle, and G the little electric lamp for bright wire illumination.
-The parts correspond quite exactly with the diagram of Fig. 132
-but the instrument is far more elegant in design than the earlier
-forms of micrometer and fortunately rid of the oil lamps that were
-once in general use. A small electric lamp with reflector throws
-a little light on the spider lines—just enough to show them distinctly.
-Or sometimes a faint light is thus diffused in the
-field against which the spider lines show dark.</p>
-
-<p>Commonly either type of illumination can be used and modified
-as occasion requires. The filar micrometer is seldom used<span class="pagenum"><a name="Page_174" id="Page_174">[Pg 174]</a></span>
-on small telescopes, since to work easily with it the instrument
-should be permanently mounted and clock-driven. Good work
-was done by some of the early observers without these aids, but
-at the cost of infinite pains and much loss of time.</p>
-
-<p>The clock drive is in fact a most important adjunct of the
-telescope when used for other purposes than ordinary visual
-observations, though for simple seeing a smooth working slow
-motion in R. A. answers well. The driving clock from the horological
-view-point is rudimentary. It consists essentially of a
-weight-driven, or sometimes spring-driven, drum, turning by a
-simple gear connection a worm which engages a carefully cut
-gear wheel on the polar axis, while prevented from running
-away by gearing up to a fast running fly-ball governor, which
-applies friction to hold the clockwork down to its rate if the speed
-rises by a minute amount. There is no pendulum in the ordinary
-sense, the regularity depending on the uniformity of the total
-friction—that due to the drive plus that applied by the governor.</p>
-
-<p>Figure 134 shows a simple and entirely typical driving clock
-by Warner &amp; Swasey. Here A is the main drum with its winding
-gear at B, C is the bevel gear, which is driven from another
-carried by A, and serves to turn the worm shaft D; E marks
-the fly balls driven by the multiplying gearing plainly visible.
-The governor acts at a predetermined rotation speed to lift the
-spinning friction disc F against its fixed mate, which can be
-adjusted by the screw G.</p>
-
-<p>The fly-balls can be slightly shifted in effective position to
-complete the regulation. These simple clocks, of which there are
-many species differing mainly in the details of the friction device,
-are capable of excellent precision if the work of driving the telescope
-is kept light.</p>
-
-<p>For large and heavy instruments, particularly if used for photographic
-work where great precision is required, it is difficult to
-keep the variations of the driving friction within the range of
-compensation furnished by the governor friction alone, and in
-such case recourse is often taken to constructions in which the
-fly balls act as relay to an electrically controlled brake, or in
-which the driving power is supplied by an electric motor suitably
-governed either continuously or periodically. For such work
-independent hand guiding mechanism is provided to supplement
-the clockwork. For equatorials of the smallest sizes, say 3 to 4
-inches aperture, spring operated driving clocks are occasionally<span class="pagenum"><a name="Page_175" id="Page_175">[Pg 175]</a></span>
-used. The general plan of operation is quite similar to the
-common weight driven forms, and where the weights to be
-carried are not excessive such clocks do good work and serve a
-very useful purpose.</p>
-
-<div class="figcenter">
-<img src="images/i_175.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 134.</span>—Typical Driving Clock. (<i>Courtesy of The Clarendon Press.</i>)</div>
-</div>
-
-<p>An excellent type of the simple spring driving clock is shown in
-Fig. 136 as constructed by Zeiss. Here 1 is the winding gear,
-2 the friction governor, and 3 the regulating gear. It will be seen
-that the friction studs are carried by the fly balls themselves,
-somewhat as in Fraunhofers’ construction a century since, and
-the regulation is very easily and quickly made by adjusting the
-height of the conical friction surface above the balls.</p>
-
-<p>For heavier work the same makers generally use a powerful
-weight driven train with four fly-balls and electric seconds control,
-sometimes with the addition of electric motor slow motions to
-adjust for R. A. in both directions.</p>
-
-<p><span class="pagenum"><a name="Page_176" id="Page_176">[Pg 176]</a></span></p>
-
-<div class="figcenter">
-<img src="images/i_176.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 135.</span>—Clark Driving Clock.</div>
-</div>
-
-<p>Figure 135 is a rather powerful clock of analogous form by
-the Clarks. It differs a little in its mechanism and especially
-in the friction gear in which the bearing disc is picked up by
-a delicately set latch and carried just long enough to effect
-the regulation. It is really remarkable that clockworks of so
-simple character as these should perform as well as experience
-shows that they do. In a few instances clocks have depended
-on air-fans for their regulating force, something after the manner
-of the driving gear of a phonograph, but though rather successful
-for light work they have found little favor in the task of
-driving equatorials. An excellent type of a second genus is the<span class="pagenum"><a name="Page_177" id="Page_177">[Pg 177]</a></span>
-pendulum controlled driving clock due to Sir David Gill. This
-has a powerful weight-driven train with the usual fly-ball governor.
-But the friction gear is controlled by a contact-making
-seconds pendulum in the manner shown diagrammatically in
-Fig. 137. Two light leather tipped rods each controlled by an
-electro magnet act upon an auxiliary brake disc carried by the
-governor spindle which is set for normal speed with one brake
-rod bearing lightly on it. Exciting the corresponding magnet
-relieves the pressure and accelerates the clock, while exciting the
-other adds braking effect and slows it.</p>
-
-<div class="figcenter">
-<img src="images/i_177.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 136.</span>—Spring Operated Driving Clock.</div>
-</div>
-
-<p>In Fig. 137 is shown from the original paper, (M. N. Nov.,
-1873), the very ingenious selective control mechanism. At P
-is suspended the contact-making seconds-pendulum making
-momentary contact by the pin Q with a mercury globule at R.
-Upon a spindle of the clock which turns once a second is fixed a
-vulcanite disc γ, δ, ε, σ. This has a rim of silver broken at the
-points γ, δ, ε, σ, by ivory spacers covering 3° of circumference.
-On each side of this disc is another, smaller, and with a complete
-silver rim. One, ηθ, is shown, connected with the contact
-spring V; its mate η′θ′, on the other side contacts with U, while
-a third contact K bears on the larger disc.</p>
-
-<p>The pair of segments σ, γ, and δ, ε, are connected to η θ, the
-other pair of segments to η′ θ′. Now suppose the discs turning
-with the arrows: If K rests on one of the insulated points when
-the pendulum throws the battery C Z into circuit nothing happens.
-If the disc is gaining on the pendulum, K, instead of resting on<span class="pagenum"><a name="Page_178" id="Page_178">[Pg 178]</a></span>
-γ as shown will contact with segment γ, σ, and actuate a relay
-via V, exciting the appropriate brake magnet.</p>
-
-<div class="figcenter">
-<img src="images/i_178.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 137.</span>—Sir David Gill’s Electric Control.</div>
-</div>
-
-<p>If the disc is losing, K contacts with segment γ, δ, and current
-will pass via η′θ′ and U to a relay that operates the other
-brake magnet and lets the clock accelerate. A fourth disc
-(not shown) on the same spindle is entirely insulated on its
-edge except at points corresponding to γ and ε, and with a
-contact spring like K.</p>
-
-<p>If the disc is neither gaining nor losing when the pendulum
-makes contact, current flows via this fourth disc and sets the<span class="pagenum"><a name="Page_179" id="Page_179">[Pg 179]</a></span>
-relay on the mid-point ready to act when needed. This clock
-is the prototype of divers electrically-braked driving clocks with
-pendulum control, and proved beautifully precise in action, like
-various kindred devices constructed since, though the whole
-genus is somewhat expensive and intricate.</p>
-
-<p>The modern tendency in driving apparatus for telescopes,
-particularly large instruments, is to utilize an electric motor for
-the source of power, using a clock mechanism merely for the
-purpose of accurately regulating the rate of the motor. We thus
-have the driving clock in its simplest form as a purely mechanical
-device worked by a sensitive fly-ball governor. The next
-important type is that in which the clock drive is precisely
-regulated by a pendulum clock, the necessary governing
-power being applied electrically as in Fig. 137 or sometimes
-mechanically.</p>
-
-<p>Finally we come to the type now under consideration where
-the instrument itself is motor driven and the function of the
-clock is that of regulating the motor. A very good example of
-such a drive is the Gerrish apparatus used for practically all the
-instruments at the various Harvard observatory stations, and
-which has proved extremely successful even for the most trying
-work of celestial photography. The schematic arrangement of
-the apparatus is shown in Fig. 138. Here an electric motor
-shown in diagram in 1, Fig. 138, is geared down to approximately
-the proper speed for turning the right ascension axis of the
-telescope. It is supplied with current either from a battery or
-in practice from the electric supply which may be at hand.
-This motor is operated on a 110 volt circuit which supplies
-current through the switch 2 which is controlled by the low
-voltage clock circuit running through the magnet 3. The
-clock circuit can be closed and opened at two points, one controlled
-by the seconds pendulum 5, the other at 7 by the stud
-on the timing wheel geared to the motor for one revolution
-per second. There is also a shunt around the pendulum break,
-closed by the magnet switch at 6. This switch is mechanically
-connected to the switch 2 by the rod 4, so that the pair open and
-close together.</p>
-
-<p>The control operates as follows: Starting with the motor at
-rest, the clock circuit is switched on, switches 2, 6 being open
-and 7 closed. At the first beat of the pendulum 2, 6 closes and
-the current, shunted across the loop containing 5, holds 2<span class="pagenum"><a name="Page_180" id="Page_180">[Pg 180]</a></span>
-closed until the motor has started and broken the clock circuit
-at the timer. The fly-wheel carries on until the pendulum
-again closes the power circuit via 2, 6, and current stays on the
-motor until the timer has completed its revolution.</p>
-
-<p>This goes on as the motor speeds up, the periodic power supply
-being shortened as the timer breaks it earlier owing to the acceleration,
-until the motor comes to its steady speed at which the
-power is applied just long enough to maintain uniformity. If
-the motor for any cause tends to overspeed the cut-off is earlier,
-while slowing down produces a longer power-period bringing the
-speed back to normal. The power period is generally &frac14; to &frac12;
-second. The power supplied to the motor is very small even in
-the example here shown, only 1 ampere at 110 volts.</p>
-
-<div class="figcenter">
-<img src="images/i_180.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 138.</span>—Diagram of Gerrish Electric Control.</div>
-</div>
-
-<p>The actual proportion of a revolution during which current is
-supplied the motor is therefore rigorously determined by the
-clock pendulum, and the motor is selected so that its revolutions
-are exactly timed to this clock pendulum which has no work to
-do other than the circuit closing, and can hence be regulated to
-keep accurate time. The small fly-wheel (9), the weight of which
-is carefully adjusted with respect to the general amount of work
-to be done, attached to the motor shaft, effectively steadies its
-action during the process of government. This Gerrish type
-has been variously modified in detail to suit the instruments to
-which it has been applied, always following however the same
-fundamental principles.</p>
-
-<p><span class="pagenum"><a name="Page_181" id="Page_181">[Pg 181]</a></span></p>
-
-<div class="figcenter">
-<img src="images/i_181.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 139.</span>—Gerrish Drive on 24 inch Reflector.</div>
-</div>
-
-<p>An admirable example of the application of this drive is
-shown in Fig. 139, the 24 inch reflector at the Harvard Observatory.
-The mount is a massive open fork, and the motor drive
-is seen on the right of the mount. There are here two motors,
-ordinary fan motors in size. The right hand motor carries the
-fly-wheel and runs steadily on under the pendulum control. The
-other, connected to the same differential gear as the driving<span class="pagenum"><a name="Page_182" id="Page_182">[Pg 182]</a></span>
-motor, serves merely for independent regulation and can be run
-in either direction by the observer to speed or slow the motion in
-R. A. These examples of clock drive are merely typical of those
-which have proved to be successful in use for various service, light
-and heavy. There are almost innumerable variations on clocks
-constructed on one or another of the general lines here indicated,
-so many variations in fact that one almost might say there are
-few driving clocks which are not in some degree special.</p>
-
-<p>The tendency at present is for large instruments very distinctly
-toward a motor-driven mechanism operating on the right
-ascension axis, and governed in one of a considerable variety of
-ways by an actual clock pendulum. For smaller instruments the
-old mechanical clock, often fitted with electric brake gear and
-now and then pendulum regulated, is capable of very excellent
-work.</p>
-
-<p>The principle of the spectroscope is rudimentarily simple, in
-the familiar decomposition of white light into rainbow colors by
-a prism. One gets the phenomena neatly by holding a narrow
-slit in a large piece of cardboard at arms length and looking at it
-through a prism held with its edge parallel to the slit. If the
-light were not white but of a mixture of definite colors each color
-present would be represented by a separate image of the slit
-instead of the images being merged into a continuous colored
-band.</p>
-
-<p>With the sun as source the continuous spectrum is crossed by
-the dark lines first mapped by Fraunhofer, each representing
-the absorption by a relatively cool exterior layer of some substance
-that at a higher temperature below gives a bright line in
-exactly the same position.</p>
-
-<p>The actual construction of the astronomical spectroscope
-varies greatly according to its use. In observations on the sun
-the distant slit is brought nearer for convenience by placing it in
-the focus of a small objective pointed toward the prisms (the
-collimator) and the spectrum is viewed by a telescope of moderate
-magnifying power to disclose more of detail. Also, since there is
-extremely bright light available, very great dispersion can be used,
-obtained by several or many prisms, so that the spectrum is
-both fairly wide, (the length of the slit) and extremely long.</p>
-
-<p>In trying to get the spectrum of a star the source is a point,
-equivalent to an extremely minute length of a very narrow slit.
-Therefore no actual slit is necessary and the chief trouble is to<span class="pagenum"><a name="Page_183" id="Page_183">[Pg 183]</a></span>
-get the spectrum wide enough and bright enough to examine.</p>
-
-<p>The simplest form of stellar spectroscope and the one in most
-common use with small telescopes is the ocular spectroscope
-arranged much like Fig. 140. This fits into the eye tube of a
-telescope and the McClean form made by Browning of London
-consists of an ordinary casing with screw collar <i>B</i>, a cylindrical
-lens <i>C</i>, a direct vision prism <i>c</i>, <i>f</i>, <i>c</i>, and an eye-cap <i>A</i>.</p>
-
-<p>The draw tube is focussed on the star image as with any other
-ocular, and the light is delivered
-through <i>C</i> to the prism
-face nearly parallel, and
-thence goes to the eye, after
-dispersion by the prism. This
-consists of a central prism, <i>f</i>,
-of large angle, made of extremely
-dense flint, to which
-are cemented a pair of prisms
-of light crown <i>c</i>, <i>c</i>, with their
-bases turned away from that
-of <i>f</i>.</p>
-
-<div class="figright">
-<img src="images/i_183.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig.</span> 140.—McClean Ocular
- Spectroscope.</div>
-</div>
-
-<p>We have already seen that the dispersions of glasses vary very
-much more than their refractions so that with proper choice of
-materials and angles the refraction of <i>f</i> is entirely compensated
-for some chosen part of the spectrum, while its dispersion quite
-overpowers that of the crown prisms and gives a fairly long
-available spectrum.</p>
-
-<p>The cylindrical lens <i>C</i> merely serves to stretch out the tiny
-round star image into a short line thereby giving the resulting
-spectrum width enough to examine comfortably. The weak
-cylindrical lens is sometimes slipped over the eye end of the
-prisms to give the needed width of spectrum instead of putting it
-ahead of the prisms.</p>
-
-<p>A small instrument of this kind used with a telescope of 3
-inches to 5 inches aperture gives a fairly good view of the spectra
-of starts above second or third magnitude, the qualities of tolerably
-bright comets and nebulæ and so forth. The visibility of
-stellar spectra varies greatly according to their type, those with
-heavy broad bands being easy to observe, while for the same
-stellar magnitude spectra with many fine lines may be quite
-beyond examination. Nevertheless a little ocular spectroscope
-enables one to see many things well worth the trouble of observing.</p>
-
-<p><span class="pagenum"><a name="Page_184" id="Page_184">[Pg 184]</a></span></p>
-
-<p>With the larger instruments, say 6 or 8 inches, one can well take
-advantage of the greater light to use a spectroscope with a slit,
-which gives somewhat sharper definition and also an opportunity
-to measure the spectrum produced.</p>
-
-<p>An excellent type of such an instrument is that shown in Fig.
-141, due to Professor Abbé. The construction is analogous to
-Fig. 140. The ocular is a Huyghenian one with the slit mechanism
-(controlled by a milled head) at A in the usual place of the
-diaphragm. The slit is therefore
-in the focus of the eye lens,
-which serves as collimating lens.
-Above is the direct vision system
-J with the usual prisms which
-are slightly adjustable laterally
-by the screw P and spring Q.</p>
-
-<div class="figleft">
-<img src="images/i_184.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 141.</span>—Abbé Ocular Spectroscope.</div>
-</div>
-
-<p>At N is a tiny transparent
-scale of wave lengths illuminated
-by a faint light reflected from
-the mirror O, and in the focus of
-the little lens R, which transfers
-it by reflection from the front
-face of the prism to the eye,
-alongside the edge of the spectrum.
-One therefore sees the
-spectrum marked off by a bright
-line wave-length scale.</p>
-
-<p>The pivot K and clamp L enable the whole to be swung side-wise
-so that one can look through the widened slit, locate the
-star, close the slit accurately upon it and swing on the prisms.
-M is the clamp in position angle. Sometimes a comparison
-prism is added, together with suitable means for throwing in
-spectra of gases or metals alongside that of the star, though these
-refinements are more generally reserved for instruments of
-higher dispersion.</p>
-
-<p>To win the advantage of accurate centering of the star in the
-field gained by the swing-out of the spectroscope in Fig. 141
-simple instruments like Fig. 140 are sometimes mounted with
-an ordinary ocular in a double nose-piece like that used for
-microscope objectives, so that either can be used at will.</p>
-
-<p>Any ordinary pocket spectroscope, with or without scale or a
-comparison prism over part of the slit, can in fact be fitted to an<span class="pagenum"><a name="Page_185" id="Page_185">[Pg 185]</a></span>
-adapter and used with the star focussed on the slit and a cylindrical
-lens, if necessary, as an eye-cap.</p>
-
-<p>Such slit spectroscopes readily give the characteristics of
-stellar spectra and those of the brighter nebulæ or of comets.
-They enable one to identify the more typical lines and compare
-them with terrestrial sources, and save for solar work are about
-all the amateur observer finds use for.</p>
-
-<p>For serious research a good deal more of an instrument is
-required, with a large telescope to collect the light, and means for
-photographing the spectra for permanent record. The cumulative
-effect of prolonged exposures makes it possible easily to
-record spectra much too faint to see with the same aperture, and
-exposures are often extended to many hours.</p>
-
-<p>Spectroscopes for such use commonly employ dense flint prisms
-of about 60° refracting angle and refractive index of about 1.65,
-one, two, or three of these being fitted to the instrument as
-occasion requires. A fine example by Brashear is shown in Fig.
-142, arranged for visual work on the 24 inch Lowell refractor.
-Here A is the slit, B the prism box, C the observing telescope, D
-the micrometer ocular with electric lamp for illuminating the
-wires, and E the link motion that keeps the prism faces at equal
-angles with collimator and observing telescope when the angle
-between these is changed to observe different parts of the spectrum.
-This precaution is necessary to maintain the best of
-definition.</p>
-
-<p>When photographs are to be taken the observing telescope is
-unscrewed and a photographic lens and camera put in its place.
-If the brightness of the object permits, three prisms are installed,
-turning the beam 180° into a camera braced to the same frame
-alongside the slit.</p>
-
-<p>For purely photographic work, too, the objective prism used
-by Fraunhofer for the earliest observation of stellar spectra is in
-wide use. It is a prism fitted in front of the objective with its
-refracting faces making equal angles with the telescope and the
-region to be observed, respectively. Its great advantages are
-small loss of light and the ability to photograph many spectra at
-once, for all the stars in the clear field of the instrument leave
-their images spread out into spectra upon the photographic
-plate.</p>
-
-<p>Figure 143 shows such an objective prism mounted in front of
-an astrographic objective. The prism is rotatable into any<span class="pagenum"><a name="Page_186" id="Page_186">[Pg 186]</a></span>
-azimuth about the axis of the objective and by the scale i and
-clamping screw r can have its refracting face adjusted with
-respect to that axis to the best position for photographing any
-part of the spectrum. Such an arrangement is typical of those
-used for small instruments say from 3 inches to 6 inches aperture.</p>
-
-<div class="figcenter">
-<img src="images/i_186.jpg" alt="" />
-<div class="caption"> <span class="smcap">Fig. 142.</span>—Typical Stellar Spectroscope.</div>
-</div>
-
-<p><span class="pagenum"><a name="Page_187" id="Page_187">[Pg 187]</a></span></p>
-
-<p>For larger objectives the prism is usually of decidedly smaller
-angle, and, if the light warrants high dispersion, several prisms
-in tandem are used. The objective prism does its best work when
-applied to true photographic objectives of the portrait lens type
-which yield a fairly large field. It is by means of big instruments
-of such sort that the spectra for the magnificent Draper Catalogue
-have been secured by the
-Harvard Observatory, mostly at the
-Arequipa station. In photographing
-with the objective prism the spectra
-are commonly given the necessary
-width for convenient examination by
-changing just a trifle the rate of the
-driving clock so that there is a slight
-and gradual drift in R. A. The refracting
-edge of the prism being turned
-parallel to the diurnal motion this drift
-very gradually and uniformly widens
-the spectrum to the extent of a few
-minutes of arc during the whole
-exposure.</p>
-
-<div class="figright">
-<img src="images/i_187.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 143.</span>—Simple Objective
- Prism.</div>
-</div>
-
-<p>When one comes to solar spectroscopy
-one meets an entirely different
-situation. In stellar work the difficulty
-is to get enough light, and the
-tendency is toward large objectives
-of relatively short focal length and
-spectroscopes of moderate dispersion.
-In solar studies there is ample light,
-and the main thing is to get an image
-big enough to be scrutinized in detail with very great dispersion.</p>
-
-<p>Especially is this true in the study of the chromospheric flames
-that rim the solar disc and blaze over its surface. To examine
-these effectively the spectroscope should have immense dispersion
-with a minimum amount of stray light in the field to interfere
-with vision of delicate details.</p>
-
-<p>In using a spectroscope like Fig. 142, if one turned the slit
-toward the landscape, the instrument being removed from the
-telescope and the slit opened wide, he could plainly see its various
-features, refracted through the prism, and appearing in such
-color as corresponded to the part of the spectrum in the line of<span class="pagenum"><a name="Page_188" id="Page_188">[Pg 188]</a></span>
-the observing telescope. In other words one sees refracted
-images quite distinctly in spite of the bending of the rays. With
-high dispersion the image seen is practically monochromatic.</p>
-
-<p>Now if one puts the spectroscope in place, brings the solar
-image tangent to the slit and then cautiously opens the slit, he
-sees the bright continuous spectrum of the sky close to the sun,
-plus any light of the particular color for which the observing
-telescope is set, which may proceed from the edge of the solar
-disc. Thus, if the setting is for the red line of hydrogen (C), one
-sees the hydrogen glow that plays in fiery pillars of cloud about
-the sun’s limb quite plainly through the opened slit, on a background
-of light streaming from the adjacent sky. To see most
-clearly one must use great dispersion to spread this background
-out into insignificance, must keep other stray light out of the
-field, and limit his view to the opened slit.</p>
-
-<div class="figcenter">
-<img src="images/i_188.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 144.</span>—Diagram of Evershed Solar Spectroscope.</div>
-</div>
-
-<p>To these ends early solar spectroscopes had many prisms in
-tandem, up to a dozen or so, kept in proper relation by complicated
-linkages analogous to the simple one shown in Fig. 142.
-Details can be found in almost any astronomical work of 40
-years ago. They were highly effective in giving dispersion but
-neither improved the definition nor cut out light reflected back
-and forth from their many surfaces.</p>
-
-<p>Of late simpler constructions have come into use of which an
-excellent type is the spectroscope designed by Mr. Evershed and
-shown in diagram in Fig. 144. Here the path of the rays is from
-the slit through the collimator objective, then through a very<span class="pagenum"><a name="Page_189" id="Page_189">[Pg 189]</a></span>
-powerful direct vision system, giving a dispersion of 30° through
-the visible spectrum, then by reflection from the mirror through
-a second such system, and thence to the observing telescope.
-The mirror is rotated to get various parts of the spectrum into
-view, and the micrometer screw that turns it gives means for
-making accurate measurement of wave lengths.</p>
-
-<p>There are but five reflecting surfaces in the prism system (for
-the cemented prism surfaces do not count for much) as against
-more than 20 in one of the older instruments of similar power,
-and as in other direct vision systems the spectrum lines are
-substantially straight instead of being strongly curved as with
-multiple single prisms. The result is the light, compact, and
-powerful spectroscope shown complete in Fig. 145, equally well
-fitted for observing the sun’s prominences and the detailed
-spectrum from his surface.</p>
-
-<div class="figcenter">
-<img src="images/i_189.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 145.</span>—Evershed Solar Spectroscope.</div>
-</div>
-
-<p>In most of the solar spectroscopes made at the present time
-the prisms are replaced by a diffraction grating. The original
-gratings made by Fraunhofer were made of wire. Two parallel
-screws of extremely fine thread formed two opposite sides of a
-brass frame. A very fine wire was then wound over these
-screws, made fast by solder on one side of each, and then cut
-away on the other, so as to leave a grating of parallel wires with
-clear spaces between.</p>
-
-<p>Today the grating is generally ruled by an automatic ruling
-engine upon a polished plate of speculum metal. The diamond
-point carried by the engine cuts very smooth and fine parallel
-furrows, commonly from 10,000 to 20,000 to the inch. The<span class="pagenum"><a name="Page_190" id="Page_190">[Pg 190]</a></span>
-spaces between the furrows reflect brilliantly and produce
-diffraction spectra.<a name="FNanchor_22_22" id="FNanchor_22_22"></a><a href="#Footnote_22_22" class="fnanchor">[22]</a></p>
-
-<p>When a grating is used instead of prisms the instrument is
-commonly set up as shown in Fig. 146. Here <i>A</i> is the collimator
-with slit upon which the solar image light falls, <i>B</i> is the observing
-telescope, and <i>C</i> the grating set in a rotatable mount with a fine
-threaded tangent screw to bring any line accurately upon the
-cross wires of the ocular.</p>
-
-<div class="figcenter">
-<img src="images/i_190.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 146.</span>—Diagram of Grating Spectroscope.</div>
-</div>
-
-<p>The grating gives a series of spectra on each side of the slit,
-violet ends toward the slit, and with deviations proportional to
-1, 2, 3, 4, etc., times the wave length of the line considered. The
-spectra therefore overlap, the ultra violet of the second order
-being superimposed on the extreme red of the first order and so
-on. Colored screens over the slit or ocular are used to get the
-overlying spectra out of the way.</p>
-
-<p>The grating spectroscopes are very advantageous in furnishing
-a wide range of available dispersions, and in giving less stray
-light than a prism train of equal power. The spectra moreover
-are very nearly “normal,” <i>i.e.</i>, the position of each line is proportional
-to its wave length instead of the blue being disproportionately
-long as in prismatic spectra.</p>
-
-<p>In examining solar prominences the widened slit of a grating
-spectroscope shows them foreshortened or stretched to an
-amount depending on the angular position of the grating, but the
-effect is easily reckoned.<a name="FNanchor_23_23" id="FNanchor_23_23"></a><a href="#Footnote_23_23" class="fnanchor">[23]</a></p>
-<p><span class="pagenum"><a name="Page_191" id="Page_191">[Pg 191]</a></span></p>
-<p>If the slit is nearly closed one sees merely a thin line, irregularly
-bright according to the shape of the prominence; a shift of the
-slit with respect to the solar image shows a new irregular section
-of the prominence in the same monochromatic light.</p>
-
-<p>These simple phenomena form the basis of one of the most
-important instruments of solar study—the spectro-heliograph.
-This was devised almost simultaneously by G. E. Hale and M.
-Deslandres about 30 years ago, and enables photographs of the
-sun to be taken in monochromatic light, showing not only the
-prominences of the limb but glowing masses of gas scattered all
-over the surface.</p>
-
-<p>The principle of the instrument is very simple. The collimator
-of a powerful grating spectroscope is provided with a slit the full
-length of the solar diameter, arranged to slide smoothly on a
-ball-bearing carriage clear across the solar disc. Just in front of
-the photographic plate set in the focus of the camera lens is
-another narrow sliding slit, which, like a focal plane shutter,
-exposes strip after strip of the plate.</p>
-
-<p>The two slits are geared together by a system of levers or
-otherwise so that they move at exactly the same uniform rate of
-speed. Thus when the front slit is letting through a monochromatic
-section of a prominence on the sun’s limb the plate-slit is
-at an exactly corresponding position. When the front slit is
-exactly across the sun’s center so is the plate slit, at each element
-of movement exposing a line of the plate to the monochromatic
-image from the moving front slit. The grating can of course be
-turned to put any required line into action but it usually is set
-for the K line (calcium), which is photographically very brilliant
-and shows bright masses of floating vapor all over the sun’s
-surface.</p>
-
-<p>Figure 147 shows an early and simple type of Professor Hale’s
-instrument. Here A is the collimator with its sliding slit, B the
-photographic telescope with its corresponding slide and C the
-lever system which connects the slides in perfectly uniform
-alignment. The source of power is a very accurately regulated
-water pressure cylinder mounted parallel with the collimator.
-The result is a complete photograph of the sun taken in monochromatic
-light of exactly defined wave length and showing the
-precise distribution of the glowing vapor of the corresponding
-substance.</p>
-
-<p>Since the spectro-heliograph of Fig. 147, which shows the princi<span class="pagenum"><a name="Page_192" id="Page_192">[Pg 192]</a></span>ple
-remarkably well, there have been made many modifications,
-in particular for adapting the scheme to the great horizontal and
-vertical fixed telescopes now in use. (For details of these see
-Cont. from the Solar Obs. Mt. Wilson, Nos. 3, 4, 23, and others).
