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+The Project Gutenberg Etext of Side-Lights On Astronomy, by Simon Newcomb
+#X in our series by Simon Newcomb
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+Title: Side-Lights On Astronomy
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+Author: Simon Newcomb
+
+Release Date: May, 2003  [Etext #4065]
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+The Project Gutenberg Etext of Side-Lights On Astronomy, by Simon Newcomb
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+
+
+SIDE-LIGHTS ON ASTRONOMY
+
+AND KINDRED FIELDS OF POPULAR SCIENCE
+
+
+ESSAYS AND ADDRESSES
+
+
+BY SIMON NEWCOMB
+
+
+
+
+CONTENTS
+
+
+PREFACE
+
+    I. THE UNSOLVED PROBLEMS OF ASTRONOMY
+   II. THE NEW PROBLEMS OF THE UNIVERSE
+  III. THE STRUCTURE OF THE UNIVERSE
+   IV. THE EXTENT OF THE UNIVERSE
+    V. MAKING AND USING A TELESCOPE
+   VI. WHAT THE ASTRONOMERS ARE DOING
+  VII. LIFE IN THE UNIVERSE
+ VIII. HOW THE PLANETS ARE WEIGHED
+   IX. THE MARINER'S COMPASS
+    X. THE FAIRYLAND OF GEOMETRY
+   XI. THE ORGANIZATION OF SCIENTIFIC RESEARCH
+  XII. CAN WE MAKE IT RAIN?
+ XIII. THE ASTRONOMICAL EPHEMERIS AND NAUTICAL ALMANAC
+  XIV. THE WORLD'S DEBT TO ASTRONOMY
+   XV. AN ASTRONOMICAL FRIENDSHIP
+  XVI. THE EVOLUTION OF THE SCIENTIFIC INVESTIGATOR
+ XVII. THE EVOLUTION OF ASTRONOMICAL KNOWLEDGE
+XVIII. ASPECTS OF AMERICAN ASTRONOMY
+  XIX. THE UNIVERSE AS AN ORGANISM
+   XX. THE RELATION OF SCIENTIFIC METHOD TO SOCIAL PROGRESS
+  XXI. THE OUTLOOK FOR THE FLYING-MACHINE
+
+
+
+
+ILLUSTRATIONS
+
+SIMON NEWCOMB
+
+PHOTOGRAPH OP THE CORONA OP THE SUN, TAKEN IN TRIPOLI DURING TOTAL
+ECLIPSE OF AUGUST 30, 1905.
+
+A TYPICAL STAR CLUSTER-CENTAURI
+
+THE GLASS DISK
+
+THE OPTICIAN'S TOOL
+
+THE OPTICIAN'S TOOL
+
+GRINDING A LARGE LENS
+
+IMAGE OF CANDLE-FLAME IN OBJECT-GLASS
+
+TESTING ADJUSTMENT OF OBJECT-GLASS
+
+A VERY PRIMITIVE MOUNTING FOR A TELESCOPE
+
+THE HUYGHENIAN EYE-PIECE
+
+SECTION OF THE PRIMITIVE MOUNTING
+
+SPECTRAL IMAGES OF STARS, THE UPPER LINE SHOWING HOW THEY APPEAR
+WITH THE EYE-PIECE PUSHED IN, THE LOWER WITH THE EYE-PIECE DRAWN
+OUT
+
+THE GREAT REFRACTOR OF THE NATIONAL OBSERVATORY AT WASHINGTON
+
+THE "BROKEN-BACKED COMET-SEEKER"
+
+NEBULA IN ORION
+
+DIP OF THE MAGNETIC NEEDLE IN VARIOUS LATITUDES
+
+STAR SPECTRA
+
+PROFESSOR LANGLEY'S AIR-SHIP
+
+
+
+
+
+
+PREFACE
+
+In preparing and issuing this collection of essays and addresses,
+the author has yielded to what he could not but regard as the too
+flattering judgment of the publishers. Having done this, it became
+incumbent to do what he could to justify their good opinion by
+revising the material and bringing it up to date. Interest rather
+than unity of thought has determined the selection.
+
+A prominent theme in the collection is that of the structure,
+extent, and duration of the universe. Here some repetition of
+ideas was found unavoidable, in a case where what is substantially
+a single theme has been treated in the various forms which it
+assumed in the light of constantly growing knowledge. If the
+critical reader finds this a defect, the author can plead in
+extenuation only the difficulty of avoiding it under the
+circumstances. Although mainly astronomical, a number of
+discussions relating to general scientific subjects have been
+included.
