diff options
Diffstat (limited to 'old/53740-0.txt')
| -rw-r--r-- | old/53740-0.txt | 10538 |
1 files changed, 0 insertions, 10538 deletions
diff --git a/old/53740-0.txt b/old/53740-0.txt deleted file mode 100644 index cdce521..0000000 --- a/old/53740-0.txt +++ /dev/null @@ -1,10538 +0,0 @@ -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 - -*** START OF THIS PROJECT GUTENBERG EBOOK THE TELESCOPE *** - - - - -Produced by Chris Curnow, Les Galloway and the Online -Distributed Proofreading Team at http://www.pgdp.net (This -file was produced from images generously made available -by The Internet Archive) - - - - - - - - - - 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 - -*** END OF THIS PROJECT GUTENBERG EBOOK THE TELESCOPE *** - -***** This file should be named 53740-0.txt or 53740-0.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/5/3/7/4/53740/ - -Produced by Chris Curnow, Les Galloway and the Online -Distributed Proofreading Team at http://www.pgdp.net (This -file was produced from images generously made available -by The Internet Archive) - - -Updated editions will replace the previous one--the old editions will -be renamed. - -Creating the works from print editions not protected by U.S. copyright -law means that no one owns a United States copyright in these works, -so the Foundation (and you!) can copy and distribute it in the United -States without permission and without paying copyright -royalties. Special rules, set forth in the General Terms of Use part -of this license, apply to copying and distributing Project -Gutenberg-tm electronic works to protect the PROJECT GUTENBERG-tm -concept and trademark. Project Gutenberg is a registered trademark, -and may not be used if you charge for the eBooks, unless you receive -specific permission. If you do not charge anything for copies of this -eBook, complying with the rules is very easy. You may use this eBook -for nearly any purpose such as creation of derivative works, reports, -performances and research. They may be modified and printed and given -away--you may do practically ANYTHING in the United States with eBooks -not protected by U.S. copyright law. Redistribution is subject to the -trademark license, especially commercial redistribution. - -START: FULL LICENSE - -THE FULL PROJECT GUTENBERG LICENSE -PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK - -To protect the Project Gutenberg-tm mission of promoting the free -distribution of electronic works, by using or distributing this work -(or any other work associated in any way with the phrase "Project -Gutenberg"), you agree to comply with all the terms of the Full -Project Gutenberg-tm License available with this file or online at -www.gutenberg.org/license. - -Section 1. General Terms of Use and Redistributing Project -Gutenberg-tm electronic works - -1.A. By reading or using any part of this Project Gutenberg-tm -electronic work, you indicate that you have read, understand, agree to -and accept all the terms of this license and intellectual property -(trademark/copyright) agreement. If you do not agree to abide by all -the terms of this agreement, you must cease using and return or -destroy all copies of Project Gutenberg-tm electronic works in your -possession. If you paid a fee for obtaining a copy of or access to a -Project Gutenberg-tm electronic work and you do not agree to be bound -by the terms of this agreement, you may obtain a refund from the -person or entity to whom you paid the fee as set forth in paragraph -1.E.8. - -1.B. "Project Gutenberg" is a registered trademark. It may only be -used on or associated in any way with an electronic work by people who -agree to be bound by the terms of this agreement. There are a few -things that you can do with most Project Gutenberg-tm electronic works -even without complying with the full terms of this agreement. See -paragraph 1.C below. There are a lot of things you can do with Project -Gutenberg-tm electronic works if you follow the terms of this -agreement and help preserve free future access to Project Gutenberg-tm -electronic works. See paragraph 1.E below. - -1.C. The Project Gutenberg Literary Archive Foundation ("the -Foundation" or PGLAF), owns a compilation copyright in the collection -of Project Gutenberg-tm electronic works. Nearly all the individual -works in the collection are in the public domain in the United -States. If an individual work is unprotected by copyright law in the -United States and you are located in the United States, we do not -claim a right to prevent you from copying, distributing, performing, -displaying or creating derivative works based on the work as long as -all references to Project Gutenberg are removed. Of course, we hope -that you will support the Project Gutenberg-tm mission of promoting -free access to electronic works by freely sharing