-The chief difficulty always is to secure entirely smooth and
-uniform motion of the two moving elements.</p>
-
-<div class="figcenter">
-<img src="images/i_192.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 147.</span>—Hale’s Spectro-heliograph (Early Form).</div>
-</div>
-
-<p>So great and interesting a branch of astronomy is the study of
-variable stars that some form of photometer should be part of
-the equipment of every telescope in serious use for celestial
-observation. An immense amount of useful work has been done
-by Argelander’s systematic method of eye observation, but it is
-far from being precise enough to disclose many of the most
-important features of variability.</p>
-
-<p><span class="pagenum"><a name="Page_193" id="Page_193">[Pg 193]</a></span></p>
-
-<p>The conventional way of reckoning by stellar magnitudes is
-conducive to loose measurements, since each magnitude of
-difference implies a light ratio of which the log is 0.4, <i>i.e.</i>, each
-magnitude is 2.512 times brighter than the following one. As a
-result of this way of reckoning the light of a star of mag. 9.9 differs
-from one of mag. 10.0 not by one per cent but by about nine.
-Hence to grasp light variations of small order one must be able to
-measure far below 0.1<sup><i>m</i></sup>.</p>
-
-<div class="figcenter">
-<img src="images/i_193.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 148.</span>-Double Image Stellar Photometer.</div>
-</div>
-
-<p>The ordinary laboratory photometer enables one to compare
-light sources of anywhere near similar color to a probable error
-of well under 0.1 per cent, but it allows a comparison between
-sharply defined juxtaposed fields from the two illuminants, a
-condition much more favorable to precision than the comparison
-of two points of light, even if fairly near together.</p>
-
-<p>Stellar photometers may in principle be divided into three
-classes. (1) Those in which two actual stars are brought into the
-same field and compared by varying the light from one or both in
-a known degree. (2) Those which bring a real star into the
-field alongside an artificial star, and again bring the two to
-equality by a known variation, usually comparing two or more
-stars via the same artificial star; (3) those which measure the
-light of a star by a definite method of extinguishing it entirely or
-just to the verge of disappearance in a known progression. Of
-each class there are divers varieties. The type of the first class
-may be taken as the late Professor E. C. Pickering’s polarizing
-photometer. Its optical principle is shown in Fig. 148. Here
-the brightness of two neighboring objects is compared by polarizing
-at 90° apart the light received from each and reducing the
-resulting images to equality by an analyzing Nicol prism. The<span class="pagenum"><a name="Page_194" id="Page_194">[Pg 194]</a></span>
-photometer is fully described, with, several other polarizing
-instruments, in H. A. Vol. II from which Fig. 148 is taken.</p>
-
-<p>A is a Nicol prism inserted in the ocular <i>B</i>, which revolves carrying
-with it a divided circle <i>C</i> read against the index <i>D</i>. In the
-tube <i>E</i> which fits the eye end of the telescope, is placed the double
-image quartz prism <i>F</i> capable of sliding either way without
-rotation by pulling the cord <i>G</i>. With the objects to be compared
-in the same field, two images of each appear. By turning the
-analyzing Nicol the fainter image of the brighter can always be
-reduced to equality with the brighter image of the fainter, and the
-amount of rotation measures the required ratio of brightness.<a name="FNanchor_24_24" id="FNanchor_24_24"></a><a href="#Footnote_24_24" class="fnanchor">[24]</a>
-This instrument works well for objects near enough to be in the
-same field of view. The distance between the images can be
-adjusted by sliding the prism <i>F</i> back and forth, but the available
-range of view is limited to a small fraction of a degree in ordinary
-telescopes.</p>
-
-<p>The meridian photometer was designed to avoid this small
-scope. The photometric device is substantially the same as
-in Fig. 148. The objects compared are brought into the field
-by two exactly similar objectives placed at a small angle so that
-the images, after passing the double image prism, are
-substantially in coincidence. In front of each of the objectives is
-a mirror. The instrument points in the east and west line and the
-mirrors are at 45° with its axis. One brings Polaris into the field,
-the other by a motion of rotation about the telescope axis can
-bring any object in or close to the meridian into the field alongside
-Polaris. The images are then compared precisely as in the
-preceding instance.<a name="FNanchor_25_25" id="FNanchor_25_25"></a><a href="#Footnote_25_25" class="fnanchor">[25]</a> There are suitable adjustments for bringing
-the images into the positions required.</p>
-
-<p>The various forms of photometer using an artificial star as
-intermediary in the comparison of real stars differ chiefly in the<span class="pagenum"><a name="Page_195" id="Page_195">[Pg 195]</a></span>
-method of varying the light in a determinate measure. Rather
-the best known is the Zöllner instrument shown in diagram in
-Fig. 149. Here <i>A</i> is the eye end of the main telescope tube.
-Across it at an angle of 45° is thrown a piece of plane parallel
-glass <i>B</i> which serves to reflect to the focus the beam from down
-the side tube, <i>C</i>, forming the artificial star.</p>
-
-<div class="figcenter">
-<img src="images/i_195.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 149.</span>—Zöllner Photometer Diagram.</div>
-</div>
-
-<p>At the end of this tube is a small hole or more often a
-diaphragm perforated with several very small holes any of
-which can be brought into the axis of the tube. Beyond at <i>D</i>,
-is the source of light, originally a lamp flame, now generally a
-small incandescent lamp, with a ground glass disc or surface
-uniformly to diffuse the light.</p>
-
-<p>Within the tube <i>C</i> lie three Nicol prisms <i>n</i>, <i>n</i><sub>1</sub>, <i>n</i><sub>2</sub>. Of these <i>n</i>,
-is fixed with respect to the mirror B and forms the analyser,
-<span class="pagenum"><a name="Page_196" id="Page_196">[Pg 196]</a></span>which <i>n</i><sub>1</sub> and <i>n</i><sub>2</sub> turn together forming the polarizing system.
-Between <i>n_1</i> and <i>n_2</i> is a quartz plate <i>e</i> cut perpendicular to the
-crystal axis. The color of the light transmitted by such a plate
-in polarized light varies through a wide range. By turning the
-Nicol <i>n_2</i> therefore, the color of the beam which forms the artificial
-star can be made to match the real star under examination,
-and then by turning the whole system <i>n_2</i>, <i>E</i>, <i>n_1</i>, reading the
-rotation on the divided circle at <i>F</i>, the real star can be matched
-in intensity by the artificial one.</p>
-
-<div class="figcenter">
-<img src="images/i_196.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 150.</span>—Wedge Photometer.</div>
-</div>
-<p>This is viewed via the lens <i>G</i> and two tiny points of light
-appear in the field of the ocular due respectively to reflection from
-the front and back of the mirror <i>B</i>, the latter slightly fainter
-than the former. Alongside or between these the real star image
-can be brought for a comparison, and by turning the polarizer
-through an angle [alpha] the images can be equalized with the real
-image. Then a similar comparison is made with a reference
-star. If A be the brightness of the former and B of the latter then</p>
-
-<p class="center">A/B = sin²α/sin²<span class="pagenum"><a name="Page_197" id="Page_197">[Pg 197]</a></span>ββ</p>
-
-<p>The Zöllner photometer was at first set up as an alt-azimuth
-instrument with a small objective and rotation in altitude about
-the axis <i>C</i>. Since the general use of electric lamps instead of the
-inconvenient flame it is often fitted to the eye end of an equatorial.</p>
-
-<p>Another very useful instrument is the modern wedge photometer,
-closely resembling the Zöllner in some respects but with a
-very different method of varying the light; devised by the late
-Professor E. C. Pickering. It is shown somewhat in diagram in
-Fig. 150. Here as before O is the eye end of the tube, B the plane
-parallel reflector, C the side tube, L the source of light D the
-diaphragm and A the lens forming the artificial star by projecting
-the hole in the diaphragm. In actual practice the diameter of
-such hole is 1/100 inch or less.</p>
-
-<div class="figcenter">
-<img src="images/i_197.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 151.</span>—Simple Polarizing Photometer.</div>
-</div>
-
-<p>The light varying device W is a “photographic wedge” set in a
-frame which is graduated on the edge and moved in front of the
-aperture by a rack and pinion at R. There are beside colored
-and shade glasses for use as occasion requires. The “photographic
-wedge” is merely a strip of fine grained photographic
-plate given an evenly graduated exposure from end to end,
-developed, and sealed under a cover glass. Its absorption is
-permanent, non-selective as to color, and it can be made to shade
-off from a barely perceptible density to any required opacity.
-Sometimes a wedge of neutral tinted glass is used in its stead.</p>
-
-<p>Before using such a “wedge photometer” the wedge must be
-accurately calibrated by observation of real or artificial stars of
-known difference in brightness. This is a task demanding much
-care and is well described, together with the whole instrument<span class="pagenum"><a name="Page_198" id="Page_198">[Pg 198]</a></span>
-by Parkhurst (Ap. J. 13, 249). The great difficulty with all
-instruments of this general type is the formation of an artificial
-star the image of which shall very closely resemble the image
-of the real star in appearance and color.</p>
-
-<p>Obviously either the real or artificial star, or both, may be
-varied in intensity by wedge or Nicols, and a very serviceable
-modification of the Zöllner instrument, with this in mind was
-recently described by Shook (Pop. Ast. 27, 595) and is shown
-in diagram in Fig. 151. Here A is the tube which fits the ordinary
-eyepiece sleeve. E is a side tube into which is fitted the extension
-D with a fitting H at its outer end into which sets the lamp
-tube G. This carries on a base plug F a small flash light bulb
-run by a couple of dry cells. At O is placed a little brass diaphragm
-perforated with a minute hole. Between this and the
-lamp is a disc of diffusing glass or paper. A Nicol prism is set
-a little ahead of O, and a lens L focusses the perforation at the
-principal focus of the telescope after reflection from the diagonal
-glass M, as in the preceding examples. I is an ordinary eyepiece
-over which is a rotatable Nicol N with a position circle K.
-At P is a third Nicol in the path of the rays from the real star,
-thereby increasing the convenient range of the instrument.
-The original paper gives the details of construction as well as
-the methods of working. Obviously the same general arrangement
-could be used for a wedge photometer using the wedge on
-either real or artificial star or both.</p>
-
-<p>The third type of visual photometer depends on reducing the
-light of the star observed until it just disappears. This plan
-was extensively employed by Professor Pritchard of Oxford some
-40 years ago. He used a sliding wedge of dark glass, carefully
-calibrated, and compared two stars by noting the point on the
-wedge at which each was extinguished. A photographic wedge
-may be used in exactly the same way.</p>
-
-<p>Another device to the same end depends on reducing the
-aperture of the telescope by a “cat’s eye,” an iris diaphragm, or
-similar means until the star is no longer visible or just disappearing.
-The great objection to such methods is the extremely
-variable sensitivity of the eye under varying stimulus of light.</p>
-
-<p>The most that can be said for the extinction photometer is
-that in skillful and experienced hands like Pritchard’s it has
-sometimes given much more consistent readings than would be
-expected. It is now and then very convenient for quick approxi<span class="pagenum"><a name="Page_199" id="Page_199">[Pg 199]</a></span>mation
-but by no courtesy can it be considered an instrument of
-precision either in astronomical or other photometry.<a name="FNanchor_26_26" id="FNanchor_26_26"></a><a href="#Footnote_26_26" class="fnanchor">[26]</a></p>
-
-<p>The photometer question should not be closed without referring
-the reader to the methods of physical photometry as developed by
-Stebbins, Guthnick and others. The first of these depends on
-the use of the selenium cell in which the electrical resistance falls
-on exposure of the selenium to light. The device is not one
-adapted to casual use, and requires very careful nursing to give
-the best results, but these are of an order of precision beyond
-anything yet reached with an astronomical visual photometer.
-Settings come down to variations of something like 2 per cent, and
-variations in stellar light entirely escaping previous methods
-become obvious.</p>
-
-<p>The photoelectric cell depends on the lowering of the apparent
-electric resistance of a layer of rarified inert gas between a platinum
-grid and an electrode of metallic potassium or other alkali
-metal when light falls on that electrode. The rate of transmission
-of electricity is very exactly proportional to the illumination,
-and can be best measured by a very sensitive electrometer.
-The results are extraordinarily consistent, and the theoretical
-“probable error” is very small, though here, as elsewhere,
-“probable error” is a rather meaningless term apt to lead to a
-false presumption of exactness. Again the apparatus is somewhat
-intricate and delicate, but gives a precision of working if anything
-a little better than that of the selenium cell, quite certainly
-below 1 per cent.</p>
-
-<p>Neither instrument constitutes an attachment to the ordinary
-telescope of modest size which can be successfully used for ordinary
-photometry, and both require reduction of results to the
-basis of visual effect.<a name="FNanchor_27_27" id="FNanchor_27_27"></a><a href="#Footnote_27_27" class="fnanchor">[27]</a> But both offer great promise in detecting<span class="pagenum"><a name="Page_200" id="Page_200">[Pg 200]</a></span>
-minute variations of light and have done admirable work. For a
-good fundamental description of the selenium cell photometer see
-Stebbins, Ap. J. <b>32</b>, 185 and for the photoelectric method see
-Guthnick A. N. <b>196</b>, 357 also A. F. and F. A. Lindemann,
-M. N. <b>39</b>, 343. The volume by Miss Furness already referred
-to gives some interesting details of both.</p>
-
-<hr class="chap" />
-
-<p><span class="pagenum"><a name="Page_201" id="Page_201">[Pg 201]</a></span></p>
-
-
-
-<div class="chapter"></div>
-<h2><a name="CHAPTER_IX" id="CHAPTER_IX">CHAPTER IX</a><br />
-
-<small>THE CARE AND TESTING OF TELESCOPES</small></h2>
-
-
-<p>A word at the start concerning the choice and purchase of
-telescopes. The question of refractors vs. reflectors has been
-already considered. The outcome of the case depends on how
-much and how often you are likely to use the instrument, and
-just what you want it for. For casual observations and occasional
-use—all that most busy buyers of telescopes can expect—the
-refractor has a decided advantage in convenience. If one
-has leisure for frequent observations, and particularly if he can
-give his telescope a permanent mount, and is going in for serious
-work, he will do well not to dismiss the idea of a reflector without
-due deliberation.</p>
-
-<p>In any case it is good policy to procure an instrument from one
-of the best makers. And if you do not buy directly of the actual
-maker it is best to deal with his accredited agents. In other
-words avoid telescopes casually picked up in the optical trade
-unless you chance to have facilities for thorough testing under
-competent guidance before purchase. No better telescopes are
-made than can be had from the best American makers. A few
-British and German makers are quite in the same class. So few
-high grade French telescopes reach this country as to cause a
-rather common, but actually unjust,<a name="FNanchor_28_28" id="FNanchor_28_28"></a><a href="#Footnote_28_28" class="fnanchor">[28]</a> belief that there are none.</p>
-
-<p>If economy must be enforced it is much wiser to try to pick up a
-used instrument of first class manufacture than to chance a new
-one at a low price. Now and then a maker of very ordinary
-repute may turn out a good instrument, but the fact is one to be
-proved—not assumed. Age and use do not seriously deteriorate
-a telescope if it has been given proper care. Some of Fraunhofer’s
-are still doing good service after a century, and occasionally
-an instrument from one of the great makers comes into the
-market at a real bargain. It may drift back to the maker for
-resale, or turn up at any optician’s shop, and in any case is better
-worth looking at than an equally cheap new telescope.</p>
-
-<p><span class="pagenum"><a name="Page_202" id="Page_202">[Pg 202]</a></span></p>
-
-<p>The condition of the tube and stand cuts little figure if they are
-mechanically in good shape. Most of the older high grade
-instruments were of brass, beautifully finished and lacquered, and
-nothing looks worse after hard usage. It is essential that the
-fitting of the parts should be accurate and that the focussing rack
-should work with the utmost smoothness. A fault just here,
-however, can be remedied at small cost. The mount, whatever
-its character, should be likewise smooth working and without a
-trace of shakiness, unless one figures on throwing it away.</p>
-
-<p>As to the objective, it demands very careful examination
-before a real test of its optical qualities. The objective with its
-cell should be taken out and closely scrutinized in a strong light
-after the superficial dust has been removed with a camel’s
-hair brush or by wiping very gently with the soft Japanese “lens
-paper” used by opticians.</p>
-
-<p>One is likely to find plenty to look at; spots, finger marks,
-obvious scratches, and what is worse a network of superficial
-scratches, or a surface with patches looking like very fine pitting.
-These last two defects imply the need of repolishing the affected
-surface, which means also more or less refiguring. Ordinary
-brownish spots and finger marks can usually be removed with
-little trouble.</p>
-
-<p>The layman, so to speak, is often warned never to remove the
-cell from a telescope but he might as well learn the simpler
-adjustments first as last. In taking off a cell the main thing is to
-see what one is about and to proceed in an orderly manner.
-If the whole cell unscrews, as often is the case in small instruments,
-the only precaution required is to put a pencil mark
-on the cell and its seat so that it can be screwed back to where
-it started.</p>
-
-<p>If as is more usual the cell fits on with three pairs of screws, one
-of each pair will form an abutment against which its mate pulls
-the cell. A pencil mark locating the position of the head of each
-of the pulling screws enables one to back them out and replace
-them without shifting the cell.</p>
-
-<p>The first inspection will generally tell whether the objective is
-worth further trouble or not. If all surfaces save the front are in
-good condition it may pay to send the objective to the maker for
-repolishing. If more than one surface is in bad shape reworking
-hardly pays unless the lens can be had for a nominal figure. In
-buying a used instrument from its original source these precau<span class="pagenum"><a name="Page_203" id="Page_203">[Pg 203]</a></span>tions
-are needless as the maker can be trusted to stand back of
-his own and to put it in first class condition.</p>
-
-<p>However, granted that the objective stands well the inspection
-for superficial defects, it should then be given a real test for
-figure and color correction, bearing in mind that objectives, even
-from first class makers, may now and then show slightly faulty
-corrections, while those from comparatively unknown sources
-may now and then turn out well. In this matter of necessary
-testing old and new glasses are quite on all fours save that one
-may safely trust the maker with a well earned reputation to make
-right any imperfections. Cleansing other than dusting off and
-cautiously wiping with damp and then dry lens paper requires
-removal of the lenses from their cell which demands real care.</p>
-
-<p>With a promising looking objective, old or new, the first test
-to be applied is the artificial star—artificial rather than natural
-since the former stays put and can be used by day or by night.
-For day use the “star” is merely the bright reflection of the sun
-from a sharply curved surface—the shoulder of a small round
-bottle, a spherical flask silvered on the inside, a small silvered
-ball such as is used for Christmas tree decoration, a bicycle ball,
-or a glass “alley” dear to the heart of the small boy.</p>
-
-<p>The object, whatever it is, should be set up in the sun against
-a dark background distant say 40 or 50 times the focal length of
-the objective to be tested. The writer rather likes a silvered ball
-cemented to a big sheet of black cardboard. At night a pin
-hole say 1/32 inch or less in diameter through cardboard or
-better, tinfoil, with a flame, or better a gas filled incandescent
-lamp behind it, answers well. The latter requires rather careful
-adjustment that the projected area of the closely coiled little
-filament may properly fill the pinhole just in front of it.</p>
-
-<p>Now if one sets up the telescope and focusses it approximately
-with a low power the star can be accurately centered in the field.
-Then if the eyepiece is removed, the tube racked in a bit, and
-the eye brought into the focus of the objective, one can inspect
-the objective for striæ. If these are absent the field will be
-uniformly bright all over. Not infrequently however one will see
-a field like Fig. 152 or Fig. 153. The former is the appearance of a
-4 inch objective that the author recently got his eye upon. The
-latter shows typical striæ of the ordinary sort. An objective of
-glass as bad as shown in Fig. 152 gives no hope of astronomical
-usefulness, and should be relegated to the porch of a seashore<span class="pagenum"><a name="Page_204" id="Page_204">[Pg 204]</a></span>
-cottage. Figure 153 may represent a condition practically
-harmless though undesirable.</p>
-
-<p>The next step is a really critical examination of the focal
-image. Using a moderately high power ocular, magnifying say
-50 to the inch of aperture, the star should be brought to the
-sharpest focus possible and the image closely examined. If the
-objective is good and in adjustment this image should be a very
-small spot of light, perfectly round, softening very slightly in its
-brilliancy toward the edge, and surrounded by two or three thin,
-sharp, rings of light, exactly circular and with well defined dark
-spaces separating them.</p>
-
-<div class="figleft"><a id="Fig_152"></a>
-<img src="images/i_204-2.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 152.</span>—A Bad Case of Striæ.</div>
-</div>
-
-<div class="figright">
-<img src="images/i_204-1.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 153.</span>—Ordinary Striæ.</div>
-</div>
-
-<p>Often from the trembling of the air the rings will seem shaky
-and broken, but still well centered on the star-disc. The general
-appearance is that shown in Fig. 154.<a name="FNanchor_29_29" id="FNanchor_29_29"></a><a href="#Footnote_29_29" class="fnanchor">[29]</a></p>
-
-<div class="figleft">
-<img src="images/i_204b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 154.</span>—A First Class
- Star Image.</div>
-</div>
-
-<p>Instead, several very different appearances may turn up.
-First, the bright diffraction rings may be visible only on one
-side of the central disc, which may itself be
-drawn out in the same direction. Second,
-the best image obtainable may be fairly
-sharp but angular or irregular instead of
-round or oval and perhaps with a hazy
-flare on one side. Third, it may be impossible
-to get a really sharp focus anywhere,
-the image being a mere blob of light with nothing definite
-about it.</p>
-
-<p><span class="pagenum"><a name="Page_205" id="Page_205">[Pg 205]</a></span></p>
-
-<p>One should be very sure that the eyepiece is clean and without
-fault before proceeding further. As to the first point a bit of
-lens paper made into a tiny swab on a sliver of soft wood will be
-of service, and the surfaces should be inspected with a pocket
-lens in a good light to make sure that the cleaning has been
-thorough. Turning the ocular round will show whether any
-apparent defects of the image turn with it.</p>
-
-<div class="figright">
-<img src="images/i_205a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 155.</span>—Effect of
-Objective Askew.</div>
-</div>
-
-<p>In the first case mentioned the next step is to rack the ocular
-gently out when the star image will expand into a more or less
-concentric series of bright interference
-rings separated by dark spaces, half a dozen
-or so resulting from a rather small movement
-out of focus. If these rings are out
-of round and eccentric like Fig. 155 one
-has a clear case of failure of the objective
-to be square with the tube, so that the
-ocular looks at the image askew.</p>
-
-<p>In the ordinary forms of objective this means that the side of
-the objective toward the brighter and less expanded part of the
-ring system is too near the ocular. This can be remedied by
-pushing that side of the objective outwards a trifle. Easing off
-the pulling screw on that side and slightly tightening the abutment
-screw makes the needed correction, which can be lessened
-if over done at the first trial, until the ring system is accurately
-centered. It is a rather fussy job but not at all difficult if one
-remembers to proceed cautiously and to use the screw driver
-gently.</p>
-
-<div class="figleft">
-<img src="images/i_205b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 156.</span>—Effect of
-Flaws in Objective.</div>
-</div>
-
-<p>In the second case, racking out the ocular a little gives a ring
-system which exaggerates just the defects of
-the image. The faults may be due to mechanical
-strain of the objective in its cell,
-which is easily cured, or to strains or flaws in
-the glass itself, which are irremediable.
-Therefore one should, with the plane of the
-objective horizontal, loosen the retaining ring
-that holds the lenses, without disturbing them,
-and then set it back in gentle contact and try the out of focus
-rings once more. If there is no marked improvement the fault
-lies in the glass and no more time should be wasted on that
-particular objective. Fig. 156 is a typical example of this fault.</p>
-
-<p>In dealing with case three it is well to give the lens a chance by<span class="pagenum"><a name="Page_206" id="Page_206">[Pg 206]</a></span>
-relieving it of any such mechanical strains, for now and then
-they will apparently utterly ruin the definition, but the prognosis
-is very bad unless the objective has been most brutally
-mishandled.</p>
-
-<p>In any case failure to give a sharply defined focus in a very
-definite plane is a warning that the lens (or mirror) is rather bad.
-In testing a reflector some pains must be taken at the start with
-both the main and the secondary mirror. Using an artificial
-star as before, one should focus and look sharply to the symmetry
-of the image, taking care to leave the instrument in observing
-position and screened from the sun for an hour or two before
-testing. Reflectors are much more sensitive to temperature than
-refractors and take longer to settle down to stability of figure.
-With a well mounted telescope of either sort a star at fair altitude
-on a fine night gives even better testing conditions than an
-artificial star, (Polaris is good in northern latitudes) but one may
-have a long wait.</p>
-
-<p>If the reflector is of good figure and well adjusted, the star
-image, in focus or out, has quite the same appearance as in a
-refractor except that with a bright star in focus one sees a thin
-sharp cross of light centered on the image, rather faint but
-perfectly distinct. This is due to the diffraction effect of the
-four thin strips that support the small
-mirror, and fades as the star is put out of
-focus.</p>
-
-<div class="figleft">
-<img src="images/i_206.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 157.</span>—Extra-focal
-Image from Reflector.</div>
-</div>
-
-<p>The rings then appear as usual, but also
-a black disc due to the shadowing of the
-small mirror. Fig. 157 shows the extra-focal
-image of a real or artificial star when
-the mirror is well centered, and the star in
-the middle of the field. There only are
-the rings round and concentric with the mirror spot. The rings
-go out of round and the spot out of center for very small departure
-from the middle of the field when the mirror is of large relative
-aperture—F/5 or F/6.</p>
-
-<p>If the star image shows flare or oval out-of-focus rings when
-central of the field, one or both mirrors probably need adjustment.
-Before laying the trouble to imperfect figure, the mirrors
-should be adjusted, the small one first as the most likely source
-of trouble. The side of the mirror toward which the flare or the
-expanded side of the ring system projects should be slightly<span class="pagenum"><a name="Page_207" id="Page_207">[Pg 207]</a></span>
-pushed away from the ocular. (Note that owing to the reflection
-this movement is the reverse of that required with a
-refractor.)</p>
-
-<p>If the lack of symmetry persists one may as well get down to
-first principles and center the mirrors at once. Perhaps the
-easiest plan is to prepare a disc of white cardboard exactly the
-size of the mirror with concentric circles laid out upon it and an
-eighth inch hole in the center. Taking out the ocular and putting
-a half inch stop in its place one can stand back, lining up the stop
-with the draw tube, and see whether the small mirror looks
-perfectly round and is concentric with the reflected circles. If
-not, a touch of the adjusting screws will be needed.</p>
-
-<p>Then with a fine pointed brush dot the center of the mirror
-itself through the hole, with white paint. Then, removing the
-card, one will see this dot accurately centered in the small mirror
-if the large one is in adjustment, and it remains as a permanent
-reference point. If the dot be eccentric it can be treated as
-before, but by the adjusting screws of the large mirror.</p>
-
-<p>The final adjustment can then be made by getting a slightly
-extra-focal star image fairly in the center of the field with a
-rather high power and making the system concentric as before
-described. This sounds a bit complicated but it really is not.
-If the large mirror is not in place, its counter cell may well be
-centered and levelled by help of a plumb line from the center of
-the small mirror and a steel square, as a starting point, the small
-mirror having been centered as nearly as may be by measurement.<a name="FNanchor_30_30" id="FNanchor_30_30"></a><a href="#Footnote_30_30" class="fnanchor">[30]</a></p>
-
-<p>So much for the general adjustment of the objective or mirror.
-Its actual quality is shown only on careful examination.</p>
-
-<p>As a starting point one may take the extra-focal system of rings
-given by an objective or mirror after proper centering. If the
-spherical aberration has thoroughly removed the appearance of
-the rings when expanded so that six or eight are visible should be
-like Fig. 158. The center should be a sharply defined bright
-point and surrounding it, and exactly concentric, should be the<span class="pagenum"><a name="Page_208" id="Page_208">[Pg 208]</a></span>
-interference rings, truly circular and gradually increasing in
-intensity outwards, the last being very noticeably the strongest.</p>
-
-<div class="figleft">
-<img src="images/i_208a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 158.</span>—Correct Extra-focal Image.</div>
-</div>
-
-<p>One can best make the test when looking through a yellow
-glass screen which removes the somewhat confusing flare due to
-imperfect achromatism and makes the appearances inside and
-outside focus closely similar.
-Just inside or outside of focus
-the appearance should be that
-of Fig. 159 for a perfectly corrected
-objective or mirror.</p>
-
-<p>Sometimes an objective will be
-found in which one edge of the
-focussed star image is notably
-red and the opposite one tinted
-with greenish or bluish, showing unsymmetrical coloring, still
-more obvious when the image is put a little out of focus. This
-means that the optical centers of crown and flint are out of line
-from careless edging of the lenses or very bad fitting. The case
-is bad enough to justify trying the only remedy available outside
-the optician’s workshop—rotating one lens upon the other and thus
-trying the pair in different relative azimuths.</p>
-
-<div class="figright">
-<img src="images/i_208b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 159.</span>—Correct Image Just
-Out of Focus.</div>
-</div>
-
-<p>The initial positions of the pair must be marked plainly, care
-must be taken not to displace the spacers 120° apart often found
-at the edges of the lenses, and the
-various positions must be tried in
-an orderly manner. One not infrequently
-finds a position in which
-the fault is negligible or disappears
-altogether, which point should be
-at once marked for reference.</p>
-
-<p>In case there is uncorrected
-spherical aberration there is departure
-from regular gradation of brightness in the rings. If
-there is a “short edge,” <i>i.e.</i>, + spherical aberration, so that rays
-from the outer zone come to a focus too short, the edge ring will
-look too strong within focus, and the inner rings relatively weak;
-with this appearance reversed outside focus. A “long edge” <i>i.e.</i>,
-- spherical aberration, shows the opposite condition, edge rings
-too strong outside focus and too weak within. Both are rather
-common faults. The “long edge” effect is shown in Figs. 160
-and 161, as taken quite close to focus.</p>
-
-<p><span class="pagenum"><a name="Page_209" id="Page_209">[Pg 209]</a></span></p>
-
-<p>It takes a rather sharp eye and considerable experience to
-detect small amounts of spherical aberration; perhaps the best
-way of judging is in quickly passing from just inside to just outside
-focus and back again, using a yellow screen and watching
-very closely for variations in brightness. Truth to tell a small
-amount of residual aberration, like that of Fig. 160, is not a
-serious matter as regards actual performance—it hurts the
-telescopist’s feelings much more than the quality of his images.</p>
-
-<div class="figcenter">
-<img src="images/i_209.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 160.</span>—Spherical Aberration Just Inside Focus.<br />
-<span class="smcap">Fig. 161.</span>—Spherical Aberration Just Outside Focus.</div>
-</div>
-
-<p>A much graver fault is zonal aberration, where some intermediate
-zone of objective or mirror comes to a focus too long or
-too short, generally damaging the definition rather seriously,
-depending on the amount of variation in focus of the faulty zone.