+
+Acknowledgment is due to the proprietors of the various
+periodicals from the pages of which most of the essays have been
+taken. Besides Harper's Magazine and the North American Review,
+these include McClure's Magazine, from which were taken the
+articles "The Unsolved Problems of Astronomy" and "How the Planets
+are Weighed." "The Structure of the Universe" appeared in the
+International Monthly, now the International Quarterly; "The
+Outlook for the Flying-Machine" is mainly from The New York
+Independent, but in part from McClure's Magazine; "The World's
+Debt to Astronomy" is from The Chautauquan; and "An Astronomical
+Friendship" from the Atlantic Monthly.
+
+SIMON NEWCOMB. WASHINGTON, JUNE, 1906.
+
+
+
+
+I
+
+THE UNSOLVED PROBLEMS OF ASTRONOMY
+
+
+The reader already knows what the solar system is: an immense
+central body, the sun, with a number of planets revolving round it
+at various distances. On one of these planets we dwell. Vast,
+indeed, are the distances of the planets when measured by our
+terrestrial standards. A cannon-ball fired from the earth to
+celebrate the signing of the Declaration of Independence, and
+continuing its course ever since with a velocity of eighteen
+hundred feet per second, would not yet be half-way to the orbit of
+Neptune, the outer planet. And yet the thousands of stars which
+stud the heavens are at distances so much greater than that of
+Neptune that our solar system is like a little colony, separated
+from the rest of the universe by an ocean of void space almost
+immeasurable in extent. The orbit of the earth round the sun is of
+such size that a railway train running sixty miles an hour, with
+never a stop, would take about three hundred and fifty years to
+cross it. Represent this orbit by a lady's finger-ring. Then the
+nearest fixed star will be about a mile and a half away; the next
+more than two miles; a few more from three to twenty miles; the
+great body at scores or hundreds of miles. Imagine the stars thus
+scattered from the Atlantic to the Mississippi, and keep this
+little finger-ring in mind as the orbit of the earth, and one may
+have some idea of the extent of the universe.
+
+One of the most beautiful stars in the heavens, and one that can
+be seen most of the year, is a Lyrae, or Alpha of the Lyre, known
+also as Vega. In a spring evening it may be seen in the northeast,
+in the later summer near the zenith, in the autumn in the
+northwest. On the scale we have laid down with the earth's orbit
+as a finger-ring, its distance would be some eight or ten miles.
+The small stars around it in the same constellation are probably
+ten, twenty, or fifty times as far.
+
+Now, the greatest fact which modern science has brought to light
+is that our whole solar system, including the sun, with all its
+planets, is on a journey towards the constellation Lyra. During
+our whole lives, in all probability during the whole of human
+history, we have been flying unceasingly towards this beautiful
+constellation with a speed to which no motion on earth can
+compare. The speed has recently been determined with a fair degree
+of certainty, though not with entire exactness; it is about ten
+miles a second, and therefore not far from three hundred millions
+of miles a year. But whatever it may be, it is unceasing and
+unchanging; for us mortals eternal. We are nearer the
+constellation by five or six hundred miles every minute we live;
+we are nearer to it now than we were ten years ago by thousands of
+millions of miles, and every future generation of our race will be
+nearer than its predecessor by thousands of millions of miles.
+
+When, where, and how, if ever, did this journey begin--when,
+where, and how, if ever, will it end? This is the greatest of the
+unsolved problems of astronomy. An astronomer who should watch the
+heavens for ten thousand years might gather some faint suggestion
+of an answer, or he might not. All we can do is to seek for some
+hints by study and comparison with other stars.