Project Gutenberg-tm -works in compliance with the terms of this agreement for keeping the -Project Gutenberg-tm name associated with the work. You can easily -comply with the terms of this agreement by keeping this work in the -same format with its attached full Project Gutenberg-tm License when -you share it without charge with others. - -1.D. The copyright laws of the place where you are located also govern -what you can do with this work. Copyright laws in most countries are -in a constant state of change. If you are outside the United States, -check the laws of your country in addition to the terms of this -agreement before downloading, copying, displaying, performing, -distributing or creating derivative works based on this work or any -other Project Gutenberg-tm work. The Foundation makes no -representations concerning the copyright status of any work in any -country outside the United States. - -1.E. Unless you have removed all references to Project Gutenberg: - -1.E.1. The following sentence, with active links to, or other -immediate access to, the full Project Gutenberg-tm License must appear -prominently whenever any copy of a Project Gutenberg-tm work (any work -on which the phrase "Project Gutenberg" appears, or with which the -phrase "Project Gutenberg" is associated) is accessed, displayed, -performed, viewed, copied or distributed: - - 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. - -1.E.2. If an individual Project Gutenberg-tm electronic work is -derived from texts not protected by U.S. copyright law (does not -contain a notice indicating that it is posted with permission of the -copyright holder), the work can be copied and distributed to anyone in -the United States without paying any fees or charges. If you are -redistributing or providing access to a work with the phrase "Project -Gutenberg" associated with or appearing on the work, you must comply -either with the requirements of paragraphs 1.E.1 through 1.E.7 or -obtain permission for the use of the work and the Project Gutenberg-tm -trademark as set forth in paragraphs 1.E.8 or 1.E.9. - -1.E.3. If an individual Project Gutenberg-tm electronic work is posted -with the permission of the copyright holder, your use and distribution -must comply with both paragraphs 1.E.1 through 1.E.7 and any -additional terms imposed by the copyright holder. Additional terms -will be linked to the Project Gutenberg-tm License for all works -posted with the permission of the copyright holder found at the -beginning of this work. - -1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm -License terms from this work, or any files containing a part of this -work or any other work associated with Project Gutenberg-tm. - -1.E.5. Do not copy, display, perform, distribute or redistribute this -electronic work, or any part of this electronic work, without -prominently displaying the sentence set forth in paragraph 1.E.1 with -active links or immediate access to the full terms of the Project -Gutenberg-tm License. - -1.E.6. You may convert to and distribute this work in any binary, -compressed, marked up, nonproprietary or proprietary form, including -any word processing or hypertext form. However, if you provide access -to or distribute copies of a Project Gutenberg-tm work in a format -other than "Plain Vanilla ASCII" or other format used in the official -version posted on the official Project Gutenberg-tm web site -(www.gutenberg.org), you must, at no additional cost, fee or expense -to the user, provide a copy, a means of exporting a copy, or a means -of obtaining a copy upon request, of the work in its original "Plain -Vanilla ASCII" or other form. Any alternate format must include the -full Project Gutenberg-tm License as specified in paragraph 1.E.1. - -1.E.7. Do not charge a fee for access to, viewing, displaying, -performing, copying or distributing any Project Gutenberg-tm works -unless you comply with paragraph 1.E.8 or 1.E.9. - -1.E.8. You may charge a reasonable fee for copies of or providing -access to or distributing Project Gutenberg-tm electronic works -provided that - -* You pay a royalty fee of 20% of the gross profits you derive from - the use of Project Gutenberg-tm works calculated using the method - you already use to calculate your applicable taxes. The fee is owed - to the owner of the Project Gutenberg-tm trademark, but he has - agreed to donate royalties under this paragraph to the Project - Gutenberg Literary Archive Foundation. Royalty payments must be paid - within 60 days following each date on which you prepare (or are - legally required to prepare) your periodic tax returns. Royalty - payments should be clearly marked as such and sent to the Project - Gutenberg Literary Archive Foundation at the address specified in - Section 4, "Information about donations to the Project Gutenberg - Literary Archive Foundation." - -* You provide a full refund of any money paid by a user who notifies - you in writing (or by e-mail) within 30 days of receipt that s/he - does not agree to the terms of the full Project Gutenberg-tm - License. You must require such a user to return or destroy all - copies of the works possessed in a physical medium and discontinue - all use of and all access to other copies of Project Gutenberg-tm - works. - -* You provide, in accordance with paragraph 1.F.3, a full refund of - any money paid for a work or a replacement copy, if a defect in the - electronic work is discovered and reported to you within 90 days of - receipt of the work. - -* You comply with all other terms of this agreement for free - distribution of Project Gutenberg-tm works. - -1.E.9. If you wish to charge a fee or distribute a Project -Gutenberg-tm electronic work or group of works on different terms than -are set forth in this agreement, you must obtain permission in writing -from both the Project Gutenberg Literary Archive Foundation and The -Project Gutenberg Trademark LLC, the owner of the Project Gutenberg-tm -trademark. Contact the Foundation as set forth in Section 3 below. - -1.F. - -1.F.1. Project Gutenberg volunteers and employees expend considerable -effort to identify, do copyright research on, transcribe and proofread -works not protected by U.S. copyright law in creating the Project -Gutenberg-tm collection. Despite these efforts, Project Gutenberg-tm -electronic works, and the medium on which they may be stored, may -contain "Defects," such as, but not limited to, incomplete, inaccurate -or corrupt data, transcription errors, a copyright or other -intellectual property infringement, a defective or damaged disk or -other medium, a computer virus, or computer codes that damage or -cannot be read by your equipment. - -1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right -of Replacement or Refund" described in paragraph 1.F.3, the Project -Gutenberg Literary Archive Foundation, the owner of the Project -Gutenberg-tm trademark, and any other party distributing a Project -Gutenberg-tm electronic work under this agreement, disclaim all -liability to you for damages, costs and expenses, including legal -fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT -LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE -PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE -TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE -LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR -INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH -DAMAGE. - -1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a -defect in this electronic work within 90 days of receiving it, you can -receive a refund of the money (if any) you paid for it by sending a -written explanation to the person you received the work from. If you -received the work on a physical medium, you must return the medium -with your written explanation. The person or entity that provided you -with the defective work may elect to provide a replacement copy in -lieu of a refund. If you received the work electronically, the person -or entity providing it to you may choose to give you a second -opportunity to receive the work electronically in lieu of a refund. If -the second copy is also defective, you may demand a refund in writing -without further opportunities to fix the problem. - -1.F.4. Except for the limited right of replacement or refund set forth -in paragraph 1.F.3, this work is provided to you 'AS-IS', WITH NO -OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT -LIMITED TO WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PURPOSE. - -1.F.5. Some states do not allow disclaimers of certain implied -warranties or the exclusion or limitation of certain types of -damages. If any disclaimer or limitation set forth in this agreement -violates the law of the state applicable to this agreement, the -agreement shall be interpreted to make the maximum disclaimer or -limitation permitted by the applicable state law. The invalidity or -unenforceability of any provision of this agreement shall not void the -remaining provisions. - -1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the -trademark owner, any agent or employee of the Foundation, anyone -providing copies of Project Gutenberg-tm electronic works in -accordance with this agreement, and any volunteers associated with the -production, promotion and distribution of Project Gutenberg-tm -electronic works, harmless from all liability, costs and expenses, -including legal fees, that arise directly or indirectly from any of -the following which you do or cause to occur: (a) distribution of this -or any Project Gutenberg-tm work, (b) alteration, modification, or -additions or deletions to any Project Gutenberg-tm work, and (c) any -Defect