-A typical case is shown in Fig. 162 taken within focus. Here
-two zones are abnormally strong showing, just as in the case of
-simple spherical aberration, too short focus. Outside of focus
-the intensities would change places, the outer and midway zones
-and center being heavy, and the strong zones of Fig. 162 weak.
-These zonal aberrations are easily detected and are rather common
-both in objectives and mirrors, though rarely as conspicuous
-as in Fig. 162.</p>
-
-<p>Another failing is the appearance of astigmatism, which,
-broadly, is due to a refracting or reflecting surface which is not
-a surface of revolution and therefore behaves differently for
-rays incident in different planes around its optical axis. In its
-commonest form the surface reflects or refracts more strongly
-along one plane than along another at right angles to it. Hence
-the two have different foci and there is no point focus at all,
-but two line foci at right angles. Figs. 163 and 164 illustrate
-this fault, the former being taken inside and the latter outside
-focus, under fairly high power. If a star image is oval and the
-major axis of this oval has turned through 90° when one passes to
-the other side of focus, astigmatism is somewhere present.</p>
-
-<p><span class="pagenum"><a name="Page_210" id="Page_210">[Pg 210]</a></span></p>
-
-<p>As more than half of humanity is astigmatic, through fault of
-the eye, one should twist the axis of the eyes some 90° around the
-axis of the telescope and look again. If the axis of the oval has
-turned with the eyes a visit to the oculist is in order. If not, it is
-worth while rotating the ocular. If the oval does not turn with it
-that particular telescope requires reworking before it can be of
-much use.</p>
-
-<div class="figleft">
-<img src="images/i_210a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 162.</span>—A Case of Zonal
- Aberration.</div>
-</div>
-
-<p>This astigmatism due to fault of figure must not be confused
-with the astigmatic difference of the
-image surfaces referred to in Chapter
-IV which is zero on the axis and not
-of material importance in ordinary
-telescopes. Astigmatism of figure on
-the contrary is bad everywhere and
-always. It should be especially looked
-out for in reflecting surfaces, curved
-or plane, since it is a common result
-of flexure.</p>
-
-<p>Passing on now from these simple tests for figure, chromatic
-aberration has to be examined. Nothing is better than an
-artificial star formed by the sun in daylight, for the preliminary
-investigation. At night Polaris is advantageous for this as for
-other tests.</p>
-
-<div class="figcenter">
-<img src="images/i_210b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 163.</span>—Astigmatism Inside Focus.
-<br /><span class="smcap">Fig. 164.</span>—Astigmatism Outside Focus.</div>
-</div>
-
-<p>The achromatization curves, Fig. 163, really tell the whole story
-of what is to be seen. When the telescope is carefully focussed
-for the bright part of the spectrum, getting the sharpest star
-image attainable, the central disc, small and clean, should be
-yellowish white, seen under a power of 60 or 70 per inch of
-aperture.</p>
-
-<p>But the red and blue rays have a longer focus and hence rim
-the image with a narrow purplish circle varying slightly in hue
-according to the character of the achromatization. Pushing<span class="pagenum"><a name="Page_211" id="Page_211">[Pg 211]</a></span>
-the ocular a little inside, focus, the red somewhat overbalances
-the blue and the purple shades toward the red. Pulling out the
-ocular very slightly one brings the deep red into focus as a minute
-central red point, just as the image begins to expand a little.
-Further outside focus a bluish or purplish flare fills the center of
-the field, while around it lies a greenish circle due to the rays
-from the middle of the secondary spectrum expanding from
-their shorter focus.</p>
-
-<p>In an under-corrected objective this red point is brighter and
-the fringe about the image, focussed or within focus, is conspicuously
-reddish. Heavy overcorrection gives a strong bluish
-fringe and the red point is dull or absent. With a low power ocular,
-unless it be given a color correction of its own, any properly corrected
-objective will seem under-corrected as already explained.</p>
-
-<p>The color correction can also be well examined by using an
-ocular spectroscope like Fig. 140, with the cylindrical lens
-removed. Examining the focussed star image thus, the spectrum
-is a narrow line for the middle color of the secondary spectrum,
-widening equally at F and B, and expanding into a sort of brush
-at the violet end. Conversely, when moved outside focus until
-the width is reduced to a narrow line at F and B, the widening
-toward the yellow and green shows very clearly the nature and
-extent of the secondary spectrum. In this way too, the actual
-foci for the several colors can easily be measured.</p>
-
-<p>The exact nature of the color correction is somewhat a matter
-of taste and of the uses for which the telescope is designed, but
-most observers agree in the desirability of the B-F correction
-commonly used as best balancing the errors of eye and ocular.
-With reflectors, achromatic or even over-corrected oculars are
-desirable. The phenomena in testing a telescope for color
-vary with the class of star observed—the solar type is a good
-average. Trying a telescope on [alpha] Lyræ emphasizes unduly the
-blue phases, while [alpha] Orionis would overdo the red.</p>
-
-<p>The simple tests on star discs in and out of focus here described
-are ample for all ordinary purposes, and a glass which passes
-them well is beyond question an admirably figured one. The
-tests are not however quantitative, and it takes an experienced
-eye to pick out quickly minor errors, which are somewhat irregular.
-One sometimes finds the ring system excellent but a sort of
-haze in the field, making the contrasts poor—bad polish or dirt,
-but figure good.</p>
-
-<p><span class="pagenum"><a name="Page_212" id="Page_212">[Pg 212]</a></span></p>
-
-<p>A test found very useful by constructors or those with laboratory
-facilities is the knife edge test, worked out chiefly by Foucault
-and widely used in examining specula. It consists in
-principle of setting up the mirror so as to bring the rays to the
-sharpest possible focus. For instance in a spherical mirror a
-lamp shining through a pin hole is placed in the centre of curvature,
-and the reflected image is brought just alongside it where it
-can be inspected by eye or eyepiece. In Fig. 165 all the rays
-which emanate from the pinhole <i>b</i> and fall on the mirror a are
-brought quite exactly to focus at <i>c</i>. The eye placed close to <i>c</i>
-will see, if the mirror surface is perfect, a uniform disc of light
-from the mirror.</p>
-
-<div class="figcenter">
-<img src="images/i_212a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 165.</span>—The Principle of the Foucault Test.</div>
-</div>
-
-<p>If now a knife edge like <i>d</i>, say a safety razor blade, be very
-gradually pushed through the focus the light will be cut off in
-a perfectly uniform manner—no zone or local spot going first.
-If some error in the surface at any point causes the reflected ray
-to miss the focus and cross ahead of or behind it as in the ray
-<i>bef</i>, then the knife edge will catch it first or last as the case may
-be, and the spot <i>e</i> will be first darkened or remain bright after
-the light elsewhere is extinguished.</p>
-
-<div class="figcenter">
-<img src="images/i_212b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 166.</span>—Foucault Test of Parabolic Mirror.</div>
-</div>
-
-<p>One may thus explore the surface piecemeal and detect not
-only zones but slight variations in the same zone with great
-precision. In case of a parabolic mirror as in Fig. 166 the test<span class="pagenum"><a name="Page_213" id="Page_213">[Pg 213]</a></span>
-is made at the focus by aid of the auxiliary plane mirror, and a
-diagonal as shown, the pinhole and knife edge being arranged
-quite as before. A very good description of the practical use of
-the knife edge test may be found in the papers of Dr. Draper and
-Mr. Ritchey already cited.</p>
-
-<p>It is also applied to refractors, in which case monochromatic
-light had better be used, and enables the experimenter to detect
-even the almost infinitesimal markings sometimes left by the
-polishing tool, to say nothing of slight variations in local figure
-which are continually lost in the general illumination about the
-field when one uses the star test in the ordinary manner.</p>
-
-<p>The set-up for the knife edge experiments should be very steady
-and smooth working to secure precise results, and it therefore is
-not generally used save in the technique of figuring mirrors, where
-it is invaluable. With micrometer motions on the knife edge,
-crosswise and longitudinally, one can make a very exact diagnosis
-of errors of figure or flexure.</p>
-
-<p>A still more delicate method of examining the perfection of
-figuring is found in the Hartmann test. (Zeit. fur Instk.,
-1904, 1909). This is essentially a photographic test, comparing
-the effect of the individual zones of the objective inside and outside
-of focus. Not only are the effects of the zones compared but
-also the effects of different parts of the same zone, so that any lack
-of symmetry in performance can be at once found and measured.</p>
-
-<p>The Hartmann test is shown diagrammatically in Fig. 167.
-The objective is set up for observing a natural or artificial star.
-Just in front of it is placed an opaque screen perforated with
-holes, as shown in section by Fig. 167, where A is the perforated
-screen. The diameters of the holes are about 1/20 the diameter of
-the objective as the test is generally applied, and there are
-usually four holes 90° apart for each zone. And such holes are
-not all in one line, but are distributed symmetrically about the
-screen, care being taken that each zone shall be represented by
-holes separated radially and also tangentially, corresponding to
-the pairs of elements in the two astigmatic image surfaces, an
-arrangement which enables the astigmatism as well as figure to
-be investigated.</p>
-
-<div class="figcenter">
-<img src="images/i_214.jpg" alt="" />
-<div class="caption"> <span class="smcap">Fig. 167.</span>—The Principle of the Hartmann Test.</div>
-</div>
-
-<p>The arrangement of holes actually found useful is shown in
-Hartmann’s original papers, and also in a very important paper by
-Plaskett (Ap. J. <i>25</i> 195) which contains the best account in
-English of Hartmann’s methods and their application. Now<span class="pagenum"><a name="Page_214" id="Page_214">[Pg 214]</a><br /><a name="Page_215" id="Page_215">[Pg 215]</a></span>
-each hole in the screen transmits a pencil of light through the
-objective at the corresponding point, and each pencil comes to a
-focus and then diverges, the foci being distributed somewhere in
-the vicinity of what one may regard as the principal focus, <i>B</i>.
-For instance in Fig. 167 are shown five pairs of apertures <i>a</i>, <i>a′</i>,
-<i>b</i>, <i>b′</i>, etc., in five different zones. Now if a photographic plate
-be exposed a few inches inside focus as at C each pencil from an
-aperture in the screen will be represented by a dot on the photograph,
-at such distance from the axis and from the corresponding
-dot on the other side of the axis as the respective inclinations of
-the pencils of light may determine.</p>
-
-<p>Similarly a plate exposed at approximately equal distance on
-the other side of the general focus, as at <i>D</i>, will show a pattern of
-dots due to the distribution of the several rays at a point beyond
-focus. Now if all the pencils from the several apertures met at
-a common focus in <i>B</i>, the two patterns on the plates <i>C</i> and <i>D</i>
-would be exactly alike and for equal distance away from focus of
-exactly the same size. In general the patterns will not exactly
-correspond, and the differences measured with the micrometer
-show just how much any ray in question has departed from
-meeting at an exact common focus with its fellows.</p>
-
-<p>For instance in the cut it will be observed that the rays <i>e</i> and
-<i>a′</i> focus barely beyond <i>C</i> and by the time they reach <i>D</i> are well
-spread apart. The relative distance of the dots upon these
-corresponding plates, with the distance between the plates, shows
-exactly at what point between <i>C</i> and <i>D</i> these particular rays
-actually did cross and come to a focus.</p>
-
-<p>Determining this is merely a matter of measuring up similar
-triangles, for the path of the rays is straight. Similarly inspection
-will show that the rays <i>d</i> and <i>d′</i> meet a little short of <i>B</i>, and
-measurement of their respective records on the plates <i>C</i> and <i>D</i>
-would show the existence of a zone intermediate in focus between
-the focus of <i>e,e′</i> and the general focus at <i>B</i>. The exact departure
-of this zone from correct focus can therefore be at once measured.</p>
-
-<p>A little further examination discloses the fact that the outer
-zone represented by the rays <i>a,b</i>, and <i>a′,b′</i> has not quite the same
-focus at the two extremities of the same diameter of the objective.
-In other words the lens is a little bit flatter at one end of this
-diameter than it is at the other, so that the rays here have considerably
-longer focus than they should, a fault by no means
-unknown although fortunately not very common.</p>
-
-<p><span class="pagenum"><a name="Page_216" id="Page_216">[Pg 216]</a></span></p>
-
-<p>It will be seen that the variations between the two screen
-patterns on <i>C</i> and <i>D</i>, together with the difference between them,
-give accurately the performance of each point of the objective
-represented by an aperture in the screen. And similar investigations
-by substantially the same method may be extended to the
-astigmatic variations, to the general color correction, and to the
-difference in the aberrations for the several colors. The original
-papers cited should be consulted for the details of applying this
-very precise and interesting test.</p>
-
-<p>It gives an invaluable record of the detailed corrections of an
-objective, and while it is one with which the ordinary observer
-has little concern there are times when nothing else can give with
-equal precision the necessary record of performance. There
-are divers other tests used for one purpose or another in examining
-objectives and mirrors, but those here described are ample
-for nearly all practical purposes, and indeed the first two commonly
-disclose all that it is necessary to know.</p>
-
-<p>Now and then one has to deal with an objective which is
-unmitigatedly dirty. It can be given a casual preliminary cleaning
-in the way already mentioned, but sometimes even this will
-not leave it in condition for testing. Then one must get down
-to the bottom of things and make a thorough job of it.</p>
-
-<p>The chief point to remember in undertaking this is that the
-thing which one is cleaning is glass, and very easy to scratch if
-one rubs dust into it, but quite easy to clean if one is careful.
-The second thing to be remembered is that once cleaned it must
-be replaced as it was before and not in some other manner.</p>
-
-<p>The possessor of a dirty objective is generally advised to take
-it to the maker or some reliable optician. If the maker is handy,
-or an optician of large experience in dealing with telescope
-objectives is available, the advice is good, but there is no difficulty
-whatever in cleaning an objective with the exercise of that
-ordinary care which the user of a telescope may be reasonably
-expected to possess.</p>
-
-<p>It is a fussy job, but not difficult, and the best advice as to how
-to clean a telescope objective is to “tub” it, literally, if beyond
-the stage where the superficial wiping described is sufficient.</p>
-
-<p>To go about the task one first sets down the objective in its
-cell on a horizontal surface and removes the screws that hold in
-the retaining ring, or unscrews the ring itself as the case may be.
-This leaves the cell and objective with the latter uppermost and<span class="pagenum"><a name="Page_217" id="Page_217">[Pg 217]</a></span>
-free to be taken out. Prepare on a table a pad of anything soft,
-a little smaller than the objective, topping the pad with soft
-and clean old cloth; then, raising up the cell at an edge, slip the
-two thumbs under it and lay the fingers lightly on the outer lens
-of the objective, then invert the whole affair upon the pad and
-lift off the cell, leaving the objective on its soft bed.</p>
-
-<p>Before anything else is done the edge of the objective should
-be marked with a hard lead pencil on the edge of both the component
-lenses, making two well defined v’s with their points
-touching. Also, if, as usual, there are three small separators
-between the edges of the flint and crown lenses, mark the position
-of each of these 1, 2, 3, with the same pencil.</p>
-
-<p>Forming another convenient pad of something soft, lift off the
-upper lens, take out the three separators and lay them in order
-on a sheet of paper without turning them upside down. Mark
-alongside each, the serial number denoting its position. Then
-when these spacers, if in good condition, are put back, they will
-go back in the same place rightside up, and the objective itself
-will go back into place unchanged.</p>
-
-<p>Now have at hand a wooden or fibre tub or basin which has
-been thoroughly washed out with soap and water and wiped
-dry. Half fill it with water slightly lukewarm and with a good
-mild toilet soap, shaving soap for example, with clean hands and
-very soft clean cloth, go at one of the lenses and give it a thorough
-washing. After this it should be rinsed very thoroughly and
-wiped dry. As to material for wiping, the main thing is that it
-must be soft and free from dust that will scratch. Old handkerchiefs
-serve a good turn.</p>
-
-<p>Dr. Brashear years ago in describing this process recommended
-cheese cloth. The present day material that goes under this
-name is far from being as soft at the start as it ought to be, and
-only the best quality of it should be used, and then only after
-very thorough soaking, rinsing and drying. The very soft towels
-used for cleaning cut glass, if washed thoroughly clean and kept
-free from dust, answer perfectly well. The cheese cloth has the
-advantage of being comparatively cheap so that it can be thrown
-away after use. Whatever the cloth, it should be kept, after
-thorough washing and drying, in a closed jar.</p>
-
-<p>Rinsing the lens thoroughly and wiping it clean and dry is the
-main second stage of cleansing. It sometimes will be found to be
-badly spotted in a way which this washing will not remove.<span class="pagenum"><a name="Page_218" id="Page_218">[Pg 218]</a></span>
-Sometimes the spotting will yield to alcohol carefully rubbed
-on with soft absorbent cotton or a bunch of lens paper.</p>
-
-<p>If alcohol fails the condition of the surface is such as to justify
-trying more strenuous means. Nitric acid of moderate strength
-rubbed on with a swab of absorbent cotton will sometimes clear
-up the spotting. If this treatment be used it should be followed
-up with a 10 per cent solution of pure caustic potash or moderately
-strong c.p. ammonia and then by very thorough rinsing.
-Glass will stand without risk cautious application of both acid
-and alkali, but the former better than the latter.</p>
-
-<p>Then a final rinsing and drying is in order. Many operators
-use a final washing with alcohol of at least 90 per cent strength
-which is allowed to evaporate with little or no wiping. Alcohol
-denatured with methyl alcohol serves well if strong enough but
-beware denatured alcohol of unknown composition. Others
-have used petroleum naphtha and things of that sort. At the
-present time these commercial petroleum products are extremely
-uncertain in quality, like gasoline, being obtained, Heaven knows
-how, from the breaking down of heavier petroleum products.</p>
-
-<p>If pure petroleum ether can be obtained it answers quite as
-well as alcohol, but unless the volatile fluid is pure it may leave
-streaks. Ordinarily neither has to be used, as after the proper
-wiping the glass comes perfectly clean. This done the glass can
-be replaced on the pad whence it came and its mate put through
-the same process.</p>
-
-<p>Flint glass is more liable to spot than the crown, but the crown
-is by no means immune against the deterioration of the surface,
-perhaps incipient devitrification, and during the war many
-objectives “went blind” from unexplained action of this character.
-As a rule the soap and water treatment applied with care
-leaves even a pretty hard looking specimen of objective in
-fairly good condition except for the scratches which previous
-users have put upon it.</p>
-
-<p>Then if the spacing pieces, usually of tinfoil, are not torn or
-corroded they can be put back into place, the one lens superimposed
-upon the other, and the pair put back into the cell by
-dropping it gently over them and re-inverting the whole, taking
-care this time to have soft cloth or lens paper under the fingers.
-Then the retaining ring can be put into place again and the
-objective is ready for testing or use as the case may be.</p>
-
-<p>If the spacers are corroded or damaged it may be necessary<span class="pagenum"><a name="Page_219" id="Page_219">[Pg 219]</a></span>
-to replace them with very thin tinfoil cut the same size and shape,
-leaving however a little extra length to turn down over the edge
-of the lower lens. They are fastened in place on the extreme
-edge only by the merest touch of mucilage, shellac or Canada balsam,
-whichever comes to hand. The one important thing is that
-the spacers should be entirely free of the sticky material where
-they lap over the edge of the lens to perform the separation.
-This lap is generally not over 1/16 of an inch, not enough to show
-at the outside of the objective when it is in its cell. When the
-upper lens is lightly pressed down into place, after the gum or
-shellac is dry, all the projecting portion can be trimmed away
-with a sharp pen-knife leaving simply the spacers in the appointed
-places from which the original ones were removed.</p>
-
-<p>Some little space has been given to this matter of cleaning
-objectives, as in many situations objectives accumulate dirt
-rather rapidly and it is highly desirable for the user to learn how
-to perform the simple but careful task of cleansing them.</p>
-
-<p>In ordinary use, when dirt beyond the reach of mere dusting
-with a camel’s hair brush has stuck itself to the exterior of an
-objective, a succession of tufts of absorbent cotton or wads of
-lens paper at first dampened with pure water or alcohol and then
-followed lightly, after the visible dirt has been gently mopped up,
-by careful wiping with the same materials, will keep the exterior
-surface in good condition, the process being just that suggested
-in the beginning of this chapter as the ordinary cleaning up preparatory
-to a thorough examination.</p>
-
-<p>The main thing to be avoided in the care of a telescope, aside
-from rough usage generally, is getting the objective wet and then
-letting it take its chances of drying. In many climates dew is a
-very serious enemy and the customary dew cap three or four
-diameters long, bright on the outside and blackened within, is of
-very great service in lessening the deposit of dew upon the glass.
-Also the dew cap keeps out much stray light that might otherwise
-do mischief by brightening the general field. In fact its function
-as a light-trap is very important especially if it is materially
-larger in diameter than the objective and provided with stops.</p>
-
-<p>The finder should be similarly protected, otherwise it will
-mysteriously go blind in the middle of an evening’s work due
-to a heavy deposit of moisture on the objective. The effect
-is an onset of dimness and bad definition which is altogether
-obnoxious.</p>
-
-<p><span class="pagenum"><a name="Page_220" id="Page_220">[Pg 220]</a></span></p>
-
-<p>As regards the metal parts of a telescope they should be treated
-like the metal parts of any other machine, while the moving
-parts require from time to time a little touch of sperm or similar
-oil like every other surface where friction may occur.</p>
-
-<p>The old fashioned highly polished and lacquered brass tube
-was practically impossible to keep looking respectably well
-provided it was really used to any considerable extent. About
-the most that could be done to it was dusting when dusty, and
-cautiously and promptly wiping off any condensed moisture.
-The more modern lacquered tubes require very little care and if
-they get in really bad condition can be relacquered without much
-expense or difficulty.</p>
-
-<p>Wooden tubes, occasionally found in old instruments, demand
-the treatment which is accorded to other highly finished wooden
-things, occasional rubbing with oil or furniture polish according
-to the character of the original surface. Painted tubes may
-occasionally require a fresh coat, which it does not require great
-skill to administer. If the surface of wooden tripods comes to
-be in bad shape it needs the oil or polish which would be accorded
-to other well finished wooden articles.</p>
-
-<p>Mountings are usually painted or lacquered and either surface
-can be renewed eventually at no great trouble. Bright parts
-may be lightly touched with oil as an ordinary rust preventive.</p>
-
-<p>Reflecting telescopes are considerably more troublesome to
-keep in order than refractors owing to the tender nature of the
-silvered surface. It may remain in good condition with fairly
-steady use for several years or it may go bad in a few months or a
-few weeks. The latter is not an unusual figure in telescopes
-used about a city where smoke is plentiful. The main thing is
-to prevent the deposit of dew on the mirror, or getting it wet in
-any other way, for in drying off the drops almost invariably
-leave spots.</p>
-
-<p>Many schemes have been proposed for the prevention of injury
-to the mirror surface. A close fitting metal cover, employed
-whenever the mirror is not in use, has given good results in many
-places. Where conditions are extreme this is sometimes lined
-with a layer of dry absorbent cotton coming fairly down upon
-the mirror surface, and if this muffler is dry, clean, and a little
-warmer than the mirror when put on, it seems to be fairly
-effective. Preferably the mirror should be kept, when not in<span class="pagenum"><a name="Page_221" id="Page_221">[Pg 221]</a></span>
-use, at a little higher temperature than the surrounding air so
-that dew will not tend to deposit upon it.</p>
-
-<p>As to actual protective measures the only thing that seems
-to be really efficient is a very thin coating of lacquer, first tried by
-Perot at the Paris Observatory. The author some ten years
-since took up the problem in protecting some laboratory mirrors
-against fumes and moisture and found that the highest grade of
-white lacquer, such as is used for the coating of fine silverware in
-the trade, answered admirably if diluted with six or eight volumes
-of the thinner sold with such commercial lacquers. It is best to
-thin the lacquer to the requisite amount and then filter.</p>
-
-<p>If now a liberal amount of the mixture is poured upon the
-mirror surface after careful dusting, swished quickly around,
-and the mirror is then immediately turned up on edge to drain
-and dry, a very thin layer of lacquer will be left upon it, only a
-fraction of a wave length thick, so that it shows broad areas of
-interference colors.</p>
-
-<p>Treated in this way and kept dry the coating will protect the
-brilliancy of the silver for a good many months even under rather
-unfavorable circumstances. After trying out the scheme rather
-thoroughly the treatment was applied to the 24 inch reflector of
-the Harvard Observatory and has been in use ever since. The
-author applied the first coating in the spring of 1913, and since
-that time it has only been necessary to resilver perhaps once in
-six months as against about as many weeks previously.</p>
-
-<p>The lacquer used in this case was the so-called “Lastina”
-lacquer made by the Egyptian Lacquer Company of New York,
-but there are doubtless others of similar grade in the market.
-It is a collodion lacquer and in recent years it has proved desirable
-to use as a thinner straight commercial amylacetate rather than
-the thinner usually provided with the lacquer, perhaps owing to
-the fact that difficulty of obtaining materials during the war
-may have caused, as in so many other cases, substitutions which,
-while perfectly good for the original purpose did not answer so
-well under the extreme conditions required in preserving telescope
-mirrors.</p>
-
-<p>The lacquer coating when thinned to the extent here recommended
-does not apparently in any way deteriorate the definition
-as some years of regular work at Harvard have shown. Some
-experimenters have, however, found difficulty, quite certainly
-owing to using too thick a lacquer. The endurance of a lacquer<span class="pagenum"><a name="Page_222" id="Page_222">[Pg 222]</a></span>
-coating where the mirror is kept free from moisture, and
-its power to hold the original brilliancy of the surface is very
-extraordinary.</p>
-
-<p>The writer took out and tested one laboratory mirror coated
-seven years before, and kept in a dry place, and found the
-reflecting power still a little above .70, despite the fact that the
-coating was so dry as to be almost powdery when touched with a
-tuft of cotton. At the start the mirror had seen some little use
-unprotected and its reflection coefficient was probably around .80.
-If the silver coating is thick as it can be conveniently made, on a
-well coated mirror, the coat of lacquer, when tarnish has begun,
-can be washed off with amylacetate and tufts of cotton until the
-surface is practically clear of it, and the silver itself repolished
-by the ordinary method and relacquered.</p>
-
-<p>There are many silvering processes in use and which one
-should be chosen for re-silvering a mirror, big or little, is quite
-largely a matter of individual taste, and more particularly experience.
-The two most used in this country are those of Dr.
-Brashear and Mr. Lundin, head of the Alvan Clark Corporation,
-and both have been thoroughly tried out by these experienced
-makers of big mirrors.</p>
-
-<p>The two processes differ in several important particulars but
-both seem to work very successfully. The fundamental thing
-in using either of them is that the glass surface to be silvered
-should be chemically clean. The old silver, if a mirror is being
-resilvered, is removed with strong nitric acid which is very
-thoroughly rinsed off after every trace of silver has been removed.
-Sometimes a second treatment with nitric acid may advantageously
-follow the first with more rinsing. The acid should be
-followed by a 10 per cent solution of c.p. caustic potash (some
-operators use c.p. ammonia as easier to clear away) rinsed off
-with the utmost thoroughness.</p>
-
-<p>On general principles the last rinsing should be with distilled
-water and the glass surface should not be allowed to dry between
-this rinsing and starting the silvering process, but the whole
-mirror should be kept under water until the time for silvering.
-In Dr. Brashear’s process the following two solutions are made
-up; first the reducing solution as follows:</p>
-
-
-<ul><li>Rock candy, 20 parts by weight.</li>
-<li>Strong nitric acid (spec. gr. 1.22), 1 part.</li>
-<li>Alcohol, 20 parts.</li>
-<li><span class="pagenum"><a name="Page_223" id="Page_223">[Pg 223]</a></span></li>
-<li>Distilled water, 200 parts.</li>
-</ul>
-
-<p>This improves by keeping and if this preparation has to be
-hurried the acid, sugar and distilled water should be boiled
-together and then the alcohol added after the solution is cooled.</p>
-
-<p>Second, make up the silvering solution in three distinct portions;
-first the silver solution proper as follows:</p>
-
-<ul>
-<li>1. 2 parts silver nitrate. 20 parts distilled water.</li>
-<li>Second, the alkali solution as follows:</li>
-<li>2. 1⅓ parts c.p. caustic potash. 20 parts distilled water.</li>
-<li>Third, the reserve silver solution as follows:</li>
-<li>3. &frac14; part silver nitrate. 16 parts distilled water.</li>
-</ul>
-
-
-<p>The working solution of silver is then prepared thus: Gradually
-add to the silver solution No. 1 the strongest ammonia, slowly
-and with constant stirring. At first the solution will turn dark
-brown and then it will gradually clear up. Ammonia should be
-added only just to the point necessary to clear the solution.</p>
-
-<p>Then add No. 2, the alkali solution. Again the mixture will
-turn dark brown and must be cautiously cleared once more with
-ammonia until it is straw colored but clear of precipitate.
-Finally add No. 3, the reserve solution, very cautiously with
-stirring until the solution grows darker and begins to show traces
-of suspended matter which will not stir out. Then filter the
-whole through absorbent cotton to free it of precipitate and it is
-ready for use. One is then ready for the actual silvering.</p>
-
-<p>Now there are two ways of working the process, with the
-mirror face up, or face down. The former is advantageous in
-allowing better inspection of the surface as it forms, and also it
-permits the mirror of a telescope to be silvered without removing
-it from the cell, as was in fact done habitually in case of the big
-reflector of the Alleghany Observatory where the conditions
-were such as to demand re-silvering once a month. The solution
-was kept in motion during the process by rocking the telescope
-as a whole.</p>
-
-<p>When silvering face up the mirror is made to form the bottom
-of the silvering vessel, being fitted with a wrapping of strong
-paraffined or waxed paper or cloth, wound several times around
-the rim of the mirror and carried up perhaps half the thickness
-of the mirror to form a retainer for the silvering solution. This
-band is firmly tied around the edge of the mirror making a water
-tight joint. Ritchey uses a copper band fitted to the edge of<span class="pagenum"><a name="Page_224" id="Page_224">[Pg 224]</a></span>
-the mirror and drawn tight by screws, and finishes making
-tight with paraffin and a warm iron.</p>
-
-<p>In silvering face down the mirror is suspended a little distance
-above the bottom of a shallow dish, preferably of earthen ware,
-containing the solution. Various means are used for supporting
-it. Thus cleats across the back cemented on with hard optician’s
-pitch answer well for small mirrors, and sometimes special
-provision is made for holding the mirror by the extreme edge in
-clamps.</p>
-
-<p>Silvering face down is in some respects less convenient but
-does free the operator from the very serious trouble of the heavy
-sediment which is deposited from the rather strong silver solution.