+
+The stars are suns. To put it in another way, the sun is one of
+the stars, and rather a small one at that. If the sun is moving in
+the way I have described, may not the stars also be in motion,
+each on a journey of its own through the wilderness of space? To
+this question astronomy gives an affirmative answer. Most of the
+stars nearest to us are found to be in motion, some faster than
+the sun, some more slowly, and the same is doubtless true of all;
+only the century of accurate observations at our disposal does not
+show the motion of the distant ones. A given motion seems slower
+the more distant the moving body; we have to watch a steamship on
+the horizon some little time to see that she moves at all. Thus it
+is that the unsolved problem of the motion of our sun is only one
+branch of a yet more stupendous one: What mean the motions of the
+stars--how did they begin, and how, if ever, will they end? So far
+as we can yet see, each star is going straight ahead on its own
+journey, without regard to its neighbors, if other stars can be so
+called. Is each describing some vast orbit which, though looking
+like a straight line during the short period of our observation,
+will really be seen to curve after ten thousand or a hundred
+thousand years, or will it go straight on forever? If the laws of
+motion are true for all space and all time, as we are forced to
+believe, then each moving star will go on in an unbending line
+forever unless hindered by the attraction of other stars. If they
+go on thus, they must, after countless years, scatter in all
+directions, so that the inhabitants of each shall see only a
+black, starless sky.
+
+Mathematical science can throw only a few glimmers of light on the
+questions thus suggested. From what little we know of the masses,
+distances, and numbers of the stars we see a possibility that the
+more slow-moving ones may, in long ages, be stopped in their
+onward courses or brought into orbits of some sort by the
+attraction of their millions of fellows. But it is hard to admit
+even this possibility in the case of the swift-moving ones.
+Attraction, varying as the inverse square of the distance,
+diminishes so rapidly as the distance increases that, at the
+distances which separate the stars, it is small indeed. We could
+not, with the most delicate balance that science has yet invented,
+even show the attraction of the greatest known star. So far as we
+know, the two swiftest-moving stars are, first, Arcturus, and,
+second, one known in astronomy as 1830 Groombridge, the latter so
+called because it was first observed by the astronomer
+Groombridge, and is numbered 1830 in his catalogue of stars. If
+our determinations of the distances of these bodies are to be
+relied on, the velocity of their motion cannot be much less than
+two hundred miles a second. They would make the circuit of the
+earth every two or three minutes. A body massive enough to control
+this motion would throw a large part of the universe into
+disorder. Thus the problem where these stars came from and where
+they are going is for us insoluble, and is all the more so from
+the fact that the swiftly moving stars are moving in different
+directions and seem to have no connection with each other or with
+any known star.
+
+It must not be supposed that these enormous velocities seem so to
+us. Not one of them, even the greatest, would be visible to the
+naked eye until after years of watching. On our finger-ring scale,
+1830 Groombridge would be some ten miles and Arcturus thirty or
+forty miles away. Either of them would be moving only two or three
+feet in a year. To the oldest Assyrian priests Lyra looked much as
+it does to us to-day. Among the bright and well-known stars
+Arcturus has the most rapid apparent motion, yet Job himself would
+not to-day see that its position had changed, unless he had noted
+it with more exactness than any astronomer of his time.
+
+Another unsolved problem among the greatest which present
+themselves to the astronomer is that of the size of the universe
+of stars. We know that several thousand of these bodies are
+visible to the naked eye; moderate telescopes show us millions;
+our giant telescopes of the present time, when used as cameras to
+photograph the heavens, show a number past count, perhaps one
+hundred millions. Are all these stars only those few which happen
+to be near us in a universe extending out without end, or do they
+form a collection of stars outside of which is empty infinite
+space? In other words, has the universe a boundary? Taken in its
+widest scope this question must always remain unanswered by us
+mortals because, even if we should discover a boundary within
+which all the stars and clusters we ever can know are contained,
+and outside of which is empty space, still we could never prove
+that this space is empty out to an infinite distance. Far outside
+of what we call the universe might still exist other universes
+which we can never see.
+
+It is a great encouragement to the astronomer that, although he
+cannot yet set any exact boundary to this universe of ours, he is
+gathering faint indications that it has a boundary, which his
+successors not many generations hence may locate so that the
+astronomer shall include creation itself within his mental grasp.
+It can be shown mathematically that an infinitely extended system
+of stars would fill the heavens with a blaze of light like that of
+the noonday sun. As no such effect is produced, it may be
+concluded that the universe has a boundary. But this does not
+enable us to locate the boundary, nor to say how many stars may
+lie outside the farthest stretches of telescopic vision. Yet by
+patient research we are slowly throwing light on these points and
+reaching inferences which, not many years ago, would have seemed
+forever beyond our powers.