you cause. - -Section 2. Information about the Mission of Project Gutenberg-tm - -Project Gutenberg-tm is synonymous with the free distribution of -electronic works in formats readable by the widest variety of -computers including obsolete, old, middle-aged and new computers. It -exists because of the efforts of hundreds of volunteers and donations -from people in all walks of life. - -Volunteers and financial support to provide volunteers with the -assistance they need are critical to reaching Project Gutenberg-tm's -goals and ensuring that the Project Gutenberg-tm collection will -remain freely available for generations to come. In 2001, the Project -Gutenberg Literary Archive Foundation was created to provide a secure -and permanent future for Project Gutenberg-tm and future -generations. To learn more about the Project Gutenberg Literary -Archive Foundation and how your efforts and donations can help, see -Sections 3 and 4 and the Foundation information page at -www.gutenberg.org Section 3. Information about the Project Gutenberg -Literary Archive Foundation - -The Project Gutenberg Literary Archive Foundation is a non profit -501(c)(3) educational corporation organized under the laws of the -state of Mississippi and granted tax exempt status by the Internal -Revenue Service. The Foundation's EIN or federal tax identification -number is 64-6221541. Contributions to the Project Gutenberg Literary -Archive Foundation are tax deductible to the full extent permitted by -U.S. federal laws and your state's laws. - -The Foundation's principal office is in Fairbanks, Alaska, with the -mailing address: PO Box 750175, Fairbanks, AK 99775, but its -volunteers and employees are scattered throughout numerous -locations. Its business office is located at 809 North 1500 West, Salt -Lake City, UT 84116, (801) 596-1887. Email contact links and up to -date contact information can be found at the Foundation's web site and -official page at www.gutenberg.org/contact - -For additional contact information: - - Dr. Gregory B. Newby - Chief Executive and Director - gbnewby@pglaf.org - -Section 4. Information about Donations to the Project Gutenberg -Literary Archive Foundation - -Project Gutenberg-tm depends upon and cannot survive without wide -spread public support and donations to carry out its mission of -increasing the number of public domain and licensed works that can be -freely distributed in machine readable form accessible by the widest -array of equipment including outdated equipment. Many small donations -($1 to $5,000) are particularly important to maintaining tax exempt -status with the IRS. - -The Foundation is committed to complying with the laws regulating -charities and charitable donations in all 50 states of the United -States. Compliance requirements are not uniform and it takes a -considerable effort, much paperwork and many fees to meet and keep up -with these requirements. We do not solicit donations in locations -where we have not received written confirmation of compliance. To SEND -DONATIONS or determine the status of compliance for any particular -state visit www.gutenberg.org/donate - -While we cannot and do not solicit contributions from states where we -have not met the solicitation requirements, we know of no prohibition -against accepting unsolicited donations from donors in such states who -approach us with offers to donate. - -International donations are gratefully accepted, but we cannot make -any statements concerning tax treatment of donations received from -outside the United States. U.S. laws alone swamp our small staff. - -Please check the Project Gutenberg Web pages for current donation -methods and addresses. Donations are accepted in a number of other -ways including checks, online payments and credit card donations. To -donate, please visit: www.gutenberg.org/donate - -Section 5. General Information About Project Gutenberg-tm electronic works. - -Professor Michael S. Hart was the originator of the Project -Gutenberg-tm concept of a library of electronic works that could be -freely shared with anyone. For forty years, he produced and -distributed Project Gutenberg-tm eBooks with only a loose network of -volunteer support. - -Project Gutenberg-tm eBooks are often created from several printed -editions, all of which are confirmed as not protected by copyright in -the U.S. unless a copyright notice is included. Thus, we do not -necessarily keep eBooks in compliance with any particular paper -edition. - -Most people start at our Web site which has the main PG search -facility: www.gutenberg.org - -This Web site includes information about Project Gutenberg-tm, -including how to make donations to the Project Gutenberg Literary -Archive Foundation, how to help produce our new eBooks, and how to -subscribe to our email newsletter to hear about new eBooks. - |