-This is the essential difficulty of the Brashear process in silvering
-face up. The trouble may be remedied by very gentle swabbing
-of the surface under the liquid with absorbent cotton, from the
-time when the silver coating begins fairly to form until it is
-completed.</p>
-
-<p>The Brashear process is most successfully worked at a temperature
-between 65° and 70° F. and some experience is required
-to determine the exact proportion of the reducing solution to be
-added to the silvering solution. Ritchey advises such quantity
-of the reducing solution as contains of sugar one-half the total
-weight of the silver nitrate used. The total amount of solution
-after mixing should cover the mirror about an inch deep. Too
-much increases the trouble from sediment and fails to give a
-clean coating. The requisite quantity of reducing solution is
-poured into the silvering solution and then immediately, if the
-mirror is face up, fairly upon it, without draining it of the water
-under which it has been standing.</p>
-
-<p>If silvering face down the face will have been immersed in a
-thin layer of distilled water and the mixed solutions are poured
-into the dish. In either case the solution is rocked and kept
-moving pretty thoroughly until the process is completed which
-will take about five minutes. If silvering is continued too long
-there is likelihood of an inferior whitish outer surface which will
-not polish well, but short of this point the thicker the coat the
-better, since a thick coat stands reburnishing where a thin one
-does not and moreover the thin one may be thin enough to
-transmit some valuable light.</p>
-
-<p>When the silvering is done the solution should be rapidly
-poured off, the edging removed or the mirror lifted out of the<span class="pagenum"><a name="Page_225" id="Page_225">[Pg 225]</a></span>
-solution, rinsed off first with tap water and then with distilled,
-and swabbed gently to clear the remaining sediment. Then the
-mirror can be set up on edge to dry. A final flowing with alcohol
-and the use of a fan hastens the process.</p>
-
-<p>In Lundin’s method the initial cleaning process is the same but
-after the nitric acid has been thoroughly rinsed off the surface is
-gently but thoroughly rubbed with a saturated solution of tin
-chloride, applied with a wad of absorbent cotton. After the
-careful rubbing the tin chloride solution must be washed off
-with the utmost thoroughness, preferably with moderately warm
-water. It is just as important to get off the tin chloride completely,
-as it is to clean completely the mirror surface by its use.
-Otherwise streaks may be left where the silvering will not take
-well.</p>
-
-<p>When the job has been properly done one can wet the whole
-surface with a film of water and it will stay wet even when the
-surface is slightly tilted. As in the Brashear process the mirror
-must be kept covered with water. Mr. Lundin always silvers
-large mirrors face up, and forms the dish by wrapping around the
-edge of the mirror a strip of bandage cloth soaked in melted
-beeswax and smoothed off by pulling it while still hot between
-metal rods to secure even distribution of the wax so as to make a
-water tight joint. This rim of cloth is tied firmly around the
-edge of the mirror and the strings then wet to draw them
-still tighter.</p>
-
-<p>Meanwhile the water should cover the mirror by &frac34; of an inch
-or more. It is to be noted that in the Lundin process ordinary
-water is usually found just as efficient as distilled water, but it is
-hardly safe to assume that such is the case, without trying it out
-on a sample of glass.</p>
-
-<p>There are then prepared two solutions, a silver solution,<br />
-
-<span class="i4">2.16 parts silver nitrate (see King, Pop. Ast <b>30</b>, 93)</span><br />
-
-<span class="i4">100 parts water.</span><br />
-
-and a reducing solution,<br />
-
-<span class="i4">4 parts Merck’s formaldehyde</span><br />
-
-<span class="i4">20 parts water.</span></p>
-
-
-<p>This latter quantity is used for each 100 parts of the above silver
-solution, and the whole quantity made up is determined by the
-amount of liquid necessary to cover the mirror as just described.</p>
-
-<p>The silver solution is cautiously and completely cleared up by
-strong ammonia as in the Brashear process. The silver and<span class="pagenum"><a name="Page_226" id="Page_226">[Pg 226]</a></span>
-reducing solutions are then mixed, the water covering the mirror
-poured quickly off, and the silvering solution immediately poured
-on. The mirror should then be gently rocked and the silver coating
-carefully watched as it forms.</p>
-
-<p>As the operation is completed somewhat coarse black grains
-of sediment will form and when these begin to be in evidence the
-solution should be poured off, the mirror rinsed in running water,
-the edging removed while the mirror is still rinsing and finally the
-sediment very gently swabbed off with wet absorbent cotton.
-Then the mirror can be set up to dry.</p>
-
-<p>The Lundin process uses a considerably weaker silver solution
-than the Brashear process, is a good deal more cleanly while in
-action, and is by experienced workers said to perform best at a
-materially lower temperature than the Brashear process, with the
-mirror, however, always slightly warmer than the solution.
-Some workers have had good results by omitting the tin chloride
-solution and cleaning up the surface by the more ordinary
-methods. In the Lundin process the solution is sufficiently clear
-for the density acquired by the silver coating to be roughly
-judged by holding an incandescent lamp under the mirror. A
-good coating should show at most only the faintest possible outline
-of the filament, even of a gas filled lamp.</p>
-
-<p>Whichever process of silvering is employed, and both work
-well, the final burnishing of the mirror after it is thoroughly
-dry is performed in the same way, starting by tying up a very
-soft ball of absorbent cotton in the softest of chamois skin.</p>
-
-<p>This burnisher is used at first without any addition, simply to
-smooth and condense the film by going over it with quick, short,
-and gentle circular strokes until the entire surface has been
-thoroughly cleaned and begins to show a tendency to take polish.
-Then a very little of the finest optical rouge should be put on to
-the same, or better another, rubber, and the mirror gone steadily
-over in a similar way until it comes to a brilliant polish.</p>
-
-<p>A good deal of care should be taken in performing this operation
-to avoid the settling of dust upon the surface since scratches will
-inevitably result. Great pains should also be taken not to take
-any chance of breathing on the mirror or in any other way getting
-the surface in the slightest degree damp. Otherwise it will not
-come to a decent polish.</p>
-
-<p>Numerous other directions for silvering will be found in the
-literature, and all of them have been successfully worked at one<span class="pagenum"><a name="Page_227" id="Page_227">[Pg 227]</a></span>
-time or another. The fundamental basis of the whole process is
-less in the particular formula used than in the most scrupulous
-care in cleaning the mirror and keeping it clean until the silvering
-is completed. Also a good bit of experience is required to enable
-one to perform the operation so as to obtain a uniform and dense
-deposit.</p>
-
-<hr class="chap" />
-
-<p><span class="pagenum"><a name="Page_228" id="Page_228">[Pg 228]</a></span></p>
-
-
-
-
-<div class="chapter"></div>
-<h2><a name="CHAPTER_X" id="CHAPTER_X">CHAPTER X</a><br />
-
-<small>SETTING UP AND HOUSING THE TELESCOPE</small></h2>
-
-
-<p>In regard to getting a telescope into action and giving it
-suitable protection, two entirely different situations present
-themselves. The first relates to portable instruments or those
-on temporary mounts, the second to instruments of position.
-As respects the two, the former ordinarily implies general use
-for observational purposes, the latter at least the possibility
-of measurements of precision, and a mount usually fitted with
-circles and with a driving clock. Portable telescopes may have
-either alt-azimuth or equatorial mounting, while those permanently
-set up are now quite universally equatorials.</p>
-
-<p>Portable telescopes are commonly small, ranging from about
-2&frac12; inches to about 5 inches in aperture. The former is the smallest
-that can fairly be considered for celestial observations. If
-thoroughly good and well mounted even this is capable of real
-usefulness, while the five inch telescope if built and equipped
-in the usual way, is quite the heaviest that can be rated as
-portable, and deserves a fixed mount.</p>
-
-<p>Setting up an alt-azimuth is the simplest possible matter.
-If on a regular tripod it is merely taken out and the tripod
-roughly levelled so that the axis in azimuth is approximately
-vertical. Now and then one sets it deliberately askew so that
-it may be possible to pass quickly between two objects at somewhat
-different altitudes by swinging on the azimuth axis.</p>
-
-<p>If one is dealing with a table tripod like Fig. 69 it should merely
-be set on any level and solid support that may be at hand, the
-main thing being to get it placed so that one may look through
-it conveniently. This is a grave problem in the case of all
-small refractors, which present their oculars in every sort of
-unreachable and uncomfortable position.</p>
-
-<p>Of course a diagonal eyepiece promises a way out of the
-difficulty, but with small apertures one hesitates to lose the
-light, and often something of definition, and the observer must
-pretty nearly stand on his head to use the finder. With well<span class="pagenum"><a name="Page_229" id="Page_229">[Pg 229]</a></span>
-adjusted circles, such are commonly found on a fixed mount,
-location of objects is easy. On a portable set-up perhaps the
-easiest remedy is a pair of well aligned coarse sights near the
-objective end of the tube and therefore within reach when
-it is pointed zenith-ward. The writer has found a low, armless,
-cheap splint rocker, such as is sold for piazza use,
-invaluable under these painful circumstances, and can cordially
-recommend it.</p>
-
-<p>Even better is an observing box and a flat cushion. The
-box is merely a coverless affair of any smooth 7/8 inch stuff
-firmly nailed or screwed together, and of three unequal dimensions,
-giving three available heights on which to sit or stand.
-The dimensions originally suggested by Chambers (<i>Handbook
-of Astronomy</i>, II, 215) were 21 × 12 × 15 inches, but the writer
-finds 18 × 10 × 14 inches a better combination.</p>
-
-<p>The fact is that the ordinary stock telescope tripod is rather
-too high for sitting, and too low for standing, comfortably.
-A somewhat stubby tripod is advantageous both in point of
-steadiness and in accessibility of the eyepiece when one is
-observing within 30° of the zenith, where the seeing is at its
-best; and a sitting position gives a much greater range of convenient
-upward vision than a standing one.</p>
-
-<p>When an equatorial mount is in use one faces the question of
-adjustment in its broadest aspect. Again two totally different
-situations arise in using the telescope. First is the ordinary
-course of visual observation for all general purposes, in which
-no precise measurements of position or dimensions are involved.</p>
-
-<p>Here exact following is not necessary, a clock drive is convenient
-rather than at all indispensable, and even circles one
-may get along without at the cost of a little time. Such is the
-usual situation with portable equatorials. One does not then
-need to adjust them to the pole with extreme precision, but
-merely well enough to insure easy following; otherwise one is
-hardly better off than with an alt-azimuth.</p>
-
-<p>In a totally different class falls the instrument with which one
-undertakes regular micrometric work, or enters upon an extended
-spectroscopic program or the use of precise photometric apparatus,
-to say nothing of photography. In such cases a permanent
-mount is almost imperative, the adjustments must be made
-with all the exactitude practicable, one finds great need of
-circles, and the lack of a clock drive is a serious handicap or worse.</p>
-
-<p><span class="pagenum"><a name="Page_230" id="Page_230">[Pg 230]</a></span></p>
-
-<p>Moreover in this latter case one usually has, and needs, some
-sort of timepiece regulated to sidereal time, without which a
-right ascension circle is of very little use.</p>
-
-<p>In broad terms, then, one has to deal, first; with a telescope
-on a portable mount, with or without position circles, generally
-lacking both sidereal clock and driving clock, and located where
-convenience dictates; second, with a telescope on a fixed mount
-in a permanent location, commonly with circles and clock,
-and with some sort of permanent housing.</p>
-
-<p>Let us suppose then that one is equipped with a 5 inch instrument
-like Fig. 168, having either the tripod mount, or the fixed
-pillar mount shown alongside it; how shall it be set up, and, if
-on the fixed mount, how sheltered?</p>
-
-<p>In getting an equatorial into action the fundamental thing
-is to place the optical axis of the telescope exactly parallel to
-the polar axis of the mount and to point the latter as nearly as
-possible at the celestial pole.</p>
-
-<p>The conventional adjustments of an equatorial telescope are
-as follows:</p>
-
-<p>1. Adjust polar axis to altitude of pole.</p>
-
-<p>2. Adjust index of declination circle.</p>
-
-<p>3. Adjust polar axis to the meridian.</p>
-
-<p>4. Adjust optical axis perpendicular to declination axis.</p>
-
-<p>5. Adjust declination axis perpendicular to polar axis.</p>
-
-<p>6. Adjust index of right ascension circle, and</p>
-
-<p>7. Adjust optical axis of finder parallel to that of telescope.</p>
-
-<p>Now let us take the simplest and commonest case, the adjustment
-of a portable equatorial on a tripod mount, when the
-instrument has a finder but neither circles nor driving clock.
-Adjustments 2 and 6 automatically drop out of sight, 5 vanishes
-for lack of any means to make the adjustment, and on a mount
-made with high precision, like the one before us, 4 is negligible
-for any purpose to which our instrument is applicable.</p>
-
-<p>Adjustments 1, 3 and 7 are left and these should be performed
-in the order 7, 1, 3, for sake of simplicity. To begin with the
-finder has cross-wires in the focus of its eyepiece, and the next
-step is to provide the telescope itself with similar cross-wires.</p>
-
-<p>These can readily be made, if not provided, by cutting out a
-disc of cardboard to fit snugly either the spring collar just in front
-of a positive eyepiece or the eyepiece itself at the diaphragm,
-if an ordinary Huygenian. Rule two diametral lines on the<span class="pagenum"><a name="Page_231" id="Page_231">[Pg 231]</a></span>
-circle struck for cutting the cardboard, crossing at the center,
-cut out the central aperture, and then very carefully stretch
-over it, guided by the diametral lines, two very fine threads or
-wires made fast with wax or shellac.</p>
-
-<div class="figcenter">
-<img src="images/i_231.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 168.</span>—Clark 5-inch with Tripod and Pier.</div>
-</div>
-
-<p>Now pointing the telescope at the most distant well defined
-object in view, rotate the spring collar or ocular, when, if the
-crossing of the threads is central, their intersection should stay<span class="pagenum"><a name="Page_232" id="Page_232">[Pg 232]</a></span>
-on the object. If not shift a thread cautiously until the error
-is corrected.</p>
-
-<p>Keeping the intersection set on the object by clamping the tube,
-one turns attention to the finder. Either the whole tube is adjustable
-in its supports or the cross-wires are capable of adjustment
-by screws just in front of the eyepiece. In either case finder tube
-or cross-wires should be shifted until the latter bear squarely upon
-the object which is in line with the cross threads of the main
-telescope. Then the adjusting screws should be tightened, and
-the finder is in correct alignment.</p>
-
-<p>As to adjustments 1 and 3, in default of circles the ordinary
-astronomical methods are not available, but a pretty close
-approximation can be made by levelling. A good machinist’s
-level is quite sensitive and reliable. The writer has one picked
-out of stock at a hardware shop that is plainly sensitive to 2′
-of arc, although the whole affair is but four inches long.</p>
-
-<p>Most mounts like the one of Fig. 168 have a mark ruled on
-the support of the polar axis and a latitude scale on one of the
-cheek pieces. Adjustment of the polar axis to the correct
-altitude is then made by placing the level on the declination
-axis, or any other convenient place, bringing it to a level, and
-then adjusting the tripod until the equatorial head can be revolved
-without disturbing this level. Then set the polar axis to the
-correct latitude and adjustment number 1 is complete for the
-purpose in hand.</p>
-
-<p>Lacking a latitude scale, it is good judgment to mark out
-the latitude by the help of the level and a paper protractor. To
-do this level the polar axis to the horizontal, level the telescope
-tube also, and clamp it in declination to maintain it parallel.
-Then fix the protractor to a bit of wood tied or screwed to the
-telescope support, drop a thin thread plumb line from a pin
-driven into the wood, the declination axis being still clamped,
-note the protractor reading, and then raise the polar axis by
-the amount of the latitude.</p>
-
-<p>Next, with a knife blade scratch a conspicuous reference line
-on the sleeve of the polar axis and its support so that when the
-equatorial head is again levelled carefully you can set approximately
-to the latitude at once.</p>
-
-<p>Now comes adjustment 3, the alignment of the polar axis to
-the meridian. One can get it approximately by setting the
-telescope tube roughly parallel with the polar axis and, sighting<span class="pagenum"><a name="Page_233" id="Page_233">[Pg 233]</a></span>
-along it, shifting the equatorial head in azimuth until the tube
-points to the pole star. Then several methods of bettering the
-adjustment are available.</p>
-
-<p>At the present date Polaris is quite nearly 1° 07′ from the true
-pole and describes a circle of that radius about it every 24 hours.
-To get the correct place of the pole with reference to Polaris
-one must have at least an approximate knowledge of the place
-of that star in its little orbit, technically its hour-angle. With
-a little knowledge of the stars this can be told off in the skies
-almost as easily as one reckons time on a clock. Fig. 169 is, in
-fact, the face of the cosmic clock, with a huge sweeping hour hand
-that he who runs may read.</p>
-
-<div class="figcenter">
-<img src="images/i_233.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 169.</span>—The Cosmic Clock.</div>
-</div>
-
-<p>It is a clock in some respects curious; it has a twenty-four
-hour face like some clocks and watches designed for Continental
-railway time; the hour hand revolves backward, (“counter-clockwise”)
-and it stands in the vertical not at noon, but at 1.20
-Star Time. The two stars which mark the tip and the reverse end
-of the hour hand are delta Cassiopeæ and zeta Ursæ Majoris
-respectively. The first is the star that marks the bend in the
-back of the great “chair,” the second (Mizar), the star which
-is next to the end of the “dipper” handle.</p>
-
-<p><span class="pagenum"><a name="Page_234" id="Page_234">[Pg 234]</a></span></p>
-
-<p>One or the other is above the horizon anywhere in the northern
-hemisphere. Further, the line joining these two stars passes
-almost exactly through the celestial pole, and also very nearly
-through Polaris, which lies between the pole and δ Cassiopeæ.
-Consequently if you want to know the hour-angle of Polaris
-just glance at the clock and note where on the face δ Cassiopeæ
-stands, between the vertical which is XXIV o’clock, and the
-horizontal, which is VI (east) or XVIII (west) o’clock.</p>
-
-<p>You can readily estimate its position to the nearest half
-hour, and knowing that the great hour hand is vertical (δ Cassiopeæ
-up) at I<sup>h</sup> 20<sup>m</sup> or (ζ Ursæ Majoris up) at XIII<sup>h</sup> 20<sup>m</sup>, you can
-make a fairly close estimate of the sidereal time.</p>
-
-<p>A little experience enables one to make excellent use of the
-clock in locating celestial objects, and knowledge of the approximate
-hour angle of Polaris thus observed can be turned to immediate
-use in making adjustment 3. To this end slip into the
-plane of the finder cross wires a circular stop of metal or paper
-having a radius of approximately 1° 15′ which means a diameter
-of 0.52 inch per foot of focal length.</p>
-
-<p>Then, leaving the telescope clamped in declination as it was
-after adjustment 1, turn it in azimuth across the pole until the
-pole star enters the field which, if the finder inverts it will do on
-the other side of the center; i.e. if it stands at IV to the naked
-eye it will enter the field apparently from the XVI o’clock quarter.
-When just comfortably inside the field, the axis of the telescope
-is pointing substantially at the pole.</p>
-
-<p>It is better to get Polaris in view before slipping in the stop
-and if it is clearly coming in too high or too low shift the altitude
-of the polar axis a trifle to correct the error. This approximate
-setting can be made even with the smallest finder and on any
-night worth an attempt at observation.</p>
-
-<p>With a finder of an inch or more aperture a very quick and
-quite accurate setting to the meridian can be made by the use
-of Fig. 170, which is a chart of all stars of 8 mag. or brighter
-within 1° 30′ of the pole. There are only three stars besides
-Polaris at all conspicuous in this region, one quite close to
-Polaris, the other two forming with it the triangle marked on
-the chart. These two are, to the left, a star of magnitude 6.4
-designated B. D. 88 112, and to the right one of magnitude 7.0,
-B. D. 89 13.</p>
-
-<p>The position of the pole for the rest of the century is marked<span class="pagenum"><a name="Page_235" id="Page_235">[Pg 235]</a></span>
-on the vertical arrow and with the stars in the field of the finder
-one can set the cross wires on the pole, the instrument remaining
-clamped in declination, within a very few minutes of arc, quite
-closely enough for any ordinary use of a portable mount. All
-this could be done even better with the telescope itself, but it is
-very rare to find an eyepiece with sufficient field.</p>
-
-<div class="figcenter">
-<img src="images/i_235.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 170.</span>—The Pole among the Stars.</div>
-</div>
-
-<p>At all events the effect of any error likely to be made in these
-adjustments is not serious for the purpose in hand, since if one
-makes an error of a minute of arc in the setting the resulting
-displacement of a star in the field will even in the most unfavorable
-case reach this full amount only after 6 hours following.
-I.e. with any given eyepiece an error of adjustment equal to the
-radius of the field will still permit following a star for an hour
-or two before it drifts inconveniently wide of the center.</p>
-
-<p>Considerable space has been devoted to these easy approximations
-in setting up, since the directions commonly given require
-circles and often a clock drive.</p>
-
-<p>In some cases one has to set up a portable equatorial where
-from necessity for clear sky space, Polaris is not visible. The
-best plan then is to set up with great care where Polaris can be
-seen, paying especial attention to the levelling. Then establish
-two meridian marks on stakes at a convenient distance by turning
-the telescope 180° on its declination axis and sighting through it<span class="pagenum"><a name="Page_236" id="Page_236">[Pg 236]</a></span>
-in both directions. Now with a surveyor’s tape transfer the
-meridian line East or West as the case may be until it can be
-used where there is clear sky room.</p>
-
-<p>Few observers near a city can get good sky room, from the
-interference of houses, trees or blazing street lamps, and the
-telescope must often be moved from one site to another to reach
-different fields. In such case it is wise to take the very first
-step toward giving the telescope a local habitation by establishing
-a definite placement for the tripod.</p>
-
-<p>To this end the three legs should be firmly linked together by
-chains that will not stretch—leg directly to leg, and not to a
-common junction. Then see to it that each leg has a strong
-and moderately sharp metal point, and, the three points of
-support being thus definitely fixed, establish the old reliable
-point-slot-plane bearing as follows:</p>
-
-<p>Lay out at the site (or sites) giving the desired clear view, a
-circle scratched on the ground of such size that the three legs
-of your tripod may rest approximately on its periphery. Then
-lay out on the circle three points 120° apart. At each point sink
-a short post 12 to 18 inches long and of any convenient diameter,
-well tarred, and firmly set with the top levelled off quite closely
-horizontal.</p>
-
-<p>To the top of each bolt a square or round of brass or iron
-about half an inch thick. The whole arrangement is indicated
-in diagram in Fig. 171. In <i>a</i> sink a conical depression such as
-is made by drilling nearly through with a 1 inch twist drill. The
-angle here should be a little broader than the point on the tripod
-leg. In <i>b</i> have planed a V shaped groove of equally broad angle
-set with its axis pointing to the conical hole in <i>a</i>. Leave the
-surface of <i>c</i> a horizontal plane.</p>
-
-<p>Now if you set a tripod leg in <i>a</i>, another in the slot at <i>b</i> and
-the third on <i>c</i>, the tripod will come in every instance to the same
-level and orientation. So, if you set up your equatorial carefully
-in the first place and leave the head clamped in azimuth, you
-can take it in and replace it at any time still in adjustment as
-exact as at the start. And if it is necessary to shift from one
-location to another you can do it without delay still holding
-accurate adjustment of the polar axis to the pole, and avoiding
-the need of readjustment.</p>
-
-<p>In case the instrument has a declination circle the original
-set-up becomes even simpler. One has only to level the tripod,<span class="pagenum"><a name="Page_237" id="Page_237">[Pg 237]</a></span>
-either with or without the equatorial head in place, and then to
-set the polar axis either vertical or horizontal, levelling the tube
-with it either by placing the level across the objective cell
-perpendicular to the declination axis, or laying it along the tube
-when horizontal.</p>
-
-<div class="figcenter">
-<img src="images/i_237.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 171.</span>—A Permanent Foothold for the Tripod.</div>
-</div>
-
-<p>Then, reading the declination circle, one can set off the co-atitude
-or latitude as the case may be and, leaving the telescope
-clamped in declination, lower or raise the polar axis until the tube
-levels to the horizontal. When the mount does not permit wide
-adjustment and has no latitude scale one is driven to laying
-out a latitude templet and, placing a straight edge under the
-equatorial head, or suspending a plumb line from the axis
-itself, setting it mechanically to latitude.</p>
-
-<p>Now suppose we are dealing with the same instrument, but
-are planning to plant it permanently in position on its pillar
-mount. It is now worth while to make the adjustments quite
-exactly, and to spend some time about it. The pillar is commonly
-assembled by well set bolts on a brick or concrete pier. The
-preliminary steps are as already described.</p>
-
-<p>The pillar is levelled across the top, the equatorial head, which
-turns upon it in azimuth, is levelled as before, the adjustment
-being made by metal wedges under the pillar or by levelling<span class="pagenum"><a name="Page_238" id="Page_238">[Pg 238]</a></span>
-screws in the mount if there are any. Then the latitude is set
-off by the scale, or by the declination circle, and the polar axis
-turned to the approximate meridian as already described.</p>
-
-<p>There is likely to be an outstanding error of a few minutes
-of arc which should in a permanent mount be reduced as far as
-practicable. At the start adjust the declination of the optical
-axis of the telescope to that of the polar axis. This is done in
-the manner suggested by Fig. 172.</p>
-
-<p>Here <i>p</i> is the polar axis and <i>d</i> the declination axis. Now if
-one sights, using the cross wires, through the telescope a star
-near the meridian, i.e., one that is changing in declination quite
-slowly, starting from the position <i>A</i> with the telescope <i>E</i>. of the
-polar axes, and turns it over 180° into the position <i>B</i>, <i>W</i>. of the
-polar axis, the prolongation of the line of sight, <i>b</i>, will fall below
-<i>a</i>, when as here the telescope points too high in the <i>A</i> position.</p>
-
-<div class="figcenter">
-<img src="images/i_238.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 172.</span>—Aligning the Optical Axis.</div>
-</div>
-
-<p>In other words the apparent altitude of the star will change
-by twice the angle between <i>A</i> and <i>p</i>. Read both altitudes on
-the declination circle and split the difference with the slow motion
-as precisely as the graduation of the declination circle permits.</p>
-
-<p>The telescope will probably not now point exactly at the star,
-but as the tube is swung from the <i>A</i> to the <i>B</i> position and back
-the visible stars will describe arcs of circles which should be
-nearly concentric with the field as defined by the stop in the
-eyepiece. If not, a very slight touch on the declination slow
-motion one way or the other will make them do so to a sufficient
-exactness, especially if a rather high power eyepiece is used.</p>
-
-<p><span class="pagenum"><a name="Page_239" id="Page_239">[Pg 239]</a></span></p>
-
-<p>The optical axis of the telescope is now parallel to the polar
-axis, but the latter may be slightly out of position in spite of
-the preliminary adjustment. Now reverting to the polar field
-of Fig. 170, swing from position <i>A</i> to <i>B</i> and back again, correcting
-any remaining eccentricity of the star arcs around the pole by
-cautious shifting of the polar axis, leaving the telescope clamped
-in declination. The first centering is around the pole of the
-instrument, the second around the celestial pole by help of a
-half dozen small stars within a half degree on both sides of it,
-magnitudes 9 and 10, easily visible in a 3” or 4” telescope, using
-the larger field of the finder for the coarse adjustment.</p>
-
-<p>If the divided circles read to single minutes or closer, which
-they generally do not on instruments of moderate size, one can
-use the readings to set the polar axis and the declination circle,
-and to make the other adjustments as well.</p>
-
-<p>In default of this help, the declination circle adjustment may
-be set to read 90° when the optical axis is brought parallel to the
-polar axis, and after the adjustment of the latter is complete,
-the R. A. circle can be set by swinging up the telescope in the
-meridian and watching for the transit of any star of known R. A.
-over the central cross wire, at which moment the circle should
-be clamped to the R. A. thus defined.</p>
-
-<p>Two possible adjustments are left, the perpendicularity of the
-polar and declination axes, and that of the optical axis to the
-declination axis. As a rule there is no provision for either of
-these, which are supposed to have been carried out by the maker.
-The latter adjustment if of any moment will disclose itself as
-a lateral wobble in trying to complete the adjustment of optical
-axis to polar axis. It can be remedied by a liner of tinfoil or
-even paper under one end of the tube’s bearing on its cradle.
-Adjustment of the former is strictly a job for the maker.</p>
-
-<p>For details of the rigorous adjustments on the larger instruments
-the reader will do well to consult Loomis’ <i>Practical Astronomy</i>
-page 28 and following.<a name="FNanchor_31_31" id="FNanchor_31_31"></a><a href="#Footnote_31_31" class="fnanchor">[31]</a> The adjustments here considered
-are those which can be effectively made without driving clock,
-finely divided circles, or exact knowledge of sidereal time. The
-first and last of these auxiliaries, however, properly belong with
-an instrument as large as Fig. 168, on a fixed mount.</p>
-
-<p>There are several rather elegant methods of adjusting the polar<span class="pagenum"><a name="Page_240" id="Page_240">[Pg 240]</a></span>
-axis to the pole which depend on the use of special graticules in
-the eyepiece, or on auxiliary devices applied to the telescope,
-the general principle being automatically to provide for setting
-off the distance between Polaris and the pole at the proper hour
-angle. A beautifully simple one is that of Gerrish (<i>Pop. Ast.</i>
-<b>29</b>, 283).</p>
-
-<p>The simple plan here outlined will generally, however, prove
-sufficient for ordinary purposes and where high precision is
-necessary one has to turn to the more conventional astronomical
-methods.</p>
-
-<p>If one gives his telescope a permanent footing such as is shown
-in Fig. 171 adjustment has rarely to be repeated. With a pillar
-mount such as we have just now been considering the instrument
-itself can be taken in doors and replaced with very slight risk
-of disturbing its setting, but some provision must be made
-for sheltering the mount.</p>
-
-<p>A tarpaulin is sometimes recommended and indeed answers
-well, particularly if a bag of rubber sheeting is drawn loosely
-over the mount first. Better still is a box cover of copper or
-galvanized iron set over the mount and closely fitting well down
-over a base clamped to the pillar with a gasket to close the joint.</p>
-
-<p>But the fact is when one is dealing with a fine instrument like
-Fig. 168 of as much as 5 inches aperture, the question of a permanent
-housing (call it observatory if you like) at once comes
-up and will not down.</p>
-
-<p>It is of course always more convenient to have the telescope
-permanently in place and ready for action. Some observers
-feel that working conditions are better with the telescope in the
-open, but most prefer a shelter from the wind, even if but partial,
-and the protection of a covering, however slight, in severe
-weather.</p>
-
-<p>In the last resort the question is mainly one of climate. Where
-nights, otherwise of the best seeing quality, are generally windless
-or with breezes so slight that the tube does not quiver a telescope
-in the open, however protected between times, works perfectly
-well.</p>
-
-<p>In other regions the clearest nights are apt to be those of a
-steady gentle wind producing great uniformity of conditions at the
-expense of occasional vibration of the instrument and of discomfort
-to the observer. Hence one finds all sorts of practice, varied
-too, by the inevitable question of expense.</p>
-
-<p><span class="pagenum"><a name="Page_241" id="Page_241">[Pg 241]</a></span></p>
-
-<p>The simplest possible housing is to provide for the fixed
-instrument a moveable cover which can be lifted or slid quite
-out of the way leaving the telescope in the open air, exposed to
-wind, but free from the disturbing air currents that play around
-the opening of a dome. Shelters of this cheap and simple sort
-have been long in use both for small and large instruments.</p>
-
-<div class="figcenter">
-<img src="images/i_241.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 173.</span>—The Simplest of Telescope Housings.</div>
-</div>
-
-<p>For example several small astrographic instruments in the
-Harvard equipment are mounted as shown in Fig. 173. Here
-are two fork mounts, each on a short pier, and covered in by
-galvanized iron hoods made in two parts, a vertical door which
-swings down, as in the camera of the foreground, and the hood
-proper, hinged to the base plate and free to swing down when
-the rear door is unlocked and opened. A little to the rear is a<span class="pagenum"><a name="Page_242" id="Page_242">[Pg 242]</a></span>
-similar astrographic camera with the hood closed. It is all very
-simple, cheap, and effective for an instrument not exceeding say
-two or three feet in focal length.</p>
-
-<p>A very similar scheme has been successfully tried on reflectors
-as shown in Fig. 174. The instrument shown is a Browning
-equatorial of 8&frac12; inches aperture. The cover is arranged to
-open after the manner of Fig. 173 and the plan proved very
-effective, preserving much greater uniformity of conditions and
-hence permitting better definition
-than in case of a similar
-instrument peering through the
-open shutter of a dome.</p>
-
-<p>Such a contrivance gets unwieldly
-in case of a refractor on
-account of the more considerable
-height of the pier and the length
-of the tube itself. But a modification
-of it may be made to
-serve exceedingly well in climates
-where working in the open is
-advantageous. A good example
-is the equatorial of the Harvard
-Observatory station at Mandeville,
-Jamaica, which has been
-thus housed for some twenty years, as shown in Fig. 175.</p>
-
-<p>This 11 inch refractor, used mainly on planetary detail, is
-located alongside the polar telescope of 12 inches aperture and
-135 feet 4 inches focal length used for making a photographic
-atlas of the moon and on other special problems. The housing,
-just big enough to take in the equatorial with the tube turned
-low, opens on the south side and then can be rolled northward on
-its track, into the position shown, where it is well clear of the
-instrument, which is then ready for use.</p>
-
-<div class="figcenter">
-<img src="images/i_242.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 174.</span>—Cover for Small Reflector.</div>
-</div>
-
-<p>The climate of Jamaica, albeit extremely damp, affords remarkably
-good seeing during a large part of the year, and permits
-use of the telescope quite in the open without inconvenience to
-the observer. The success of this and all similar housing plans
-depends on the local climate more than on anything else—chiefly
-on wind during the hours of good seeing. An instrument quite
-uncovered suffers from gusts far more than one housed under a
-dome, which is really the sum of the whole matter, save that a<span class="pagenum"><a name="Page_243" id="Page_243">[Pg 243]</a></span>
-dome to a slight extent does shelter the observer in extremely
-cold weather.</p>
-
-<p>Even very large reflectors can be housed in similar fashion
-if suitably mounted. For example in Fig. 176 is shown the 36
-inch aperture reflector of the late Dr. Common, which was
-fitted with an open fork equatorial mounting. Here the telescope
-itself, with its short pier and forked polar axis, is shown in dotted
-lines.</p>
-
-<div class="figcenter">
-<img src="images/i_243.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 175.</span>—Sliding Housing for 11-inch Refractor.</div>
-</div>
-
-<p>Built about it is a combined housing and observing stand
-rotatable on wheels <i>T</i> about a circular track <i>R</i>. The housing
-consists of low corrugated metal sides and ends, here shown
-partly broken away, of dimensions just comfortably sufficient
-to take in the telescope when the housing is rotated to the north
-and south position, and the tube turned down nearly flat southward.
-A well braced track <i>WW</i> extends back along the top of
-the side housing and well to the rear. On this track rolls the
-roof of the housing <i>X,X,X</i>, with a shelter door at the front end.</p>
-
-<p><span class="pagenum"><a name="Page_244" id="Page_244">[Pg 244]</a></span></p>
-
-<div class="figcenter">
-<img src="images/i_244.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 176.</span>—Sliding Housing for a Big Reflector.</div>
-</div>
-
-<p><span class="pagenum"><a name="Page_245" id="Page_245">[Pg 245]</a></span></p>
-
-<p>The members <i>U</i> constitute a framing which supports at once
-the housing and the observing platform, to which access is had
-by a ladder, <i>Z</i>, provided with a counterbalanced observing seat.
-The instrument is put into action by clearing the door at the
-end of the roof, running the roof back to the position shown in
-the dotted lines, raising the tube, and then revolving the whole
-housing into whatever position is necessary to permit the proper
-setting of the tube.</p>
-
-<div class="figcenter">
-<img src="images/i_245.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 177.</span>—Sliding Roof Observatory.</div>
-</div>
-
-<p>This arrangement worked well but was found a bit troublesome
-owing to wind and weather. With a skeleton tube and in a
-favorable climate the plan would succeed admirably providing
-an excellent shelter for a large telescope at very low cost.</p>
-
-<p>Since a fork mount allows the tube to lie flat, such an instrument,
-up to say 8 or 10 inches aperture can be excellently protected
-by covers fitting snugly upon a base and light enough to
-lift off as a whole.</p>
-
-<p>The successful use of all these shelters however depends on
-climatic conditions. They require circumstances allowing observation
-in the open, as with tripod mounts, and afford no protec<span class="pagenum"><a name="Page_246" id="Page_246">[Pg 246]</a></span>tion
-from wind or cold. Complete protection for the observer
-cannot be had, except by some of the devices shown in Chapter
-V, but conditions can be improved by permanent placement in
-an observatory, simple or elaborate, as the builder may wish.</p>
-
-<p>The word observatory may sound formidable, but a modest
-one can be provided at less expense than a garage for the humblest
-motor car. The chief difference in the economic situation is
-that not even the most derided car can be picked up and carried
-into the back hall for shelter, and it really ought not to be left
-out in the weather.</p>
-
-<p>The next stage of evolution is the telescope house with a
-sliding roof in one or more sections—ordinarily two. In this
-case the building itself is a simple square structure large enough
-to accommodate the instrument with maneuvering room around
-it. The side walls are carried merely high enough to give clearance
-to the tube when turned nearly flat and to give head room
-to the observer. The roof laps with a close joint in the middle
-and each half rolls on a track supported beyond the ends of the
-building by an out-rigger arranged in any convenient manner.</p>
-
-<p>When the telescope is in use the roof sections are displaced
-enough to give an ample clear space for observing, often wide
-open as shown in Fig. 177, which is the house of the 16 inch Metcalf
-photographic doublet at the Harvard Observatory. This
-instrument is in an open fork mount like that shown in Fig. 139.</p>
-
-<p>The sliding roof type is on the whole the simplest structure
-that can be regarded as an observatory in the sense of giving
-some shelter to the observer as well as the instrument. It gives
-ample sky room for practical purposes even to an instrument
-with a fork mount, since in most localities the seeing within
-30° or so of the horizon is decidedly bad. If view nearer the
-horizon is needed it can readily be secured by building up the
-pier a bit.</p>
-
-<p>Numberless modifications of the sliding roof type will suggest
-themselves on a little study. One rather interesting one is used
-in the housing of the 24 inch reflector of the Harvard Observatory,
-11 feet 3 inches in focal length, the same of which the drive in its
-original dome is shown in Fig. 139. As now arranged the lower
-part of the observatory remains while the upper works are quite
-similar in principle to the housing of Dr. Common’s 3 foot reflector
-of Fig. 176. The cover open is shown in Fig. 178. It will be
-seen that on the north side of the observatory there is an out-rigger<span class="pagenum"><a name="Page_247" id="Page_247">[Pg 247]</a></span>
-on which the top housing slides clear of the low revolving turret
-which gives access to the ocular fitting used generally to carry the
-plate holder, and the eyepiece for following when required.</p>
-
-<p>The tube cannot be brought to the horizontal, but it easily
-commands all the sky-space that can advantageously be used
-in this situation, and the protection given the telescope when
-not in use is very complete. To close the observatory the tube
-is brought north and south and turned low and the sliding roof
-is then run back into its fixed position. The turret is very easily
-turned by hand.</p>
-
-<div class="figcenter">
-<img src="images/i_247.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 178.</span>—Turret Housing of the 24-inch Harvard Reflector.</div>
-</div>
-
-<p>Of course for steady work with the maximum shelter for
-observer obtainable without turning to highly special types of
-housing, the familiar dome is the astronomer’s main reliance.
-It is in the larger sizes usually framed in steel and covered with
-wood, externally sheathed in copper or steel. Sometimes in smaller
-domes felt covered with rubberoid serves a good purpose, and
-painted canvas is now and then used, with wooden framing.</p>
-
-<p>But even the smallest dome of conventional construction is
-heavy and rather expensive, and for home talent offers many
-difficulties, especially with respect to the shutter and shutter<span class="pagenum"><a name="Page_248" id="Page_248">[Pg 248]</a></span>
-opening. A hemisphere is neither easy to frame nor to cover,
-and the curved sliding shutter is especially troublesome.</p>
-
-<div class="figcenter">
-<img src="images/i_248.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 179.</span>—The Original “Romsey” Observatory.</div>
-</div>
-
-<p>Hence for small observatories other forms of revolving roof
-are desirable, and quite the easiest and cheapest contrivance is
-that embodied in the “Romsey” type of observatory, devised
-half a century ago by that accomplished amateur the Rev. E. L.
-Berthon, vicar of Romsey. The feature of his construction is
-an unsymmetrical peak in the revolving roof which permits the
-ordinary shutter to be replaced by a hinged shutter like the
-skylight in a roof, exposing the sky beyond the zenith when
-open, and closing down over a coaming to form a water tight
-joint.</p>
-
-<p><span class="pagenum"><a name="Page_249" id="Page_249">[Pg 249]</a></span></p>
-
-<p>Berthon’s original description of his observatory, which accommodated
-a 9&frac14; inch reflector, may be found in Vol. 14 of the
-<i>English Mechanic and World of Science</i> whence Fig. 179 is taken.
-In this plate Fig. 1 shows the complete elevation and Fig. 2
-the ground plan, each to a scale of a eighth of an inch to the foot.
-In the plan, <i>A,A</i>, are the main joists, <i>P</i> the pier for the telescope,
-T that for the transit, and <i>C</i> the clock. Figs. 3, 4, and 5 are of
-details. In the last named <i>A</i> is a rafter, <i>b</i> the base ring, <i>c</i> the
-plate, <i>d</i> one of the sash rollers carrying the roof, and <i>e</i> a lateral
-guide roller holding the roof in place.</p>
-
-<p>The structure can readily be built without the transit shelter,
-and in fact now-a-days most observers find it easier to pick up
-their time by wireless. The main bearing ring is cut out of
-ordinary 7/8 inch board, in ten or a dozen, or more, sections
-according to convenience, done in duplicate, joints lapping, and
-put very firmly together with screws set up hard. Sometimes
-3 layers are thus used.</p>
-
-<p>The roof in the original “Romsey” observatory was of painted
-canvas, but rubberoid or galvanized iron lined with roofing
-paper answers well. The shutter can be made single or double
-in width, and counterbalanced if necessary. The framing may
-be of posts set in the ground as here shown, or with sills resting
-on a foundation, and the walls of any construction—matched
-boards of any kind, cement on wire lath, hollow tile, or concrete
-blocks.</p>
-
-<p>Chambers’ <i>Handbook of Astronomy</i> Vol. II contains quite
-complete details of the “Romsey” type of observatory and is
-easier to get at than the original description.</p>
-
-<p>A very neat adaptation of the plan is shown in Fig. 180, of
-which a description may be found in <i>Popular Astronomy</i> <b>28</b>, 183.
-This observatory was about 9 feet in diameter, to house a 4
-inch telescope, and was provided with a rough concrete foundation
-on which was built a circular wall 6 feet high of hollow glazed
-tile, well levelled on top. To this was secured a ring plate built
-up in two layers, carrying two circles of wooden strips with a
-couple of inches space between them for a runway. In this
-ran 6 two-inch truck castors secured to a similar ring plate
-on which was built up the frame of the “dome” arranged
-as shown. Altogether a very neat and workmanlike affair,
-in this case built largely by the owner but permitting construction
-at very small expense almost anywhere. Another interesting<span class="pagenum"><a name="Page_250" id="Page_250">[Pg 250]</a></span>
-modification of the same general plan in the same volume just
-cited is shown in Fig. 181. This is also for a 4 inch refractor and
-the dome proper is but 8 feet 4 inches in diameter. Like the
-preceding structure the foundation is of concrete but the walls are
-framed in spruce and sheathed in matched boards with a “beaver-board”
-lining.</p>
-
-<div class="figcenter">
-<img src="images/i_250.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 180.</span>—A More Substantial “Romsey” Type.</div>
-</div>
-
-<p>The ring plate is three-ply, 12 sections to the layer, and its
-mate on which the dome is assembled is similarly formed, though
-left with the figure of a dodecagon to match the dome. The
-weight is carried on four rubber tired truck rollers, and there
-are lateral guide rollers on the plan of those in Fig. 179.</p>
-
-<p>The dome itself however, is wholly of galvanized iron, in 12
-gores joined with standing seams, turned, riveted, and soldered.<span class="pagenum"><a name="Page_251" id="Page_251">[Pg 251]</a><br /><a name="Page_252" id="Page_252">[Pg 252]</a></span>
-There is a short shutter at the zenith sliding back upon a frame,
-while the main shutter is removed from the outside by handles.</p>
-
-<div class="figcenter">
-<img src="images/i_251.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 181.</span>—Detail of Light Metal Dome for Small Observatory.</div>
-</div>
-
-<p>Observatories of the Romsey or allied types can be erected
-at very moderate cost, varying considerably from place to place,
-but running at present say from $200 to $600, and big enough to
-shelter refractors of 4 to 6 inches aperture. The revolving roofs
-will range from 9 to 12 feet in diameter. If reflectors are in use,
-those of about double these apertures can be accommodated
-since the reflector is ordinarily much the shorter for equal
-aperture.</p>
-
-<p>The sliding roof, not to say the sliding shelter, forms of housing
-cost somewhat less, depending on the construction adopted.
-Going to brick may double the figures quoted, but such solidity
-is generally quite needless, though it is highly desirable that the
-cover of a valuable instrument should be fire-proof and not easily
-broken open. The stealing of objectives and accessories is not
-unknown, and vandalism is a risk not to be forgotten. But to
-even the matter up, housing a telescope is rather an easy thing
-to accomplish, and as a matter of fact for the price of a very
-modest motor car one can both buy and house an instrument
-big enough to be of genuine service.</p>
-
-<hr class="chap" />
-
-<p><span class="pagenum"><a name="Page_253" id="Page_253">[Pg 253]</a></span></p>
-
-
-
-
-<div class="chapter"></div>
-<h2><a name="CHAPTER_XI" id="CHAPTER_XI">CHAPTER XI</a><br />
-
-<small>SEEING AND MAGNIFICATION</small></h2>
-
-
-<p>Few things are more generally disappointing than one’s first
-glimpse of the Heavens through a telescope. The novice is fed
-up with maps of Mars as a great disc full of intricate markings,
-and he generally sees a little wriggling ball of light with no more
-visible detail than an egg. It is almost impossible to believe
-that, at a fair opposition, Mars under the power of even the
-smallest astronomical telescope really looks as big as the full moon.
-Again, one looks at a double star to see not two brilliant little
-discs resplendent in color, but an indeterminate flicker void of
-shape and hue.</p>
-
-<p>The fact is, that most of the time over most of the world
-seeing conditions are bad, so that the telescope does not have a
-fair chance, and on the whole the bigger the telescope the worse
-the chance. One famous English astronomer, possessed of a
-fine refractor that would be reckoned large even now-a-days,
-averred that he had seen but one first class night in fifteen
-years past.</p>
-
-<p>The case is really much less bad than this implies, for even in
-rather unfavorable climates many a night, at some o’clock or
-other, will furnish an hour or two of pretty good seeing, while
-now and then, without any apparent connection with the previous
-state of the weather, a night will turn up when the pictures
-in the popular astronomies come true, the stars shrink to steady
-points set in clean cut rings, and no available power seems too
-high.</p>
-
-<p>One can get a good idea of the true inwardness of bad seeing
-by trying to read a newspaper through an opera glass across a
-hot stove. If the actual movements in the atmosphere could be
-made visible they would present a strange scene of turbulence—rushing
-currents taking devious courses up and around obstacles,
-slowly moving whirlpools, upward slants such as gulls hug on
-the quarter of a liner, great downward rushes dreaded by the
-aviator, and over it all incessant ripples in every direction.</p>
-
-<p><span class="pagenum"><a name="Page_254" id="Page_254">[Pg 254]</a></span></p>
-
-<p>And movements of air are usually associated with changes of
-temperature, as over the stove, varying the refraction and contorting
-the rays that come from a distant star until the image is
-quite ruined.</p>
-
-<p>The condition for excellence of definition is that the atmosphere
-through which we see shall be homogeneous, whatever its temperature,
-humidity, or general trend of movement. Irregular
-refraction is the thing to be feared, particularly if the variations
-are sudden and frequent. Hence the common troubles near the
-ground and about buildings, especially where there are roofs and
-chimneys to radiate heat—even in and about an observatory dome.</p>
-
-<p>Professor W. H. Pickering, who has had a varied experience
-in climatic idiosyncrasies, gives the Northern Atlantic seaboard
-the bad preëminence of having the worst observing conditions
-of any region within his knowledge. The author cheerfully
-concurs, yet now and then, quite often after midnight, the air
-steadies and, if the other conditions are good, definition becomes
-fairly respectable, sometimes even excellent.</p>
-
-<p>Temperature and humidity as such, seem to make little
-difference, and a steady breeze unless it shakes the instrument is
-relatively harmless. Hence we find the most admirable definition
-in situations as widely different as the Harvard station at
-Mandeville, Jamaica; Flagstaff, Arizona 7000 feet up and snow
-bound in winter; Italy, and Egypt. The first named is warm and
-with very heavy rainfall and dew, the second dry with rather
-large seasonal variation of temperature, and the others temperate
-and hot respectively.</p>
-
-<p>Perhaps the most striking evidence of the importance of uniformity
-was noted by Evershed at an Indian station where good
-conditions immediately followed the flooding of the rice fields
-with its tendency to stabilize the temperature. Mountain
-stations may be good as at Flagstaff, Mt. Hamilton, or Mt.
-Wilson, or very bad as Pike’s Peak proved to be, probably owing
-to local conditions.</p>
-
-<p>In fact much of the trouble comes from nearby sources, atmospheric
-waves and ripples rather than large movements, ripples
-indeed often small compared with the aperture of the telescope
-and sometimes in or not far outside of the tube itself.</p>
-
-<p>Aside from these difficulties, there are still others which have
-to do with the transparency of the atmosphere with respect to its
-suspended matter. This does not affect the definition as such,<span class="pagenum"><a name="Page_255" id="Page_255">[Pg 255]</a></span>
-but it cuts down the light to a degree that may interfere seriously
-with the observation of faint stars and nebulæ. The smoke
-near a city aggravates the situation, but in particular it depends
-on general weather conditions which may be persistent or merely
-temporary.</p>
-
-<p>Often seeing conditions may be admirable save for this lack
-of transparency in the atmosphere, so that study of the moon,
-of planetary markings and even of double stars, not too faint,
-may go on quite unimpeded. The actual loss of light may reach
-however a magnitude or more, while the sky is quite cloudless
-and without a trace of fog or noticeable haziness by day.</p>
-
-<p>There have been a good many nights the past year (1921)
-when Alcor (80 Ursæ Majoris) the tiny neighbor of Mizar, very
-nearly of the 4th magnitude, has been barely or not at all visible
-while the seeing otherwise was respectably good. Ordinarily
-stars of 6<sup><i>m</i></sup> should be visible in a really clear night, and in a
-brilliant winter sky in the temperate zones, or in the clear air of
-the tropics, a good many eyes will do better than this, reaching
-6<sup><i>m</i></sup>.5 or even 7<sup><i>m</i></sup>, occasionally a bit more.</p>
-
-<p>The relation of air waves and such like irregularities to telescopic
-vision was rather thoroughly investigated by Douglass
-more than twenty years ago (Pop. Ast. <b>6</b>, 193) with very interesting
-results. In substance, from careful observation with telescopes
-from 4 inches up to 24 inches aperture, he found that the
-real trouble came from what one may call ripples, disturbances
-from say 4 inches wave length down to &frac34; inch or less. Long
-waves are rare and relatively unimportant since their general
-effect is to cause shifting of the image as a whole rather than the
-destruction of detail which accompanies the shorter waves.</p>
-
-<p>This rippling of the air is probably associated with the contact
-displacements in air currents such as on a big scale become
-visible in cloud forms. Clearly ripples, marked as they are by
-difference of refraction, located in front of a telescope objective,
-produce different focal lengths for different parts of the objective
-and render a clean and stable image quite out of the question.</p>
-
-<p>In rough terms Douglass found that waves of greater length
-than half the aperture did not materially deteriorate the image,
-although they did shift it as a whole, while waves of length less
-than one third the aperture did serious mischief to the definition,
-the greater as the ripples were shorter, and the image itself more
-minute in dimension or detail.</p>
-
-<p><span class="pagenum"><a name="Page_256" id="Page_256">[Pg 256]</a></span></p>
-
-<p>Hence there are times when decreasing the aperture of an
-objective by a stop improves the seeing considerably by increasing
-the relative length of the air waves. Such is in fact found to be
-the case in practical observing, especially when the seeing with a
-large aperture is decidedly poor. In other words one may often
-gain more by increased steadiness than he loses by lessened
-“resolving power,” the result depending somewhat on the class
-of observation which chances to be under way.</p>
-
-<p>And this brings us, willy-nilly, to the somewhat abstruse
-matter of resolving power, depending fundamentally upon the
-theory of diffraction of light, and practically upon a good many
-other things that modify the character of the diffraction pattern,
-or the actual visibility of its elements.</p>
-
-<p>When light shines through a hole or a slit the light waves are
-bent at the margins and the several sets, eventually overlapping,
-interfere with each other so as to produce a pattern of bright and
-dark elements depending on the size and shape of the aperture,
-and distributed about a central bright image of that aperture.
-One gets the effect well in looking through an open umbrella at a
-distant street light. The outer images of the pattern are fainter
-and fainter as they get away from the central image.</p>
-
-<p>Without burdening the reader for the moment with details to be
-considered presently, the effect in telescopic vision is that a star
-of real angular diameter quite negligible, perhaps 0.″001 of arc,
-is represented by an image under perfect conditions like Fig. 154,
-of quite perceptible diameter, surrounded by a system of rings,
-faint but clear-cut, diminishing in intensity outwards. When
-the seeing is bad no rings are visible and the central disc is a
-mere bright blur several times larger than it ought to be.</p>
-
-<p>The varying appearance of the star image is a very good index
-of the quality of the seeing, so that, having a clear indication of
-this appearance, two astronomers in different parts of the world
-can gain a definite idea of each other’s relative seeing conditions.
-To this end a standard scale of seeing, due largely to the efforts
-of Prof. W. H. Pickering, has come into rather common use.
-(H. A. <b>61</b> 29). It is as follows, based on observations with a
-5 inch telescope.</p>
-
-
-<p class="center">STANDARD SCALE OF SEEING</p>
-
-<p>1. Image usually about twice the diameter of the third ring.</p>
-
-<p>2. Image occasionally twice the diameter of the third ring.</p>
-
-<p><span class="pagenum"><a name="Page_257" id="Page_257">[Pg 257]</a></span></p>
-
-<p>3. Image of about the same diameter as the third ring, and
-brighter at the centre.</p>
-
-<p>4. Disc often visible, arcs (of rings) sometimes seen on brighter
-stars.</p>
-
-<p>5. Disc always visible, arcs frequently seen on brighter stars.</p>
-
-<p>6. Disc always visible, short arcs constantly seen.</p>
-
-<p>7. Disc sometimes sharply defined, (<i>a</i>) long arcs. (<i>b</i>) Rings
-complete.</p>
-
-<p>8. Disc always sharply defined, (<i>a</i>) long arcs. (<i>b</i>) Rings complete
-all in motion.</p>
-
-<p>9. Rings, (<i>a</i>) Inner ring stationary, (<i>b</i>) Outer rings momentarily
-stationary.</p>
-
-<p>10. Rings all stationary, (<i>a</i>) Detail between the rings sometimes
-moving. (<i>b</i>) No detail between the rings.</p>
-
-<p>The first three scale numbers indicate very bad seeing; the
-next two, poor; the next two, good; and the last three, excellent.
-One can get some idea of the extreme badness of scale divisions
-1, 2, 3, in realizing that the third bright diffraction ring is nearly
-4 times the diameter of the proper star-disc.</p>
-
-<p>It must be noted that for a given condition of atmosphere the
-seeing with a large instrument ranks lower on the scale than with
-a small one, since as already explained the usual air ripples
-are of dimensions that might affect a 5 inch aperture imperceptibly
-and a 15 inch aperture very seriously.</p>
-
-<p>Douglass (loc. cit.) made a careful comparison of seeing conditions
-for apertures up to 24 inches and found a systematic
-difference of 2 or 3 scale numbers between 4 or 6 inches aperture,
-and 18 or 24 inches. With the smallest aperture the image
-showed merely bodily motion due to air waves that produced
-serious injury to the image in the large apertures, as might be
-expected.</p>
-
-<p>There is likewise a great difference in the average quality of
-seeing as between stars near the zenith and those toward the
-horizon, due again to the greater opportunity for atmospheric
-disturbances in the latter case. Pickering’s experiments (loc.
-cit.) show a difference of nearly 3 scale divisions between say
-20° and 70° elevation. This difference, which is important, is
-well shown in Fig. 182, taken from his report.</p>
-
-<p>The three lower curves were from Cambridge observations,
-the others obtained at various Jamaica stations. They clearly
-show the systematic regional differences, as well as the rapid<span class="pagenum"><a name="Page_258" id="Page_258">[Pg 258]</a></span>
-falling off in definition below altitude 40°, which points the importance
-of making provision for comfortable observing above this
-altitude.</p>
-
-<div class="figcenter">
-<img src="images/i_258a.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 182.</span>—Variation of Seeing with Altitude.</div>
-</div>
-
-<div class="figcenter">
-<img src="images/i_258b.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 183.</span>—Airy’s Diffraction Pattern.</div>
-</div>
-
-<p>The relation of the diffraction pattern as disclosed in the
-moments of best seeing to its theoretical form is a very interesting
-one. The diffraction through a theoretically perfect objective<span class="pagenum"><a name="Page_259" id="Page_259">[Pg 259]</a></span>
-was worked out many years ago by Sir George Airy who calculated
-the exact distribution of the light in the central disc and the
-surrounding rings.</p>
-
-<p>This is shown from the centre outwards in Fig. 183, in which
-the ordinates of the curve represent relative intensities while the
-abscissæ represent to an arbitrary scale the distances from the
-axis. It will be at once noticed that the star image, brilliant at
-its centre, sinks, first rapidly and then more slowly, to a minimum
-and then very gradually rises to the maximum of the first
-bright ring, then as slowly sinks again to increase for the second
-ring and so on.</p>
-
-<div class="figcenter">
-<img src="images/i_259.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 184.</span>—Diffraction Solid for a Star.</div>
-</div>
-
-<p>For unity brightness in the centre of the star disc the maximum
-brightness of the first ring is 0.017, of the second 0.004 and the
-third 0.0016. The rings are equidistant and the star disc has a
-radius substantially equal to the distance between rings. One’s
-vision does not follow down to zero the intensities of the rings or
-of the margin of the disc, so that the latter has an apparent
-diameter materially less than the diameter to the first diffraction
-minimum, and the rings themselves look sharper and thinner
-than the figure would show, even were the horizontal scale much<span class="pagenum"><a name="Page_260" id="Page_260">[Pg 260]</a></span>
-diminished. The eye does not descend in the presence of bright
-areas to its final threshold of perception.</p>
-
-<p>One gains a somewhat vivid idea of the situation by passing
-to three dimensions as in Fig. 184, the “diffraction solid” for a
-star, a conception due to M. André (Mem. de l’Acad. de Lyon
-<b>30</b>, 49). Here the solid represents in volume the whole light
-received and the height taken at any point, the intensity at that
-point.</p>
-
-<p>A cross section at any point shows the apparent diameter of
-the disc, its distance to the apex the remaining intensity, and
-the volume above the section the remaining total light. Substantially
-85% of the total light belongs to the central cone, for
-the theoretical distribution.</p>
-
-<p>Granting that the eye can distinguish from the background
-of the sky, in presence of a bright point, only light above a certain
-intensity, one readily sees why the discs of faint stars look small,
-and why shade glasses are sometimes useful in wiping out the
-marginal intensities of the solid. There are physiological factors
-that alter profoundly the appearance of the actual star image,
-despite the fact that the theoretical diffraction image for the
-aperture is independent of the star’s magnitude.</p>
-
-<p>Practically the general reduction of illumination in the fainter
-stars cuts down the apparent diameters of their discs, and reduces
-the number of rings visible against the background of the sky.</p>
-
-<p>The scale of the diffraction system determines the resolving
-power of the telescope. This scale is given in Airy’s original
-paper (Cambr. Phil. Trans. <b>1834</b> p. 283), from which the angle α
-to any maximum or minimum in the ring system is defined by</p>
-
-<p class="center">sin α = <i>n</i>λ/<i>R</i></p>
-
-<p>in which λ is numerically the wave length of any light considered
-and <i>R</i> is the radius of the objective.</p>
-
-<p>We therefore see that the ring system varies in dimension
-inversely with the aperture of the objective and directly with the
-wave length considered. Hence the bigger the objective the
-smaller the disc and its surrounding ring system; and the greater
-the wave length, i.e. the redder the light, the bigger the diffraction
-system. Evidently there should be color in the rings but
-it very seldom shows on account of the faintness of the
-illumination.</p>
-
-<p>Now the factor <span class="u"><i>n</i></span> is for the first dark ring 0.61, and for the first<span class="pagenum"><a name="Page_261" id="Page_261">[Pg 261]</a></span>
-bright ring 0.81, as computed from Airy’s general theory, and
-therefore if we reckon that two stars will be seen as separate
-when the central disc of one falls on the first dark ring of the
-other the angular distance will be</p>
-
-<p class="center">Sin α = 0.61 λ/<i>R</i>′</p>
-
-<p>and, taking λ at the brightest part of the spectrum i.e., about
-560 μμ, in the yellow green, with α taken for sin α, we can
-compute this assumed separating power for any aperture. Thus
-560 μμ being very nearly 1/45,500 inch, and assuming a 5 inch
-telescope, the instrument should on this basis show as double two
-stars whose centres are separated by 1.″1 of arc.</p>
-
-<p>In actual fact one can do somewhat better than this, showing
-that the visible diameter of the central disc is in effect less than
-the diameter indicated by the diffraction pattern, owing to the
-reasons already stated. Evidently the brightness of the star is a
-factor in the situation since if very bright the disc gains apparent
-size, and when very faint there is sufficient difficulty in seeing
-one star, let alone a pair.</p>
-
-<p>The most thorough investigation of this matter of resolving
-power was made by the Rev. W. R. Dawes many years ago
-(Mem. R.A.S. <b>35</b>, 158). His study included years of observation
-with telescopes of different sizes, and his final result was to
-establish what has since been known as “Dawes’ Limit.”</p>
-
-<p>To sum up Dawes’ results he established the fact that on the
-average a one inch aperture would enable one to separate two
-6th magnitude stars the centers of which were separated by 4.56″.
-Or, to generalize from this basis, the separating power of any
-telescope is for very nearly equal stars, moderately bright,
-4″.56/<i>A</i> where <i>A</i> is the aperture of the telescope in inches.</p>
-
-<p>Many years of experience have emphasized the usefulness of
-this approximate rule, but that it is only approximate must be
-candidly admitted. It is a limit decidedly under that just
-assigned on the basis of the theory of diffraction for the central
-bright wave-lengths of the spectrum. Attempts have been
-made to square the two figures by assuming in the diffraction
-theory a wave length of 1/55,000 inch, but this figure corresponds
-to a point well up into the blue, of so low luminosity that it is of
-no importance whatever in the visual use of a telescope.</p>
-
-<p>The fact is that the visibility of two neighboring bright points<span class="pagenum"><a name="Page_262" id="Page_262">[Pg 262]</a></span>
-as distinct, depends on a complex of physical and physiological
-factors, the exact relations of which have never been unravelled.
-To start with we have the principles of diffraction as just
-explained, which define the relation of the stellar disc to the
-center of the first dark ring, but we know that under no circumstances
-can one see the disc out to this limit, since vision fails
-to take cognizance of the faint rim of the image. The apparent
-diameter of the diffraction solid therefore corresponds to a
-section taken some distance above the base, the exact point
-depending on the sensitiveness of the particular observer’s eye,
-the actual brilliancy of the center of the disc, and the corresponding
-factors for the neighboring star.</p>
-
-<div class="figcenter">
-<img src="images/i_262.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 185.</span>—Diffraction Solid for a Disc.</div>
-</div>
-
-<p>Under favorable circumstances one would not go far amiss in
-taking the visible diameter of the disc at about half that reckoned
-to the center of the first dark ring. This figure in fact corresponds
-to what has been shown to be within the grasp of a good
-observer under favorable conditions, as we shall presently see.</p>
-
-<p>On the other hand, if the stars are decidedly bright there is
-increase of apparent diameter of the disc due to the phenomenon
-known as irradiation, the spreading of light about its true image
-on the retina which corresponds quite closely to the halation
-produced by a bright spot on a photographic plate.</p>
-
-<p>If, on the contrary, the stars are very faint the total amount of
-light available is not sufficient to make contrast over and above
-the background sufficient to disclose the two points as separate,
-while if the pair is very unequal the brighter one will produce
-sufficient glare to quite over-power the light from the smaller
-one so that the eye misses it entirely.</p>
-
-<p>A striking case of this is found in the companion to Sirius,
-an extremely difficult object for ordinary telescopes although the
-distance to the companion is about 10.6″ and its magnitude<span class="pagenum"><a name="Page_263" id="Page_263">[Pg 263]</a></span>
-is 8.4, making a superlatively easy double for the very smallest
-telescope save for the overpowering effect of the light of the
-large star. Another notoriously difficult object for small
-telescopes is δ Cygni, a beautiful double of which the smaller
-component falls unpleasantly near the first diffraction maximum
-of the primary in which it is apt to be lost.</p>
-
-<p>“Dawes’ Limit” is therefore subject to many qualifying factors.
-Lewis, in the papers already referred to (Obs. <b>37</b>, 378)
-did an admirable piece of investigation in going through the
-double star work of about two score trained observers working
-with telescopes all the way from 4 inches to 36 inches aperture.</p>
-
-<p>From this accumulation of data several striking facts stand
-out. First there is great difference between individual observers
-working with telescopes of similar aperture as respects their
-agreement with “Dawes’ Limit,” showing the effect of variation
-in the physiological factors as well as instrumental ones.</p>
-
-<p>Second, there is also a very large difference between the
-facility of observing equal bright pairs and equal faint pairs, or
-unequal pairs of any kind, again emphasizing the physiological
-as well as the physical factors.</p>
-
-<p>Finally, there is most unmistakable difference between small
-and large apertures in their capacity to work up to or past the
-standard of “Dawes’Limit.” The smaller telescopes are clearly
-the more efficient as would be anticipated from the facts just
-pointed out regarding the different effect of the ordinary and
-inescapable atmospheric waves on small and large instruments.</p>
-
-<p>The big telescopes are unquestionably as good optically
-speaking as the small ones but under the ordinary working conditions,
-even as good as those a double star observer seeks, the
-smaller aperture by reason of less disturbance from atmospheric
-factors does relatively much the better work, however good the
-big instrument may be under exceptional conditions.</p>
-
-<p>This is admirably shown by the discussion of the beautiful
-work of the late Mr. Burnham, than whom probably no better
-observer of doubles has been known to astronomy. His records
-of discovery with telescopes of 6, 9.4, 12, 18&frac12; and 36 inches
-show the relative ease of working to the theoretical limit with
-instruments not seriously upset by ordinary atmospheric waves.</p>
-
-<p>With the 6 inch aperture Burnham reached in the average 0.53
-of Dawes’ limit, quite near the rough figure just suggested, and
-he also fell well inside Dawes’ limit with the 9.4 inch instrument.<span class="pagenum"><a name="Page_264" id="Page_264">[Pg 264]</a></span>
-With none of the others did he reach it and in fact fell short of
-it by 15 to 60%. All observations being by the same notably
-skilled observer and representing discoveries of doubles, so that no
-aid could have been gained by familiarity, the issue becomes exceedingly
-plain that size with all its advantages in resolving power
-brings serious countervailing limitations due to atmosphere.</p>
-
-<p>But a large aperture has besides its possible separating power
-one advantage that can not be discounted in “light grasp,” the
-power of discerning faint objects. This is the thing in which a
-small telescope necessarily fails. The “light grasp” of the
-telescope obviously depends chiefly on the area of the objective,
-and visually only in very minor degree on the absorption of the
-thicker glass in the case of a large lens.</p>
-
-<p>According to the conventional scale of star magnitudes as now
-in universal use, stars are classified in magnitudes which differ
-from each other by a light ratio of 2.512. a number the logarithm
-of which is 0.4, a relation suggested by Pogson some forty years
-ago. A second magnitude star therefore gives only about 40%
-of the light of a first magnitude star, while a third magnitude star
-gives again a little less than 40% of the light of a second magnitude
-star and so on.</p>
-
-<p>But doubling the aperture of a telescope increases the available
-area of the objective four times and so on, the “light grasp”
-being in proportion to the square of the aperture. Thus a 10
-inch objective will take in and deliver nearly 100 times as much
-light as would a 1 inch aperture. If one follows Pogson’s scale
-down the line he will find that this corresponds exactly to 5
-stellar magnitudes, so that if a 1 inch aperture discloses, as it
-readily does, a 9th magnitude star, a 10 inch aperture should
-disclose a 14th magnitude star.</p>
-
-<p>Such is substantially in fact the case, and one can therefore
-readily tabulate the minimum visible for an aperture just as he
-can tabulate the approximate resolving power by reference to
-Dawes’ limit. Fig. 186 shows in graphic form both these relations
-for ready reference, the variation of resolving power with
-aperture, and that of “light grasp,” reckoned in stellar
-magnitudes.</p>
-
-<p>It is hardly necessary to state that considerable individual and
-observational differences will be found in each of these cases,
-in the latter amounting to not less than 0.5 to 1.0 magnitude
-either way. The scale is based on the 9th magnitude star just<span class="pagenum"><a name="Page_265" id="Page_265">[Pg 265]</a></span>
-being visible with 1 inch aperture, whereas in fact under varying
-conditions and with various observers the range may be from the
-8th to 10th magnitude. All these things, however convenient,
-must be taken merely at their true value as good working
-approximations.</p>
-
-<p>Even the diffraction theory can be taken only as an approximation
-since no optical surface is absolutely perfect and in
-the ordinary refracting telescope there is a necessary residual
-chromatic aberration beside whatever may remain of spherical
-errors.</p>
-
-<div class="figcenter">
-<img src="images/i_265.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 186.</span>—Light-grasp and Resolving Power.</div>
-</div>
-
-<p>It is a fact therefore, as has been shown by Conrady (M.N.
-<b>79</b> 575) following up a distinguished investigation by Lord
-Rayleigh (Sci. Papers <b>1</b> 415), that a certain small amount of
-aberration can be tolerated without material effect on the
-definition, which is very fortunate considering that the secondary
-spectrum represents aberrations of about &frac12;,000 of the focal
-length, as we have already seen.</p>
-
-<p>The chief effect of this, as of very slight spherical aberration,
-is merely to reduce the maximum intensity of the central disc
-of the diffraction pattern and to produce a faint haze about it
-which slightly illuminates the diffraction minima. The visible<span class="pagenum"><a name="Page_266" id="Page_266">[Pg 266]</a></span>
-diameter of the disc and the relative distribution of intensity in
-it is not however materially changed so that the main effect is a
-little loss and scattering of light.</p>
-
-<p>With larger aberrations these effects are more serious but
-where the change in length of optical path between the ray
-proceeding through the center of the objective and that from the
-margin does not exceed ¼λ the injury to the definition is substantially
-negligible and virtually disappears when the image is
-focussed for the best definition, the loss of maximum intensity
-in the star disc amounting to less than 20%.</p>
-
-<p>Even twice this error is not a very serious matter and can be
-for the most part compensated by a minute change of focus as is
-very beautifully shown in a paper by Buxton(M. N. <b>81</b>, 547),
-which should be consulted for detail of the variations to be
-effected.</p>
-
-<p>Conrady finds a given change <i>dp</i> in the difference in lengths of
-the optical paths, related to the equivalent linear change of
-focus, <i>df</i>, as follows:—</p>
-
-<p class="center">
-<i>df</i> = 8<i>dp</i>(<i>f</i>/<i>A</i>)²<br />
-</p>
-
-<p>A being the aperture and f the focal length, which indicates for
-telescopes of ordinary focal ratio a tolerance of the order of
-±0.01 inch before getting outside the limit λ for variation of
-path.</p>
-
-<p>For instruments of greater relative aperture the precision of
-focus and in general the requirements for lessened aberration
-are far more severe, proportional in fact to the square of this
-aperture. Hence the severe demands on a reflector for exact
-figure. An instrument working at F/5 or F/6 is extremely sensitive
-to focus and demands great precision of figure to fall within
-permissible values, say ¼λ to ½λ, for <i>dp</i>.</p>
-
-<p>Further, with a given value of <i>dp</i> and the relation established
-by the chromatic aberration, <i>i.e.</i>, about <i>f</i>/2000, a relation is also
-determined between <i>f</i> and <i>A</i>, required to bring the aberration
-within limits. The equation thus found is</p>
-
-<p class="center">
-<i>f</i> = 2.8<i>A</i>²<br />
-</p>
-
-<p>This practically amounts to the common F/15 ratio for an aperture
-of approximately 5 inches. For smaller apertures a greater<span class="pagenum"><a name="Page_267" id="Page_267">[Pg 267]</a></span>
-ratio can be well used, for larger, a relatively longer focus is
-indicated, the penalty being light spread into a halo over the
-diffraction image and reducing faint contrasts somewhat
-seriously.</p>
-
-<p>This is one of the factors aside from atmosphere, interfering
-with the full advantage of large apertures in refractors. While as
-already noted small amounts of spherical aberration may be to a
-certain extent focussed out, the sign of <i>df</i> must change with the
-sign of the residual aberration, and a quick and certain test of the
-presence of spherical aberration is a variation in the appearance
-of the image inside and outside focus.</p>
-
-<p>To emphasize the importance of exact knowledge of existing
-aberrations note Fig. 187, which shows the results of Hartmann
-tests on a typical group of the world’s large objectives. All
-show traces of residual zones, but differing greatly in magnitude
-and position as the attached scales show. The most conspicuous
-aberrations are in the big Potsdam photographic refractor, the
-least are in the 24 inch Lowell refractor. The former has since
-been refigured by Schmidt and revised data are not yet available;
-the latter received its final figure from the Lundins after the last
-of the Clarks had passed on.</p>
-
-<p>Now a glance at the curves shows that the bad zone of the
-Potsdam glass was originally near the periphery, (I), hence both
-involved large area and, from Conrady’s equation, seriously
-enlarged <i>df</i> due to the large relative aperture at the zone. An
-aberrant zone near the axis as in the stage (III) of the Potsdam
-objective or in the Ottawa 15 inch objective is much less harmful
-for corresponding reasons. Such differences have a direct bearing
-on the use of stops, since these may do good in case of peripheral
-aberration and harm when the faults are axial. Unless the
-aberrations are known no general conclusions can be drawn as
-to the effect of stops. Even in the Lowell telescope shown as a
-whole in Fig. 188, the late Dr. Lowell found stops to be useful
-in keeping down atmospheric troubles and reducing the illumination
-although they could have had no effect in relation to figure.
-Fig. 188 shows at the head of the tube a fitting for a big iris
-diaphragm, controlled from the eye-end, the value of which was
-well demonstrated by numerous observers.</p>
-
-<p>There are, too, cases in which a small instrument, despite
-intrinsic lack of resolving power, may actually do better work
-than a big one. Such are met in instances where extreme con<span class="pagenum"><a name="Page_268" id="Page_268">[Pg 268]</a><br /><a name="Page_269" id="Page_269">[Pg 269]</a></span>trast
-of details is sought, as has been well pointed out by Nutting
-(Ap. J. <b>40</b>, 33) and the situation disclosed by him finds amplification
-in the extraordinary work done by Barnard with a cheap
-lantern lens of 1&frac12; inch diameter and 5&frac12; inches focus (Pop. Ast.,
-<b>6</b>, 452).</p>
-
-<div class="figcenter">
-<img src="images/i_268.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 187.</span>—Hartmann Tests of Telescopes [From Hartmann’s Measures].</div>
-</div>
-
-<p>The fact is that every task must seek its own proper instrument.
-And in any case the interpretation of observed results
-is a matter that passes far beyond the bounds of geometrical
-optics, and involves physiological factors that are dominant in
-all visual problems.</p>
-
-<p>With respect to the visibility of objects the general diffraction
-theory again comes into play. For a bright line, for
-example, the diffraction figure is no longer chiefly a cone like
-Fig. 183, but a similar long wedge-shaped figure, with wave-like
-shoulders corresponding to the diffraction rings. The visibility
-of such a line depends not only on the distribution of intensity in
-the theoretical wedge but on the sensitiveness of the eye and the
-nature of the background and so forth, just as in the case of a
-star disc.</p>
-
-<p>If the eye is from its nature or state of adaptation keen enough
-on detail but not particularly sensitive to slight differences of
-intensity, the line will very likely be seen as if a section were
-made of the wedge near its thin edge. In other words the
-line will appear thin and sharp as the diffraction rings about a
-star frequently do.</p>
-
-<p>With an eye very sensitive to light and small differences of
-contrast the appearance of absolutely the same thing may
-correspond to a section through the wedge near its base, in other
-words to a broad strip shading off somewhat indistinctly at the
-edges, influenced again by irradiation and the character of the
-background.</p>
-
-<p>If there be much detail simultaneously visible the diffraction
-patterns may be mixed up in a most intricate fashion and one
-can readily see the confusion which may exist in correlating
-the work of various observers on things like planetary and lunar
-detail.</p>
-
-<p>In the planetary case the total image is a complex of illuminated
-areas of diffraction at the edges, which may be represented
-as the diffraction solid of Fig. 185, in which the dotted lines show
-what may correspond fairly to the real diameter of the planet,
-the edge shading off in a way again complicated by irradiation.</p>
-
-<p><span class="pagenum"><a name="Page_270" id="Page_270">[Pg 270]</a></span></p>
-
-<div class="figcenter">
-<img src="images/i_270.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 188.</span>—The Lowell Refractor Fitted with Iris Diaphragm.</div>
-</div>
-
-<p><span class="pagenum"><a name="Page_271" id="Page_271">[Pg 271]</a></span></p>
-
-<p>Fancy detail superimposed on a disc of this sort and one has a
-vivid idea of the difficulty of interpreting observations.</p>
-
-<p>It would be an exceedingly good thing if everyone who uses
-his telescope had the advantage of at least a brief course in
-microscopy, whereby he would gain very much in the practical
-understanding of resolving power, seeing conditions, and the
-interpretation of the image. The principles regarding these
-matters are in fact very much the same with the two great instruments
-of research.</p>
-
-<p>Aperture, linear in the case of the telescope and the so-called
-numerical in the case of the microscope, bear precisely the same
-relation to resolution, the minimum resolvable detail being in
-each case directly proportional to aperture in the senses here
-employed.</p>
-
-<p>Further, although the turbulence of intervening atmosphere
-does not interfere with the visibility of microscopic detail, a
-similar disturbing factor does enter in the form of irregular and
-misplaced illumination. It is a perfectly easy matter to make
-beautifully distinct detail quite vanish from a microscopic image
-merely by mismanagement of the illumination, just as unsteady
-atmosphere will produce substantially the same effect in the
-telescopic image.</p>
-
-<p>In the matter of magnification the two cases run quite parallel,
-and magnification pushed beyond what is justified by the resolving
-power of the instrument does substantially little or no good.
-It neither discloses new detail nor does it bring out more sharply
-detail which can be seen at all with a lower power.</p>
-
-<p>The microscopist early learns to shun high power oculars,
-both from their being less comfortable to work with, and from
-their failing to add to the efficiency of the instrument except in
-some rare cases with objectives of very high resolving power.
-Furthermore in the interpretation of detail the lessons to be
-learned from the two instruments are quite the same, although
-one belongs to the infinitely little and the other to the infinitely
-great.</p>
-
-<p>Nothing is more instructive in grasping the relation between
-resolving power, magnification, and the verity of detail, than the
-study under the microscope of some well known objects. For
-example, in Fig. 189 is shown a rough sketch of a common diatom,
-<i>Navicula Lyra</i>. The tiny siliceous valve appears thus under an
-objective of slightly insufficient resolving power. The general<span class="pagenum"><a name="Page_272" id="Page_272">[Pg 272]</a></span>
-form of the object is clearly perceived, as well as the central
-markings, standing boldly out in the form which suggests the
-specific name. No trace of any finer detail appears and no
-amount of dexterity in arranging the illumination or increase of
-magnifying power will show any more than here appears, the
-drawing being one actually made with the camera lucida, using
-an objective of numerical aperture just too small to resolve the
-details of the diatoms on this particular slide.</p>
-
-<p>Figure 189<i>a</i> shows what happens when, with the same magnifying
-power, an objective of slightly greater aperture is employed.
-Here the whole surface of the valve is marked with fine striations,
-beautifully sharp and distinct like the lines of a steel
-engraving. There is a complete change of aspect wrought by an
-increase of about 20% in the resolving power. Again nothing
-further can be made out by an increase of magnification, the
-only effect being to make the outlines a little hazier and the view
-therefore somewhat less satisfactory.</p>
-
-<div class="figcenter">
-<img src="images/i_272.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 189.</span>—The Stages of Resolution.</div>
-</div>
-
-<p>Finally in Fig. 189<i>b</i> we have again the same valve under the
-same magnifying power, but here obtained from an objective
-of numerical aperture 60% above that used for the main figure.
-The sharp striæ now show their true character. They had their
-origin in lines of very clearly distinguished dots, which are
-perfectly distinct, and are due to the resolving power at last being
-sufficient to show the detail which previously merely formed a
-sharp linear diffraction pattern entirely incapable of being resolved
-into anything else by the eye, however much it might
-be magnified.</p>
-
-<p><span class="pagenum"><a name="Page_273" id="Page_273">[Pg 273]</a></span></p>
-
-<p>Here one has, set out in unmistakable terms, the same kind
-of differences which appear in viewing celestial detail through
-telescopes of various aperture. What cannot be seen at all with
-a low aperture may be seen with higher ones under totally different
-aspects; while in each case the apparent sharpness and
-clarity of the image is somewhat extraordinary.</p>
-
-<p>Further in Fig. 189<i>b</i> in using the resolving power of the objective
-of high numerical aperture, the image may be quite wrecked
-by a little carelessness in focussing, or by mismanagement of
-light, so that one would hardly know that the valve had markings
-other than those seen with the objectives of lower aperture, and
-under these circumstances added magnification would do more
-harm than good. In precisely the same way mismanagement of
-the illumination in Fig. 189<i>a</i> would cause the striæ to vanish and
-with <i>Navicula Lyra</i>, as with many other diatoms, the resolution
-into striæ is a thing which often depends entirely on careful
-lighting, and the detail flashes into distinctness or vanishes with a
-suddenness which is altogether surprising. For “lighting”
-read “atmosphere,” and you have just the sort of conditions
-that exist in telescope vision.</p>
-
-<p>With respect to magnifying powers what has already been
-said is sufficient to indicate that on the whole the lowest power
-which discloses to the eye the detail within the reach of the
-resolving power of the objective is the most satisfactory.</p>
-
-<p>Every increase above this magnifies all the optical faults of
-the telescope and the atmospheric difficulties as well, beside
-decreasing the diameter of the emergent pencil which enters the
-eye, and thereby causing serious loss of acuity. For the eye
-like any other optical instrument loses resolving power with
-decrease of effective aperture, and, besides, a very narrow beam
-entering it is subject to the interference of entoptic defects, such
-as floating motes and the like, to a serious extent.</p>
-
-<p>Figure 190 shows from Cobb’s experiments (Am. Jour. of Physiol.,
-<b>35</b>, 335) the effect of reduction of ocular aperture upon acuity.
-The curve shows very plainly that for emergent pencils below a
-millimeter (1/25 inch) in diameter, visual acuity falls off almost
-in direct proportion to the decreasing aperture. Below this figure
-there can be only incidental gains, such as may be due to opening
-up double stars and simultaneously so diminishing the general
-illumination as to render the margins of the star discs a little
-less conspicuous.</p>
-
-<p><span class="pagenum"><a name="Page_274" id="Page_274">[Pg 274]</a></span></p>
-
-<p>An emergent pencil of this diameter is not quite sufficient for
-the average eye to utilize fully the available resolving power and
-some excess of magnification even though it actually diminishes
-visual acuity materially, may be of some service.</p>
-
-<div class="figcenter">
-<img src="images/i_274.jpg" alt="" />
-<div class="caption"><span class="smcap">Fig. 190.</span>—Resolving Power of the Eye.</div>
-</div>
-
-<p>Increased acuity will of course be gained for the same magnification
-in using an objective of greater diameter, to say nothing
-of increased resolving power, at the cost, of course, of relatively
-greater atmospheric troubles.</p>
-
-<p>To come down to figures as to the resolving power of the eye,
-often repeated experiments have shown that two points offering
-strong contrast with the background can be noted as separate
-by the normal eye when at an angular separation of about 3′
-of arc. People, as we have seen, differ considerably in acuity
-so that now and then individuals will considerably better this
-figure, while others, far less keen sighted, may require a separation
-of 4′ or even 5′.</p>
-
-<p>The pair of double stars ε<sub>1</sub>, ε<sub>2</sub>, Lyræ, separated by 3′ 27″
-mags. nearly 4 and 5 respectively, can be seen as separate<span class="pagenum"><a name="Page_275" id="Page_275">[Pg 275]</a></span>
-by those of fairly keen vision, while Mizar and Alcor, 11′
-apart, seem thrown wide to nearly every one. On the other
-hand the writer has never known anybody who could separate
-the two components of Asterope of the Pleiades, distant a scant
-2&frac12; but of mags. 6.5 and 7.0 only, while Pleione and Atlas,
-distance about 5&frac14;′, mags. 6.5 and 4, are very easy.</p>
-
-<p>Assuming for liberality that the separation constant is in the
-neighborhood of 5′ one can readily estimate the magnification
-that for any telescope will take full advantage of its resolving
-power. As we have already seen this resolving power is practically
-4.″56/<i>A</i> for equal stars moderately bright. <a id="An_objective"></a>An objective of
-4.56′ inches aperture has a resolving constant of 1″ and to
-develop this should take a magnification of say 300, about 65
-to the inch of aperture, requiring a focal length of ocular about
-0.20 to 0.25 inch for telescopes of normal relative aperture, and
-pushing the emergent pencil down to little more than 0.02 inch,—rather
-further than is physiologically desirable. Except for these
-extreme stunts of separation, half to two thirds this power is
-preferable and conditions under which one can advantageously
-go above this limit are very rare indeed.</p>
-
-<p>A thoroughly good objective or mirror will stand quite 100
-magnification to the inch without, as the microscopist would say,
-“breaking down the image,” but in at least nine cases out of ten
-the result will be decidedly unsatisfactory.</p>
-
-<p>As the relative aperture of the instrument increases, other
-things being equal, one is driven to oculars of shorter and shorter
-focus to obtain the same magnification and soon gets into trouble.
-Very few oculars below 0.20 inch in focus are made, and such
-are rarely advisable, although occasionally in use down to 0.15
-inch or thereabouts. The usual F/15 aperture is a figure quite
-probably as much due to the undesirability of extremely short
-focus oculars as to the easier corrections of the objective.</p>
-
-<p>In the actual practice of experienced observers the indications
-of theory are well borne out. Data of the habits of many observers
-of double stars are of record and the accomplished veteran
-editor of <i>The Observatory</i>, Mr. T. Lewis, took the trouble in one
-of his admirable papers on “Double Star Astronomy” (Obs. <b>36</b>,
-426) to tabulate from the original sources the practice of a large
-group of experts. The general result was to show the habitual
-use with telescopes of moderate size of powers around 50 per<span class="pagenum"><a name="Page_276" id="Page_276">[Pg 276]</a></span>
-inch of aperture, now and then on special occasions raised to the
-neighborhood of 70 per inch.</p>
-
-<p>But the data showed unequivocally just what has been already
-indicated, that large apertures, suffering severely as they generally
-do from turbulence of the air, will not ordinarily stand their
-due proportion of magnification. With the refractors of 24 inches
-aperture and upwards the records show that even in this double
-star work, where, if anywhere, high power counts, the general
-practice ran in the vicinity of 30 per inch of aperture.</p>
-
-<p>Analyzing the data more completely in this respect Mr.
-Lewis found that the best practise of the skilled observers studied
-was approximately represented by the empirical equation</p>
-
-<p><i>m</i> = 140 √<i>A</i></p>
-
-<p>Of course the actual figures must vary with the conditions of
-location and the general quality of the seeing, as well as the
-work in hand. For other than double star work the tendency will
-be generally toward lower powers. The details which depend
-on shade perception rather than visual acuity are usually hurt
-rather than helped when magnified beyond the point at which
-they are fairly resolved, quite as in the case of the microscope.</p>
-
-<p>Now and then they may be made more distinct by the judicious
-use of shade glasses. Quite apart from the matter of the high
-powers which can advantageously be used on a telescope, one
-must for certain purposes consider the lowest powers which are
-fairly applicable. This question really turns on the largest
-utilizable emergent pencil from the eye piece. It used to be
-commonly stated that ⅛ inch for the emergent pencil was
-about a working maximum, leading to a magnification of 8 per
-inch of aperture of the objective. This in view of our present
-knowledge of the eye and its properties is too low an estimate of
-pupillary aperture. It is a fact which has been well known for
-more than a decade that in faint light, when the eye has become
-adapted to its situation, the pupil opens up to two or three times
-this diameter and there is no doubt that a fifth or a fourth of an
-inch aperture can be well utilized, provided the eye is properly
-dark-adapted. For scrutinizing faint objects, comet sweeping
-and the like, one should therefore have one ocular of very wide
-field and magnifying power of 4 or 5 per inch of aperture, the
-main point being to secure a field as wide is practicable. One
-may use for such purposes either a very wide field Huyghenian,<span class="pagenum"><a name="Page_277" id="Page_277">[Pg 277]</a></span>
-or, if cross wires are to be used, a Kellner form. Fifty degrees of
-field is perfectly practicable with either. As regards the rest
-of the eyepiece equipment the observer may well suit his own
-convenience and resources. Usually one ocular of about half
-the maximum power provided will be found extremely convenient
-and perhaps oftener used than either the high or low power.
-Oculars of intermediate power and adapted for various purposes
-will generally find their way into any telescopic equipment. And
-as a last word do not expect to improve bad conditions by
-magnifying. If the seeing is bad with a low power, cap the
-telescope and await a better opportunity.</p>
-
-<hr class="chap" />
-
-<p><span class="pagenum"><a name="Page_278" id="Page_278">[Pg 278]</a><br /><a name="Page_279" id="Page_279">[Pg 279]</a></span></p>
-
-
-
-
-<div class="chapter"></div>
-<h2><a name="APPENDIX" id="APPENDIX">APPENDIX</a><br />
-
-<small>WORK FOR THE TELESCOPE</small></h2>
-
-
-<p>To make at first hand the acquaintance of the celestial bodies
-is, in and of itself, worth the while, as leading the mind to a
-new sense of ultimate values. To tell the truth the modern man
-on the whole knows the Heavens less intimately than did his
-ancestors. He glances at his wrist-watch to learn the hour and
-at the almanac to identify the day. The rising and setting of
-the constellations, the wandering of the planets among the
-stars, the seasonal shifting of the sun’s path—all these are a
-sealed book to him, and the intricate mysteries that lie in the
-background are quite unsuspected.</p>
-
-<p>The telescope is the lifter of the cosmic veil, and even for
-merely disclosing the spectacular is a source of far-reaching
-enlightenment. But for the serious student it offers opportunities
-for the genuine advancement of human knowledge
-that are hard to underestimate. It is true that the great modern
-observatories can gather information on a scale that staggers
-the private investigator. But in this matter fortune favors
-the pertinacious, and the observer who settles to a line of deliberate
-investigation and patiently follows it is likely to find his
-reward. There is so much within the reach of powerful instruments
-only, that these are in the main turned to their own
-particular spheres of usefulness.</p>
-
-<p>For modest equipment there is still plenty of work to do.
-The study of variable stars offers a vast field for exploration,
-most fruitful perhaps with respect to the irregular and long-period
-changes of which our own Sun offers an example. Even
-in solar study there are transient phenomena of sudden eruptions
-and of swift changes that escape the eye of the spectro-heliograph,
-and admirable work can be done, and has been done,
-with small telescopes in studying the spectra of sun spots</p>
-
-<p>Temporary stars visible to the naked eye or to the smallest
-instruments turn up every few years and their discovery has
-usually fallen to the lot of the somewhat rare astronomer,
-professional or amateur, who knows the field of stars as he knows<span class="pagenum"><a name="Page_280" id="Page_280">[Pg 280]</a></span>
-the alphabet. The last three important novæ fell to the amateurs—two
-to the same man. Comets are to be had for the
-seeking by the persistent observer with an instrument of fair
-light-grasp and field; one distinguished amateur found a pair
-within a few days, acting on the theory that small comets are
-really common and should be looked for—most easily by one
-who knows his nebulæ, it should be added.</p>
-
-<p>And within our small planetary system lies labor sufficient
-for generations. We know little even about the superficial
-characters of the planets, still less about their real physical
-condition. We are not even sure about the rotation periods of
-Venus and Neptune. The clue to many of the mysteries requires
-eternal vigilance rather than powerful equipment, for the
-appearance of temporary changes may tell the whole story.
-The old generation of astronomers who believed in the complete
-inviolability of celestial order has been for the most part gathered
-to its fathers, and we now realize that change is the law of the
-universe. Within the solar system there are planetary surfaces
-to be watched, asteroids to be scanned for variability or change
-of it, meteor swarms to be correlated with their sources, occultations
-to be minutely examined, and when one runs short of these,
-our nearest neighbor the Moon offers a wild and physically
-unknown country for exploration. It is suspected with good
-reason of dynamic changes, to say nothing of the possible last
-remnants of organic life.</p>
-
-<p>Much of this work is well within the useful range of instruments
-of three to six inches aperture. The strategy of successful
-investigation is in turning attention upon those things which are
-within the scope of one’s equipment, and selecting those which
-give promise of yielding to a well directed attack. And to this
-end efforts correlated with those of others are earnestly to be
-advised. It is hard to say too much of the usefulness of directed
-energies like those of the Variable Star Association and similar
-bodies. They not only organize activities to an important
-common end, but strengthen the morale of the individual
-observer.</p>
-
-<hr class="chap" />
-
-<p><span class="pagenum"><a name="Page_281" id="Page_281">[Pg 281]</a></span></p>
-
-
-
-
-<div class="chapter"></div>
-<h2><a name="INDEX" id="INDEX">INDEX</a></h2>
-
-
-<div class="index">
-<ul class="index">
-<li class="ifrst">A</li>
-
-<li class="indx">Abbé, roof prism, <a href='#Page_162'>162</a></li>
-
-<li class="indx">Aberration, compensated by minute change of focus, <a href='#Page_266'>266</a></li>
-<li class="isub1">illuminates the diffraction minima, <a href='#Page_265'>265</a></li>
-<li class="isub1">relation determines of focus and aperture, <a href='#Page_266'>266</a></li>
-
-<li class="indx">Achromatic long relief ocular, <a href='#Page_146'>146</a></li>
-<li class="isub1">objective, <a href='#Page_77'>77</a></li>
-
-<li class="indx">Achromatism, condition for, <a href='#Page_78'>78</a></li>
-<li class="isub1">determination of, <a href='#Page_78'>78</a></li>
-<li class="isub1">imperfection of, <a href='#Page_87'>87</a></li>
-
-<li class="indx">Adjustment where Polaris invisible, <a href='#Page_235'>235</a></li>
-
-<li class="indx">Air waves, length of, <a href='#Page_255'>255</a></li>
-
-<li class="indx">Alt-azimuth mount for reflector, <a href='#Page_102'>102</a></li>
-<li class="isub1">mounts, with slow motions, <a href='#Page_102'>102</a></li>
-<li class="isub1">setting up an, <a href='#Page_228'>228</a></li>
-
-<li class="indx">Anastigmats, <a href='#Page_84'>84</a></li>
-
-<li class="indx">Annealing, pattern of strain, <a href='#Page_68'>68</a></li>
-
-<li class="indx">Astigmatism, <a href='#Page_84'>84</a>, <a href='#Page_209'>209</a></li>
-<li class="isub1">of figure, <a href='#Page_210'>210</a></li>
-
-<li class="indx">Astronomy, dawn of popular, <a href='#Page_19'>19</a></li>
-
-
-<li class="ifrst">B</li>
-
-<li class="indx">Bacon, Roger, alleged description of telescopes, <a href='#Page_6'>6</a></li>
-
-<li class="indx">Barlow lens, <a href='#Page_152'>152</a></li>
-
-<li class="indx">“Bent,” objective, <a href='#Page_86'>86</a></li>
-
-<li class="indx">Binocular, <a href='#Page_2'>2</a></li>
-<li class="isub1">advantage of, exaggerated, <a href='#Page_151'>151</a></li>
-<li class="isub1">for strictly astronomical use, <a href='#Page_152'>152</a></li>
-<li class="isub1">telescopes for astronomical use, <a href='#Page_163'>163</a></li>
-
-
-<li class="ifrst">C</li>
-
-<li class="indx">Camouflage, in optical patents, <a href='#Page_97'>97</a></li>
-
-<li class="indx">Cassegrain, design for reflecting telescope, <a href='#Page_22'>22</a></li>
-
-<li class="indx">Cassegrain, sculptor and founder of statues, <a href='#Page_22'>22</a></li>
-
-<li class="indx">Cell, taking off from a telescope, <a href='#Page_202'>202</a></li>
-
-<li class="indx">Chromatic aberration, <a href='#Page_11'>11</a>, <a href='#Page_76'>76</a></li>
-<li class="isub1">investigation of, <a href='#Page_210'>210</a></li>
-<li class="isub1">correction, differences in, <a href='#Page_91'>91</a></li>
-<li class="isub1">error of the eye, <a href='#Page_90'>90</a></li>
-
-<li class="indx">Clairault’s condition, <a href='#Page_81'>81</a></li>
-<li class="isub1">two cemented forms for, <a href='#Page_81'>81</a></li>
-
-<li class="indx">Clarks, portable equatorial mounting, <a href='#Page_109'>109</a></li>
-<li class="isub1">terrestrial prismatic eyepiece, <a href='#Page_158'>158</a></li>
-
-<li class="indx">Clock, the cosmic, <a href='#Page_233'>233</a></li>
-
-<li class="indx">Clock drive, <a href='#Page_110'>110</a>, <a href='#Page_174'>174</a></li>
-
-<li class="indx">Clock mechanism, regulating rate of motor, <a href='#Page_179'>179</a></li>
-
-<li class="indx">Coddington lens, <a href='#Page_137'>137</a></li>
-
-<li class="indx">Cœlostat constructions, <a href='#Page_126'>126</a></li>
-<li class="isub1">tower telescopes, <a href='#Page_127'>127</a></li>
-
-<li class="indx">Color correction, commonly used, <a href='#Page_211'>211</a></li>
-<li class="isub1">examined by spectroscope, <a href='#Page_211'>211</a></li>
-<li class="isub1">of the great makers, <a href='#Page_90'>90</a></li>
-
-<li class="indx">Coma-free, condition combined with Clairault’s, <a href='#Page_83'>83</a></li>
-
-<li class="indx">Comet seeker, Caroline Herschel’s <a href='#Page_118'>118</a></li>
-<li class="isub1">seekers with triple objective, <a href='#Page_119'>119</a></li>
-
-<li class="indx">Crowns distinguished from flints, <a href='#Page_64'>64</a></li>
-
-<li class="indx">Curves, struggle for non-spherical, <a href='#Page_18'>18</a></li>
-
-
-<li class="ifrst">D</li>
-
-<li class="indx">Davon micro-telescope, <a href='#Page_148'>148</a></li>
-
-<li class="indx">Dawes’ Limit, <a href='#Page_261'>261</a></li>
-<li class="isub1">in physiological factors, <a href='#Page_263'>263</a></li>
-
-<li class="indx">Declination circle, <a href='#Page_108'>108</a></li>
-<li class="isub1">adjustment of, <a href='#Page_239'>239</a>
-<span class="pagenum"><a name="Page_282" id="Page_282">[Pg 282]</a></span></li>
-<li class="indx">Declination circle, adjustment by, <a href='#Page_237'>237</a></li>
-<li class="isub1">facilitates setting up instrument, <a href='#Page_110'>110</a></li>
-
-<li class="indx">Definition condition for excellence of, <a href='#Page_254'>254</a></li>
-<li class="isub1">good in situations widely different, <a href='#Page_254'>254</a></li>
-
-<li class="indx">DeRheita, <a href='#Page_12'>12</a></li>
-<li class="isub1">constructed binoculars, <a href='#Page_13'>13</a></li>
-<li class="isub1">terrestrial ocular, <a href='#Page_13'>13</a></li>
-
-<li class="indx">Descartes’ dioptrics, publication of, <a href='#Page_11'>11</a></li>
-<li class="isub1">lens with elliptical curvature, <a href='#Page_12'>12</a></li>
-
-<li class="indx">Dew cap, <a href='#Page_219'>219</a></li>
-
-<li class="indx">Diaphragms, importance of, <a href='#Page_43'>43</a></li>
-
-<li class="indx">Diffraction figure for bright line, <a href='#Page_269'>269</a></li>
-<li class="isub1">pattern, <a href='#Page_256'>256</a></li>
-<li class="isub1">solid, apparent diameter of, <a href='#Page_262'>262</a></li>
-<li class="isub1">solid of planet, <a href='#Page_269'>269</a></li>
-<li class="isub1">solid for a star, <a href='#Page_260'>260</a></li>
-<li class="isub1">spectra, <a href='#Page_190'>190</a></li>
-<li class="isub1">system, scale of, <a href='#Page_260'>260</a></li>
-<li class="isub1">varies inversely with aperture, <a href='#Page_260'>260</a></li>
-<li class="isub1">through objective, <a href='#Page_258'>258</a></li>
-
-<li class="indx">Digges, account suggests camera obscura, <a href='#Page_7'>7</a></li>
-
-<li class="indx">Dimensions, customary, telescope of, <a href='#Page_24'>24</a></li>
-
-<li class="indx">Discs, inspection of glass, <a href='#Page_66'>66</a></li>
-<li class="isub1">roughing to form, <a href='#Page_69'>69</a></li>
-
-<li class="indx">Distortion, <a href='#Page_86'>86</a></li>
-
-<li class="indx">Dolland, John, <a href='#Page_28'>28</a></li>
-<li class="isub2">published his discovery of achromatism, <a href='#Page_29'>29</a></li>
-<li class="isub1">Peter, early triple objective, <a href='#Page_29'>29</a></li>
-
-<li class="indx">Dome wholly of galvanized iron, <a href='#Page_250'>250</a></li>
-
-<li class="indx">Domes, <a href='#Page_246'>246</a></li>
-
-<li class="indx">Driving clock, a simple, <a href='#Page_174'>174</a></li>
-<li class="isub1">pendulum controlled, <a href='#Page_177'>177</a></li>
-<li class="isub1">clocks spring operated, <a href='#Page_175'>175</a></li>
-
-
-<li class="ifrst">E</li>
-
-<li class="indx">English equatorial, <a href='#Page_110'>110</a></li>
-<li class="isub1">mounts, mechanical stability of, <a href='#Page_113'>113</a></li>
-
-<li class="indx">Equatorial, adjustments of, <a href='#Page_230'>230</a></li>
-
-<li class="indx">Equatorial, coudé, <a href='#Page_124'>124</a></li>
-<li class="isub1">mount, different situations in using, <a href='#Page_229'>229</a></li>
-<li class="isub1">mount, first by Short, <a href='#Page_104'>104</a></li>
-<li class="isub1">mount, pier overhung, <a href='#Page_115'>115</a></li>
-<li class="isub1">mount in section, <a href='#Page_107'>107</a></li>
-<li class="isub1">two motions necessary in, <a href='#Page_106'>106</a></li>
-
-<li class="indx">Equilibrating levers, devised by T. Grubb, <a href='#Page_39'>39</a></li>
-
-<li class="indx">Evershed, direct vision solar spectroscope, <a href='#Page_189'>189</a></li>
-
-<li class="indx">Eye lens, simple, preferred by Sir W. Herschel, <a href='#Page_136'>136</a></li>
-
-<li class="indx">Eyepiece, compensating, <a href='#Page_142'>142</a></li>
-<li class="isub1">Huygenian, <a href='#Page_139'>139</a></li>
-<li class="isub1">Huygenian, achromatism of, <a href='#Page_140'>140</a></li>
-<li class="isub1">Huygenian, with cross wires, <a href='#Page_140'>140</a></li>
-<li class="isub1">Huygenian, field of, <a href='#Page_141'>141</a></li>
-<li class="isub1">Huygenian focal length of, <a href='#Page_143'>143</a></li>
-<li class="isub1">measuring focus of, <a href='#Page_136'>136</a></li>
-<li class="isub1">microscope form, <a href='#Page_147'>147</a>, <a href='#Page_148'>148</a></li>
-<li class="isub1">monocentric, <a href='#Page_139'>139</a></li>
-<li class="isub1">a simple microscope, <a href='#Page_134'>134</a></li>
-<li class="isub1">Tolles solid, <a href='#Page_141'>141</a></li>
-
-
-<li class="ifrst">F</li>
-
-<li class="indx">Field, curvature of, <a href='#Page_85'>85</a></li>
-<li class="isub1">glass, arrangement of parts, <a href='#Page_151'>151</a></li>
-<li class="isub2">Galilean, <a href='#Page_150'>150</a></li>
-<li class="isub2">lens diameter possible, <a href='#Page_150'>150</a></li>
-
-<li class="indx">Field lens, <a href='#Page_139'>139</a></li>
-
-<li class="indx">Figuring locally, <a href='#Page_73'>73</a></li>
-<li class="isub1">process of, <a href='#Page_73'>73</a></li>
-
-<li class="indx">Filar micrometer, <a href='#Page_172'>172</a></li>
-
-<li class="indx">Finder, <a href='#Page_108'>108</a>, <a href='#Page_132'>132</a></li>
-<li class="isub1">adjustment of, <a href='#Page_230'>230</a></li>
-
-<li class="indx">Fine grinding, <a href='#Page_69'>69</a></li>
-
-<li class="indx">Fixed eyepiece mounts, <a href='#Page_118'>118</a></li>
-
-<li class="indx">Flints, highly refractive due to Guinand, <a href='#Page_36'>36</a></li>
-
-<li class="indx">Foucault, <a href='#Page_39'>39</a></li>
-<li class="isub1">development of silver on glass reflector, <a href='#Page_41'>41</a></li>
-<li class="isub1">knife edge test, <a href='#Page_212'>212</a>
-<span class="pagenum"><a name="Page_283" id="Page_283">[Pg 283]</a></span></li>
-<li class="indx">Foucault, methods of working and testing, <a href='#Page_41'>41</a></li>
-
-<li class="indx">Fraunhofer, <a href='#Page_36'>36</a></li>
-<li class="isub1">applied condition of absence of coma, <a href='#Page_82'>82</a></li>
-<li class="isub1">form of objectives, <a href='#Page_37'>37</a></li>
-<li class="isub1">long list of notable achievements, <a href='#Page_38'>38</a></li>
-
-<li class="indx">“Front view” telescope, <a href='#Page_32'>32</a></li>
-<li class="isub1">mechanical difficulty of, <a href='#Page_33'>33</a></li>
-
-<li class="indx">Furnaces, glass, classes of, <a href='#Page_59'>59</a></li>
-
-
-<li class="ifrst">G</li>
-
-<li class="indx">Galilean telescope, small field of, <a href='#Page_9'>9</a></li>
-
-<li class="indx">Galileo, exhibited telescope to senators of Venice, <a href='#Page_8'>8</a></li>
-<li class="isub1">grasps the general principles, <a href='#Page_7'>7</a></li>
-<li class="isub1">produces instrument magnifying <a href='#Page_32'>32</a> times, <a href='#Page_8'>8</a></li>
-
-<li class="indx">Gascoigne, William, first using genuine micrometer, <a href='#Page_12'>12</a></li>
-
-<li class="indx">Gauss, Objective, <a href='#Page_82'>82</a></li>
-
-<li class="indx">Gerrish, application of drive, <a href='#Page_181'>181</a></li>
-<li class="isub1">motor drive, <a href='#Page_179'>179</a></li>
-
-<li class="indx">Ghosts, <a href='#Page_137'>137</a></li>
-
-<li class="indx">Glass, dark, as sunshade, <a href='#Page_166'>166</a></li>
-<li class="isub1">forming and annealing, <a href='#Page_62'>62</a></li>
-<li class="isub1">inspection of raw, <a href='#Page_61'>61</a></li>
-<li class="isub1">losses by volatilization, <a href='#Page_58'>58</a></li>
-<li class="isub1">materials of, <a href='#Page_59'>59</a></li>
-<li class="isub1">origin of, <a href='#Page_57'>57</a></li>
-<li class="isub1">persistent bubbles in, <a href='#Page_58'>58</a></li>
-<li class="isub1">a solid solution, <a href='#Page_57'>57</a></li>
-
-<li class="indx">Grating spectroscopes, <a href='#Page_190'>190</a></li>
-
-<li class="indx">Gratings, spectroscope, <a href='#Page_189'>189</a></li>
-
-<li class="indx">Gregory, James, described construction which bears his name, <a href='#Page_19'>19</a></li>
-<li class="isub1">failed of material success, <a href='#Page_20'>20</a></li>
-
-<li class="indx">Grubb, Sir Howard, objectives, <a href='#Page_74'>74</a></li>
-
-<li class="indx">Guinand, Pierre Louis, improvements in optical glass, <a href='#Page_36'>36</a></li>
-
-
-<li class="ifrst">H</li>
-
-<li class="indx">Hadley, disclosed test for true figure, <a href='#Page_27'>27</a></li>
-<li class="isub1">John, real inventor of reflector, <a href='#Page_25'>25</a></li>
-
-<li class="indx">Hadley’s reflector, tested with satisfactory results, <a href='#Page_26'>26</a></li>
-
-<li class="indx">Hall, Chester Moor, designed first achromatic telescope, <a href='#Page_27'>27</a></li>
-<li class="isub1">had telescopes made as early as 1733, <a href='#Page_27'>27</a></li>
-
-<li class="indx">Hand telescope, magnifying power, <a href='#Page_150'>150</a></li>
-<li class="isub1">monocular, <a href='#Page_151'>151</a></li>
-
-<li class="indx">Hartmann test, <a href='#Page_213'>213</a></li>
-<li class="isub1">on large objectives, <a href='#Page_267'>267</a></li>
-<li class="isub1">principle of, <a href='#Page_214'>214</a></li>
-
-<li class="indx">Hartness, turret telescope, <a href='#Page_130'>130</a>, <a href='#Page_131'>131</a></li>
-
-<li class="indx">Heliometer, principle of, <a href='#Page_171'>171</a></li>
-
-<li class="indx">Hensoldt, prism form, <a href='#Page_163'>163</a></li>
-
-<li class="indx">Herschel’s discovery of Uranus, <a href='#Page_32'>32</a></li>
-<li class="isub1">forty foot telescope, <a href='#Page_34'>34</a></li>
-<li class="isub1">Sir John, <a href='#Page_35'>35</a></li>
-<li class="isub1">Sir John, proposed defining condition, <a href='#Page_81'>81</a></li>
-<li class="isub1">Sir William, <a href='#Page_31'>31</a></li>
-
-<li class="indx">Herschel’s time, instruments of, <a href='#Page_35'>35</a></li>
-
-<li class="indx">Hevelius, construction for objective of <a href='#Page_150'>150</a> feet, <a href='#Page_17'>17</a></li>
-<li class="isub1">directions for designing Galilean and Keplerian telescopes, <a href='#Page_14'>14</a></li>
-<li class="isub1">invention of first periscope, <a href='#Page_15'>15</a></li>
-<li class="isub1">Johannes, <a href='#Page_13'>13</a></li>
-<li class="isub1">mention of advantage of plano convex lens, <a href='#Page_14'>14</a></li>
-<li class="isub1">mentions telescope due to DeRheita, <a href='#Page_14'>14</a></li>
-
-<li class="indx">Housing reflector of 36 inch aperture, <a href='#Page_243'>243</a></li>
-<li class="isub1">rolling on track, <a href='#Page_242'>242</a></li>
-<li class="isub1">simplest instrument for fixed, <a href='#Page_241'>241</a></li>
-
-<li class="indx">Huygens, Christian, devised methods of grinding &amp; polishing, <a href='#Page_16'>16</a></li>
-
-<li class="indx">Huygens’ eyepiece, introduction of, <a href='#Page_24'>24</a></li>
-
-<li class="indx">Huygens, sketch of Mars, <a href='#Page_16'>16</a></li>
-
-
-<li class="ifrst">I</li>
-
-<li class="indx">Image, correct extra focal, <a href='#Page_208'>208</a></li>
-<li class="isub1">critical examination of, <a href='#Page_204'>204</a>
-<span class="pagenum"><a name="Page_284" id="Page_284">[Pg 284]</a></span></li>
-<li class="indx">Image, curvature of, <a href='#Page_87'>87</a></li>
-<li class="isub1">seen without eyepiece, <a href='#Page_134'>134</a></li>
-<li class="isub1">showing unsymmetrical coloring, <a href='#Page_208'>208</a></li>
-
-<li class="indx">Interference rings, eccentric, <a href='#Page_205'>205</a></li>
-
-<li class="indx">Irradiation, <a href='#Page_262'>262</a></li>
-
-
-<li class="ifrst">J</li>
-
-<li class="indx">Jansen, Zacharius, <a href='#Page_4'>4</a></li>
-
-
-<li class="ifrst">K</li>
-
-<li class="indx">Kellner, ocular, <a href='#Page_145'>145</a></li>
-
-<li class="indx">Kepler, astronomical telescope, <a href='#Page_10'>10</a></li>
-<li class="isub1">differences of from Galilean form, <a href='#Page_10'>10</a></li>
-
-<li class="indx">Knife edge test of parabolic mirror, <a href='#Page_212'>212</a></li>
-
-
-<li class="ifrst">L</li>
-
-<li class="indx">Lacquer, endurance of coating, <a href='#Page_223'>223</a></li>
-
-<li class="indx">Latitude scale, <a href='#Page_232'>232</a></li>
-
-<li class="indx">Lenses, determinate forms for, <a href='#Page_80'>80</a></li>
-
-<li class="indx">Lens, magnifying power of, <a href='#Page_134'>134</a></li>
-<li class="isub1">“crossed,” <a href='#Page_24'>24</a></li>
-<li class="isub1">polishing the fine ground, <a href='#Page_70'>70</a></li>
-<li class="isub1">power of, <a href='#Page_78'>78</a></li>
-<li class="isub1">triple cemented, a useful ocular, <a href='#Page_138'>138</a></li>
-<li class="isub1">simple achromatic, <a href='#Page_137'>137</a></li>
-<li class="isub1">single, has small field, <a href='#Page_137'>137</a></li>
-<li class="isub1">spotted, cleaning of, <a href='#Page_217'>217</a></li>
-
-<li class="indx">Light grasp and resolving power, <a href='#Page_265'>265</a></li>
-<li class="isub1">small telescope fails in, <a href='#Page_264'>264</a></li>
-
-<li class="indx">Light ratio of star magnitudes, <a href='#Page_264'>264</a></li>
-
-<li class="indx">Light transmitted by glass, <a href='#Page_53'>53</a></li>
-
-<li class="indx">Lippershey, Jan, <a href='#Page_2'>2</a></li>
-<li class="isub1">discovery, when made, <a href='#Page_5'>5</a></li>
-<li class="isub1">retainer to, <a href='#Page_3'>3</a></li>
-
-<li class="indx">Lunette à Napoleon Troisiéme, <a href='#Page_154'>154</a>, <a href='#Page_155'>155</a>, <a href='#Page_162'>162</a></li>
-
-
-<li class="ifrst">M</li>
-
-<li class="indx">Magnifying power, directly as ratio of increase in tangent, <a href='#Page_135'>135</a></li>
-<li class="isub1">powers, increase of, <a href='#Page_273'>273</a></li>
-
-<li class="indx">Marius, Simon, <a href='#Page_5'>5</a></li>
-<li class="isub1">used with glasses from spectacles, <a href='#Page_5'>5</a></li>
-
-<li class="indx">Marius, picked up satellites of Jupiter, <a href='#Page_5'>5</a></li>
-
-<li class="indx">Meridian photometer, <a href='#Page_194'>194</a></li>
-
-<li class="indx">Metius, James, <a href='#Page_4'>4</a></li>
-
-<li class="indx">Metius, tale of, <a href='#Page_4'>4</a></li>
-
-<li class="indx">Micrometer, double image, <a href='#Page_171'>171</a></li>
-<li class="isub1">square bar, <a href='#Page_171'>171</a></li>
-
-<li class="indx">Micrometers, <a href='#Page_168'>168</a></li>
-
-<li class="indx">Micrometry, foundations of, <a href='#Page_12'>12</a></li>
-
-<li class="indx">Mirror’s, aberrations of, <a href='#Page_92'>92</a></li>
-<li class="isub1">adjustment of, <a href='#Page_206'>206</a></li>
-<li class="isub1">concave spherical, <a href='#Page_92'>92</a></li>
-<li class="isub1">final burnishing of, <a href='#Page_226'>226</a></li>
-<li class="isub1">hyperboloidal, <a href='#Page_96'>96</a></li>
-<li class="isub1">lacquer coating for surface, <a href='#Page_221'>221</a></li>
-<li class="isub1">mounting, by Browning, <a href='#Page_49'>49</a></li>
-<li class="isub1">parabolic oblique, shows aberration, <a href='#Page_95'>95</a></li>
-<li class="isub1">surface, prevention of injury to, <a href='#Page_220'>220</a></li>
-
-<li class="indx">Mittenzwey ocular, <a href='#Page_141'>141</a></li>
-
-<li class="indx">Mountain stations, good or very bad, <a href='#Page_254'>254</a></li>
-
-<li class="indx">Mounts, alt-azimuth and equatorial, <a href='#Page_98'>98</a></li>
-
-<li class="indx">Myopia, glasses for, came slowly, <a href='#Page_2'>2</a></li>
-
-
-<li class="ifrst">N</li>
-
-<li class="indx">Navicula Lyra, stages of resolution of, <a href='#Page_271'>271</a></li>
-
-<li class="indx">Newton, abandoned parabolic mirror, <a href='#Page_21'>21</a></li>
-<li class="isub1">blunder in experiment, <a href='#Page_20'>20</a></li>
-<li class="isub1">gave little information about material for mirrors, <a href='#Page_23'>23</a></li>
-<li class="isub1">Isaac, attempt at a reflector, <a href='#Page_20'>20</a></li>
-
-<li class="indx">Normal spectra, <a href='#Page_190'>190</a></li>
-
-
-<li class="ifrst">O</li>
-
-<li class="indx">Objective, adjustable mount for, <a href='#Page_44'>44</a></li>
-<li class="isub1">adjusting screws of, <a href='#Page_44'>44</a></li>
-<li class="isub1">Clark’s form, <a href='#Page_83'>83</a></li>
-<li class="isub1">cleansing, <a href='#Page_203'>203</a></li>
-<li class="isub1">examination of, <a href='#Page_202'>202</a>
-<span class="pagenum"><a name="Page_285" id="Page_285">[Pg 285]</a></span></li>
-<li class="indx">Objective, four-part, <a href='#Page_85'>85</a></li>
-<li class="isub1">Fraunhofer flint-ahead, <a href='#Page_83'>83</a></li>
-<li class="isub1">how to clean, <a href='#Page_216'>216</a></li>
-<li class="isub1">spacers, to take out, <a href='#Page_217'>217</a></li>
-<li class="isub1">typical striæ in, <a href='#Page_203'>203</a></li>
-
-<li class="indx">Objective prism, photographing with, <a href='#Page_185'>185</a>, <a href='#Page_187'>187</a></li>
-
-<li class="indx">Objectives, crown glass equiconvex, <a href='#Page_80'>80</a></li>
-<li class="isub1">over-achromatized, <a href='#Page_90'>90</a></li>
-<li class="isub1">rated on focal length for green <a href='#Page_24'>24</a></li>
-
-<li class="indx">Observatories, cost of Romsey, <a href='#Page_252'>252</a></li>
-
-<li class="indx">Observatory at small expense, <a href='#Page_249'>249</a></li>
-<li class="isub1">Romsey, description of, <a href='#Page_249'>249</a></li>
-<li class="isub1">with simple sliding roof, <a href='#Page_245'>245</a></li>
-
-<li class="indx">Observing box, <a href='#Page_229'>229</a></li>
-
-<li class="indx">Oblique fork alt-azimuth, <a href='#Page_100'>100</a></li>
-
-<li class="indx">Ocular, apparent angular field of, <a href='#Page_146'>146</a></li>
-<li class="isub1">terrestrial, <a href='#Page_147'>147</a></li>
-<li class="isub1">Tolles terrestrial, <a href='#Page_147'>147</a></li>
-<li class="isub1">typical form, <a href='#Page_45'>45</a></li>
-
-<li class="indx">Oculars, radius of curvature of image in, <a href='#Page_146'>146</a></li>
-<li class="isub1">undesirability of short focus, <a href='#Page_275'>275</a></li>
-
-<li class="indx">Open fork mount, <a href='#Page_115'>115</a></li>
-<li class="isub1">well suited to big reflectors, <a href='#Page_117'>117</a></li>
-
-<li class="indx">Optical axis, to adjust declination of, <a href='#Page_238'>238</a></li>
-
-<li class="indx">Optical glass, classes of, <a href='#Page_63'>63</a></li>
-<li class="isub1">data and analysis of, <a href='#Page_64'>64</a></li>
-<li class="isub1">industry, due to single man, <a href='#Page_36'>36</a></li>
-<li class="isub1">production of, <a href='#Page_60'>60</a></li>
-
-<li class="indx">Orthoscopic ocular, <a href='#Page_145'>145</a></li>
-
-
-<li class="ifrst">P</li>
-
-<li class="indx">Parallactic mount, <a href='#Page_104'>104</a></li>
-
-<li class="indx">Petition for annulment of Dolland’s patent, <a href='#Page_29'>29</a></li>
-
-<li class="indx">Photometer, artificial star Zöllner, <a href='#Page_194'>194</a></li>
-<li class="isub1">extinction, <a href='#Page_198'>198</a></li>
-<li class="isub1">photoelectric cell, <a href='#Page_199'>199</a></li>
-<li class="isub1">precision of astronomical, <a href='#Page_199'>199</a></li>
-<li class="isub1">selenium cell, <a href='#Page_199'>199</a></li>
-<li class="isub1">Zöllner, <a href='#Page_197'>197</a></li>
-
-<li class="indx">Photometers, three classes in stellar, <a href='#Page_193'>193</a></li>
-
-<li class="indx">“Photo-visual, objective,” <a href='#Page_89'>89</a></li>
-
-<li class="indx">Pillar-and-claw stand, <a href='#Page_98'>98</a></li>
-
-<li class="indx">Pillar mount, <a href='#Page_240'>240</a></li>
-
-<li class="indx">Pitch, optician’s, <a href='#Page_71'>71</a></li>
-
-<li class="indx">Placement for tripod legs, <a href='#Page_236'>236</a></li>
-
-<li class="indx">Polar and coudé forms of reflector, <a href='#Page_125'>125</a></li>
-<li class="isub1">axis, adjustment of by level, <a href='#Page_232'>232</a></li>
-<li class="isub1">axis, alignment to meridian, <a href='#Page_232'>232</a></li>
-<li class="isub1">axis, setting with finder altitude of, <a href='#Page_234'>234</a></li>
-<li class="isub1">telescope, <a href='#Page_119'>119</a>, <a href='#Page_122'>122</a></li>
-
-<li class="indx">Polaris, hour angle of, <a href='#Page_233'>233</a></li>
-<li class="isub1">a variable star, <a href='#Page_199'>199</a></li>
-
-<li class="indx">Polarizing photometer, <a href='#Page_193'>193</a></li>
-
-<li class="indx">Pole, position, <a href='#Page_234'>234</a></li>
-
-<li class="indx">Polishing machine, <a href='#Page_70'>70</a></li>
-<li class="isub1">surface of tool, <a href='#Page_72'>72</a></li>
-<li class="isub1">tool, <a href='#Page_71'>71</a></li>
-
-<li class="indx">Porro’s second form, <a href='#Page_157'>157</a></li>
-<li class="isub1">work, original description of, <a href='#Page_156'>156</a></li>
-
-<li class="indx">Porta, description unintelligible, <a href='#Page_7'>7</a></li>
-
-<li class="indx">Portable equatorial, adjustment of, <a href='#Page_230'>230</a></li>
-<li class="isub1">telescopes, mounting of, <a href='#Page_228'>228</a></li>
-
-<li class="indx">Porter polar reflector, <a href='#Page_130'>130</a></li>
-
-<li class="indx">Position angle micrometer of Lowell Observatory, <a href='#Page_173'>173</a></li>
-
-<li class="indx">Powers, lowest practicable, <a href='#Page_276'>276</a></li>
-
-<li class="indx">Prismatic inversion, Porro’s first form, <a href='#Page_155'>155</a></li>
-
-<li class="indx">Prismatic inverting system, the first, <a href='#Page_154'>154</a></li>
-
-<li class="indx">Prisms, Dove’s, <a href='#Page_154'>154</a></li>
-
-<li class="indx">Prism field glasses, stereoscopic effect of, <a href='#Page_159'>159</a></li>
-
-<li class="indx">Prism glass, <a href='#Page_152'>152</a></li>
-<li class="isub1">loss of light in, <a href='#Page_160'>160</a></li>
-<li class="isub1">objectives of, <a href='#Page_161'>161</a></li>
-<li class="isub1">weak points of, <a href='#Page_160'>160</a></li>
-
-
-<li class="ifrst">R</li>
-
-<li class="indx">Resolving constant, magnification to develop, <a href='#Page_275'>275</a></li>
-<li class="isub1">power and verity of detail, <a href='#Page_2'>2</a></li>
-<li class="isub1">power of the eye, <a href='#Page_274'>274</a>
-<span class="pagenum"><a name="Page_286" id="Page_286">[Pg 286]</a></span></li>
-<li class="indx">Reticulated micrometer, <a href='#Page_169'>169</a></li>
-
-<li class="indx">Reversion prism, <a href='#Page_153'>153</a></li>
-
-<li class="indx">Right ascension circle, <a href='#Page_108'>108</a></li>
-
-<li class="indx">Ring micrometer, <a href='#Page_169'>169</a></li>
-<li class="isub1">computation of results of, <a href='#Page_170'>170</a></li>
-
-<li class="indx">Ring system faults due to strain, <a href='#Page_205'>205</a></li>
-
-<li class="indx">“Romsey” observatory type, <a href='#Page_248'>248</a></li>
-
-<li class="indx">Rack motion in altitude, <a href='#Page_100'>100</a></li>
-
-<li class="indx">Ramsden, ocular, <a href='#Page_144'>144</a></li>
-
-<li class="indx">Reflection, coefficient of, from silvered surface, <a href='#Page_54'>54</a></li>
-
-<li class="indx">Reflector costs, <a href='#Page_55'>55</a></li>
-<li class="isub1">cover for, <a href='#Page_242'>242</a></li>
-<li class="isub1">development in England, <a href='#Page_41'>41</a></li>
-<li class="isub1">for astrophysical work, <a href='#Page_56'>56</a></li>
-<li class="isub1">light-grasp of, <a href='#Page_53'>53</a></li>
-<li class="isub1">relative aperture of, <a href='#Page_50'>50</a></li>
-<li class="isub1">section of Newtonian, <a href='#Page_45'>45</a></li>
-<li class="isub1">skeleton construction, <a href='#Page_49'>49</a></li>
-<li class="isub1">suffers from scattered light, <a href='#Page_56'>56</a></li>
-<li class="isub1">working field of, <a href='#Page_55'>55</a></li>
-
-<li class="indx">Refractive index, <a href='#Page_63'>63</a></li>
-
-<li class="indx">Refractors and reflectors, relative advantages of, <a href='#Page_52'>52</a></li>
-<li class="isub1">few made after advent of reflector, <a href='#Page_27'>27</a></li>
-<li class="isub1">in section, <a href='#Page_43'>43</a></li>
-<li class="isub1">light transmission of, <a href='#Page_53'>53</a></li>
-
-<li class="indx">Refractors, relative equivalent apertures of, <a href='#Page_54'>54</a></li>
-<li class="isub1">tubes of, <a href='#Page_42'>42</a></li>
-
-
-<li class="ifrst">S</li>
-
-<li class="indx">Scheiner, Christopher, use of Kepler’s telescope, <a href='#Page_11'>11</a></li>
-<li class="isub1">devised parallactic mount, <a href='#Page_11'>11</a></li>
-
-<li class="indx">Secondary spectrum, <a href='#Page_87'>87</a></li>
-<li class="isub1">new glasses reducing, <a href='#Page_88'>88</a></li>
-
-<li class="indx">Seeing, <a href='#Page_257'>257</a></li>
-<li class="isub1">conditions, for difference of aperture, <a href='#Page_257'>257</a></li>
-<li class="isub1">conditions generally bad, <a href='#Page_253'>253</a></li>
-<li class="isub1">standard scale of, <a href='#Page_256'>256</a></li>
-<li class="isub1">true inwardness of bad, <a href='#Page_253'>253</a></li>
-
-<li class="indx">Separating power, to compute, <a href='#Page_261'>261</a></li>
-
-<li class="indx">Short, James, mastered art of figuring paraboloid, <a href='#Page_27'>27</a></li>
-<li class="isub1">took up Gregorian construction with success, <a href='#Page_27'>27</a></li>
-
-<li class="indx">Shortened telescope, <a href='#Page_152'>152</a></li>
-
-<li class="indx">Sights, on portable mount, <a href='#Page_229'>229</a></li>
-
-<li class="indx">Silver films, condition of, <a href='#Page_54'>54</a></li>
-
-<li class="indx">Silvering, Ludin’s process, <a href='#Page_225'>225</a></li>
-<li class="isub1">processes, <a href='#Page_222'>222</a></li>
-<li class="isub1">process, Dr. Brashear’s, <a href='#Page_222'>222</a></li>
-
-<li class="indx">Sine condition, Abbé’s, <a href='#Page_82'>82</a></li>
-
-<li class="indx">Slit, spectroscope, Abbé type, <a href='#Page_184'>184</a></li>
-
-<li class="indx">Snow cœlostat telescope, <a href='#Page_127'>127</a></li>
-
-<li class="indx">Solar diagonal, <a href='#Page_166'>166</a></li>
-<li class="isub1">eye piece diaphragms in, <a href='#Page_168'>168</a></li>
-<li class="isub1">early spectroscopes, <a href='#Page_188'>188</a></li>
-<li class="isub1">polarizing eyepiece, <a href='#Page_167'>167</a></li>
-<li class="isub1">spectroscope, <a href='#Page_187'>187</a></li>
-
-<li class="indx">Spacers, <a href='#Page_44'>44</a>, <a href='#Page_218'>218</a></li>
-
-<li class="indx">Spectacle lenses, combination of, <a href='#Page_2'>2</a></li>
-
-<li class="indx">Spectacles for presbyopia, <a href='#Page_2'>2</a></li>
-<li class="isub1">invention of, <a href='#Page_1'>1</a></li>
-
-<li class="indx">Spectra, visibility of stellar, <a href='#Page_183'>183</a></li>
-
-<li class="indx">Spectro-heliograph, principle of, <a href='#Page_191'>191</a></li>
-<li class="isub1">simple type of Hale’s, <a href='#Page_191'>191</a></li>
-
-<li class="indx">Spectroscope, <a href='#Page_182'>182</a></li>
-<li class="isub1">construction of astronomical, <a href='#Page_182'>182</a></li>
-<li class="isub1">of Lowell refractor, <a href='#Page_185'>185</a></li>
-<li class="isub1">ocular, McClean form, <a href='#Page_183'>183</a></li>
-
-<li class="indx">Specula, small, methods of support, <a href='#Page_49'>49</a></li>
-
-<li class="indx">Speculum metal composition of, <a href='#Page_24'>24</a></li>
-
-<li class="indx">Sphenoid prisms, <a href='#Page_158'>158</a>, <a href='#Page_163'>163</a></li>
-
-<li class="indx">Spherical aberration, <a href='#Page_11'>11</a></li>
-<li class="isub1">amount of, <a href='#Page_80'>80</a></li>
-<li class="isub1">annulling in both directions, <a href='#Page_84'>84</a></li>
-<li class="isub1">examination for, <a href='#Page_207'>207</a></li>
-<li class="isub1">quick test of, <a href='#Page_267'>267</a></li>
-<li class="isub1">remedy for, <a href='#Page_79'>79</a></li>
-<li class="isub1">concave mirror, errors of, <a href='#Page_22'>22</a></li>
-
-<li class="indx">Star, appearance of, <a href='#Page_204'>204</a></li>
-<li class="isub1">artificial, <a href='#Page_66'>66</a>, <a href='#Page_203'>203</a></li>
-<li class="isub1">diagonal, <a href='#Page_165'>165</a></li>
-<li class="isub1">disc, apparent diameter of, <a href='#Page_259'>259</a></li>
-<li class="isub1">image of reflector, <a href='#Page_206'>206</a></li>
-
-<li class="indx">Steinheil, achromatic ocular, <a href='#Page_144'>144</a></li>
-<li class="isub1">Karl August, silvering specula, <a href='#Page_39'>39</a></li>
-
-<li class="indx">Striæ, location of, <a href='#Page_67'>67</a></li>
-
-<li class="indx">Surface, treatment of deterioration of, <a href='#Page_218'>218</a>
-<span class="pagenum"><a name="Page_287" id="Page_287">[Pg 287]</a></span></li>
-
-<li class="ifrst">T</li>
-
-<li class="indx">Taylor, triplets with reduced secondary spectrum, <a href='#Page_89'>89</a></li>
-
-<li class="indx">Telescopes, choice and purchase of, <a href='#Page_201'>201</a></li>
-<li class="isub1">Early in 1610 made in England, <a href='#Page_6'>6</a></li>
-<li class="isub1">first, <a href='#Page_3'>3</a></li>
-<li class="isub1">the first astronomical, <a href='#Page_9'>9</a></li>
-<li class="isub1">improvement of early, <a href='#Page_11'>11</a></li>
-<li class="isub1">lineage of, <a href='#Page_1'>1</a></li>
-<li class="isub1">name devised, <a href='#Page_9'>9</a></li>
-
-<li class="indx">Telescopes, portable and fixed, <a href='#Page_108'>108</a></li>
-<li class="isub1">1609, for sale in Paris, <a href='#Page_5'>5</a></li>
-<li class="isub1">size and mounting of early, <a href='#Page_14'>14</a></li>
-
-<li class="indx">Telescopic vision, discovery of, <a href='#Page_2'>2</a></li>
-
-<li class="indx">Templets, designed curves of, <a href='#Page_69'>69</a></li>
-
-<li class="indx">Tests for striæ and annealing, <a href='#Page_68'>68</a></li>
-
-<li class="indx">Transparency, lack of in atmosphere, <a href='#Page_255'>255</a></li>
-
-
-<li class="indx">Triplet, cemented, <a href='#Page_85'>85</a></li>
-
-<li class="indx">Turret housing of reflector, <a href='#Page_244'>244</a></li>
-
-
-<li class="ifrst">V</li>
-
-<li class="indx">Variable stars, <a href='#Page_192'>192</a></li>
-
-
-<li class="ifrst">W</li>
-
-<li class="indx">Wedge calibrated by observation, <a href='#Page_197'>197</a></li>
-<li class="isub1">photographic, <a href='#Page_197'>197</a></li>
-<li class="isub1">photometer, <a href='#Page_197'>197</a></li>
-
-<li class="indx">Wind, shelter from, <a href='#Page_240'>240</a></li>
-
-
-<li class="ifrst">Z</li>
-
-<li class="indx">Zeiss, binocular of extreme stereoscopic effect, <a href='#Page_161'>161</a></li>
-
-<li class="indx">Zöllner, photometer modification of, <a href='#Page_198'>198</a></li>
-
-<li class="indx">Zonal aberration, <a href='#Page_209'>209</a></li>
-</ul>
-</div>
-
-
-<div class="footnotes"><h3>FOOTNOTES:</h3>
-
-<div class="footnote">
-
-<p><a name="Footnote_1_1" id="Footnote_1_1"></a><a href="#FNanchor_1_1"><span class="label">[1]</span></a> There is a very strong probability that Jansen was the inventor of the
-compound microscope about the beginning of the seventeenth century.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_2_2" id="Footnote_2_2"></a><a href="#FNanchor_2_2"><span class="label">[2]</span></a> The statement by Galileo that he “fashioned” these first lenses can
-hardly be taken literally if his very speedy construction is to be credited.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_3_3" id="Footnote_3_3"></a><a href="#FNanchor_3_3"><span class="label">[3]</span></a> Scheiner also devised a crude parallactic mount which he used in his solar
-observations, probably the first European to grasp the principle of the
-equatorial. It was only near the end of the century that Roemer followed his
-example, and both had been anticipated by Chinese instruments with sights.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_4_4" id="Footnote_4_4"></a><a href="#FNanchor_4_4"><span class="label">[4]</span></a> He attempted to polish them on cloth, which in itself was sufficient to
-guarantee failure.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_5_5" id="Footnote_5_5"></a><a href="#FNanchor_5_5"><span class="label">[5]</span></a> In Fig 13, <i>A</i> is the support of the tube and focussing screw, <i>B</i> the main
-mirror, an inch in diameter, <i>CD</i> the oblique mirror, <i>E</i> the principal focus,
-<i>F</i> the eye lens, and <i>G</i> the member from which the oblique mirror is carried.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_6_6" id="Footnote_6_6"></a><a href="#FNanchor_6_6"><span class="label">[6]</span></a> In fact a “four foot telescope of Mr. Newton’s invention” brought
-before the Royal Society two weeks after his original paper, proved only
-fair in quality, was returned somewhat improved at the next meeting,
-and then was referred to Mr. Hooke to be perfected as far as might be,
-after which nothing more was heard of it.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_7_7" id="Footnote_7_7"></a><a href="#FNanchor_7_7"><span class="label">[7]</span></a> Commonly, but it appears erroneously, ascribed to Lord Mansfield.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_8_8" id="Footnote_8_8"></a><a href="#FNanchor_8_8"><span class="label">[8]</span></a> This was probably due not only to unfavorable climate, but to the fact
-that Herschel, with all his ingenuity, does not appear to have mastered
-the casting difficulty, and was constrained to make his big speculum of Cu
-75 per cent, Sn 25 per cent, a composition working rather easily and taking
-beautiful, but far from permanent, polish. He never seems to have used
-practically the SnCu<sub>4</sub> formula, devised empirically by Mudge (Phil. Trans.
-<i>67</i>, 298), and in quite general use thereafter up to the present time.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_9_9" id="Footnote_9_9"></a><a href="#FNanchor_9_9"><span class="label">[9]</span></a> An <i>F</i>/3 mirror of 1<i>m</i> aperture by Zeiss was installed in the observatory
-at Bergedorf in 1911, and a similar one by Schaer is mounted at Carre, near
-Geneva.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_10_10" id="Footnote_10_10"></a><a href="#FNanchor_10_10"><span class="label">[10]</span></a> More recently his condition proves to be quite the exact equivalent of
-Abbé’s <i>sine condition</i> which states that the sine of the angle made with the
-optical axis by a ray entering the objective from a given axial point shall
-bear a uniform ratio to the sine of the corresponding angle of emergence,
-whatever the point of incidence. For parallel rays along the axis this
-reduces to the requirement that the sines of the angles of emergence shall
-be proportional to the respective distances of the incident rays from the axis.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_11_11" id="Footnote_11_11"></a><a href="#FNanchor_11_11"><span class="label">[11]</span></a> It is interesting to note that in computing Fig. 54<i>a</i> for the sine condition,
-the other root of the quadratic gave roughly the Gaussian form of
-Fig. 53.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_12_12" id="Footnote_12_12"></a><a href="#FNanchor_12_12"><span class="label">[12]</span></a> The curvature of the image is the thing which sets a limit to shortening
-the relative focus, as already noted, for the astigmatic image surfaces as
-we have seen, fall rapidly apart away from the axis, and both curvatures
-are considerable. The tangential is the greater, corresponding roughly to
-a radius notably less than ⅓ the focal length, while the radial fits a radius
-of less than ⅔ this length with all ordinary glasses, given forms correcting
-the ordinary aberrations. The curves are concave towards the objective
-except in “anastigmats” and some objectives having bad aberrations
-otherwise. Their approximate curvatures assuming a semiangular aperture
-for an achromatic objective not over say 5°, have been shown to be,
-to focus unity
-</p>
-<p>
-ρ<sub>r</sub> = 1 + (1/(ν-ν′)(ν/n - ν′/n′), and ρ<sub>t</sub> = 3 + 1/(ν-ν′)(ν/n - ν′/n′)
-</p>
-<p>
-ρ_r and ρ_t being the respective reciprocals of the radii. The surfaces are really
-somewhat egg shaped rather than spherical as one departs from the axis.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_13_13" id="Footnote_13_13"></a><a href="#FNanchor_13_13"><span class="label">[13]</span></a> The doublet costs about one and a half times, and the triplet more than
-twice the price of an ordinary achromatic of the same aperture.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_14_14" id="Footnote_14_14"></a><a href="#FNanchor_14_14"><span class="label">[14]</span></a> A very useful treatment of the aberrations of parabolic mirrors by Poor
-is in Ap. J. 7, 114. In this is given a table of the maximum dimension of a
-star disc off the axis in reflectors of various apertures. This table condenses
-to the closely approximate formula
-</p>
-
-<p>
-a = lld/f²<br />
-</p>
-
-<p>
-where a is the aberrational diameter of the star disc, in seconds of arc, d the
-distance from the axis in minutes of arc, f the denominator of the F ratio
-(F/8 &amp;c.) and 11, a constant. Obviously the separating power of a telescope
-(see Chap. X) being substantially 4.″56/D where D is the diameter of
-objective or mirror in inches, the separating power will be impaired when
-a &gt; 4.″56/D. In the photographic case the critical quantity is not 4.″56/D, but
-the maximum image diameter tolerable for the purpose in hand.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_15_15" id="Footnote_15_15"></a><a href="#FNanchor_15_15"><span class="label">[15]</span></a> Instruments with a polar axis were used by Scheiner as early as 1627;
-by Roemer about three quarters of a century later, and previously had
-been employed, using sights rather than telescopes, by the Chinese; but
-these were far from being equatorials in the modern sense.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_16_16" id="Footnote_16_16"></a><a href="#FNanchor_16_16"><span class="label">[16]</span></a> Contributions from the Solar Obs. #23, Hale, which should be seen for
-details.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_17_17" id="Footnote_17_17"></a><a href="#FNanchor_17_17"><span class="label">[17]</span></a> A more precise method, depending on an actual measurement of the
-angle subtended by the diameter of the eyepiece diaphragm as seen through
-the eye end of the ocular and its comparison with the same angular diameter
-reckoned from the objective, is given by Schaeberle. M. N. <b>43</b>, 297.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_18_18" id="Footnote_18_18"></a><a href="#FNanchor_18_18"><span class="label">[18]</span></a> The angular field a is defined by
-</p>
-
-<p>
-tan ½a = γ/F
-</p>
-
-<p>
-where γ is, numerically, the radius of the field sharp enough for the purpose
-in hand, and F the effective focal length of the ocular.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_19_19" id="Footnote_19_19"></a><a href="#FNanchor_19_19"><span class="label">[19]</span></a> There are binoculars on the market which are to outward appearance
-prism glasses, but which are really ordinary opera glasses mounted with intent
-to deceive, sometimes bearing a slight variation on the name of some well
-known maker.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_20_20" id="Footnote_20_20"></a><a href="#FNanchor_20_20"><span class="label">[20]</span></a> r the radius of the ring, is given by, r = (15/2)(t′-t) cos
-Dec., t′-t being the seconds taken for transit.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_21_21" id="Footnote_21_21"></a><a href="#FNanchor_21_21"><span class="label">[21]</span></a> (For full discussion of this instrument see Chandler, Mem. Amer. Acad.
-Arts &amp; Sci. 1885, p. 158).</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_22_22" id="Footnote_22_22"></a><a href="#FNanchor_22_22"><span class="label">[22]</span></a> For the principle of diffraction spectra see Baly, Spectroscopy; Kayser,
-Handbuch d. Specktroskoie or any of the larger textbooks of physics.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_23_23" id="Footnote_23_23"></a><a href="#FNanchor_23_23"><span class="label">[23]</span></a> The effect on the observed height of a prominence is h = h′ sin c/sin t,
-where h is the real height, h′ the apparent height, c the angle made by the
-grating face with the collimator, and t that with the telescope (Fig. 146).</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_24_24" id="Footnote_24_24"></a><a
-href="#FNanchor_24_24"><span class="label">[24]</span></a> If A be the
-brightness of one object and B that of the other, α the reading of the
-index when one image disappears and β the reading when the two images
-are equal then A/B = tan²(α-β). There are four positions of the Nicol,
-90° apart, for which equality can be established, and usually all are
-read and the mean taken. (H. A. II, 1.)</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_25_25" id="Footnote_25_25"></a><a href="#FNanchor_25_25"><span class="label">[25]</span></a> For full description and method see H. A. Vol. 14, also Miss
-Furness’ admirable “Introduction to the Study of Variable Stars,” p. 122,
-et seq. Some modifications are described in H. A. Vol. 23. These direct
-comparison photometers give results subject to some annoying small corrections,
-but a vast amount of valuable work has been done with them in the
-Harvard Photometry.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_26_26" id="Footnote_26_26"></a><a href="#FNanchor_26_26"><span class="label">[26]</span></a> The general order of precision attained by astronomical photometers is
-shown in the discovery, photographically, by Hertzsprung in 1911, that
-Polaris, used as a standard magnitude for many years, is actually a variable.
-Its period is very near to four days, its photographic amplitude 0.17 and its
-visual amplitude about 0.1, <i>i.e.</i>, a variation of ± 5 per cent in the light was
-submerged in the observational uncertainties, although once known it was
-traced out in the accumulated data without great difficulty.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_27_27" id="Footnote_27_27"></a><a href="#FNanchor_27_27"><span class="label">[27]</span></a> Such apparatus is essentially appurtenant to large instruments only, say
-of not less than 12″ aperture and preferably much more. The eye is
-enormously more sensitive as a detector of radiant energy than any device of
-human contrivance, and thus small telescopes can be well used for visual
-photometry, the bigger instruments having then merely the advantage of
-reaching fainter stars.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_28_28" id="Footnote_28_28"></a><a href="#FNanchor_28_28"><span class="label">[28]</span></a> E. g., the beautiful astrographic and other objectives turned out by
-the brothers Henry.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_29_29" id="Footnote_29_29"></a><a href="#FNanchor_29_29"><span class="label">[29]</span></a> This and several of the subsequent figures are taken from quite the best
-account of testing objectives: “On the Adjustment and Testing of Telescope
-Objectives.” T. Cooke &amp; Sons, York, 1891, a little brochure unhappily
-long since out of print. A new edition is just now, 1922, announced.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_30_30" id="Footnote_30_30"></a><a href="#FNanchor_30_30"><span class="label">[30]</span></a> Sometimes with ever so careful centering the ring system in the middle
-of the field is still eccentric with respect to the small mirror, showing that
-the axis of the parabola is not perpendicular to the general face of the mirror.
-This can usually be remedied by the adjusting screws of the main mirror as
-described, but now and then it is necessary actually to move over the small
-mirror into the real optical axis. Draper (loc. cit.) gives some experiences
-of this sort.</p></div>
-
-<div class="footnote">
-
-<p><a name="Footnote_31_31" id="Footnote_31_31"></a><a href="#FNanchor_31_31"><span class="label">[31]</span></a> See also two valuable papers by Sir Howard Grubb, <i>The Observatory</i>, Vol.
-VII, pp. 9, 43. Also in Jour. Roy. Ast. Soc. Canada, Dec., 1921, Jan. 1922.</p></div></div>
-
-
-<div class="transnote">
-<h3>Transcriber's Notes</h3>
-
-<p>Obvious typographical errors have been silently corrected. Variations
-in hyphenation and accents have been standardised but all other spelling and
-punctuation remains unchanged.</p>
-
-<p>In caption of <a href="#Fig_49">Fig. 49</a>.—Spherical Aberration of Concave Lens. Concave
-has been changed to Convex</p>
-
-<p>In “<a href="#An_objective">An objective of 4.56′ inches</a> aperture has a resolving constant of
-1″ and to develop this should take a magnification of say 300,” 1″ has
-been hand altered in the original and may be 1′.</p>
-
-<p>The table “<a href="#Characteristics_of_Optical_Glasses">Characteristics of Optical Glasses</a>″ has been divided to fit
-within the width restriction.</p>
-
-<p>The images corresponding to <a href="#Fig_152">Figs. 152</a> and 153 were reversed in the
-original. This has been corrected.</p>
-</div>
-
-
-
-
-
-
-
-
-<pre>
-
-
-
-
-
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