+
+Every one now knows that the Milky Way, that girdle of light which
+spans the evening sky, is formed of clouds of stars too minute to
+be seen by the unaided vision. It seems to form the base on which
+the universe is built and to bind all the stars into a system. It
+comprises by far the larger number of stars that the telescope has
+shown to exist. Those we see with the naked eye are almost equally
+scattered over the sky. But the number which the telescope shows
+us become more and more condensed in the Milky Way as telescope
+power is increased. The number of new stars brought out with our
+greatest power is vastly greater in the Milky Way than in the rest
+of the sky, so that the former contains a great majority of the
+stars. What is yet more curious, spectroscopic research has shown
+that a particular kind of stars, those formed of heated gas, are
+yet more condensed in the central circle of this band; if they
+were visible to the naked eye, we should see them encircling the
+heavens as a narrow girdle forming perhaps the base of our whole
+system of stars. This arrangement of the gaseous or vaporous stars
+is one of the most singular facts that modern research has brought
+to light. It seems to show that these particular stars form a
+system of their own; but how such a thing can be we are still
+unable to see.
+
+The question of the form and extent of the Milky Way thus becomes
+the central one of stellar astronomy. Sir William Herschel began
+by trying to sound its depths; at one time he thought he had
+succeeded; but before he died he saw that they were unfathomable
+with his most powerful telescopes. Even today he would be a bold
+astronomer who would profess to say with certainty whether the
+smallest stars we can photograph are at the boundary of the
+system. Before we decide this point we must have some idea of the
+form and distance of the cloudlike masses of stars which form our
+great celestial girdle. A most curious fact is that our solar
+system seems to be in the centre of this galactic universe,
+because the Milky Way divides the heavens into two equal parts,
+and seems equally broad at all points. Were we looking at such a
+girdle as this from one side or the other, this appearance would
+not be presented. But let us not be too bold. Perhaps we are the
+victims of some fallacy, as Ptolemy was when he proved, by what
+looked like sound reasoning, based on undeniable facts, that this
+earth of ours stood at rest in the centre of the heavens!
+
+A related problem, and one which may be of supreme importance to
+the future of our race, is, What is the source of the heat
+radiated by the sun and stars? We know that life on the earth is
+dependent on the heat which the sun sends it. If we were deprived
+of this heat we should in a few days be enveloped in a frost which
+would destroy nearly all vegetation, and in a few months neither
+man nor animal would be alive, unless crouching over fires soon to
+expire for want of fuel. We also know that, at a time which is
+geologically recent, the whole of New England was covered with a
+sheet of ice, hundreds or even thousands of feet thick, above
+which no mountain but Washington raised its head. It is quite
+possible that a small diminution in the supply of heat sent us by
+the sun would gradually reproduce the great glacier, and once more
+make the Eastern States like the pole. But the fact is that
+observations of temperature in various countries for the last two
+or three hundred years do not show any change in climate which can
+be attributed to a variation in the amount of heat received from
+the sun.
+
+The acceptance of this theory of the heat of those heavenly bodies
+which shine by their own light--sun, stars, and nebulae--still
+leaves open a problem that looks insoluble with our present
+knowledge. What becomes of the great flood of heat and light which
+the sun and stars radiate into empty space with a velocity of one
+hundred and eighty thousand miles a second? Only a very small
+fraction of it can be received by the planets or by other stars,
+because these are mere points compared with their distance from
+us. Taking the teaching of our science just as it stands, we
+should say that all this heat continues to move on through
+infinite space forever. In a few thousand years it reaches the
+probable confines of our great universe. But we know of no reason
+why it should stop here. During the hundreds of millions of years
+since all our stars began to shine, has the first ray of light and
+heat kept on through space at the rate of one hundred and eighty
+thousand miles a second, and will it continue to go on for ages to
+come? If so, think of its distance now, and think of its still
+going on, to be forever wasted! Rather say that the problem, What
+becomes of it? is as yet unsolved.
+
+Thus far I have described the greatest of problems; those which we
+may suppose to concern the inhabitants of millions of worlds
+revolving round the stars as much as they concern us. Let us now
+come down from the starry heights to this little colony where we
+live, the solar system. Here we have the great advantage of being
+better able to see what is going on, owing to the comparative
+nearness of the planets. When we learn that these bodies are like
+our earth in form, size, and motions, the first question we ask
+is, Could we fly from planet to planet and light on the surface of
+each, what sort of scenery would meet our eyes? Mountain, forest,
+and field, a dreary waste, or a seething caldron larger than our
+earth? If solid land there is, would we find on it the homes of
+intelligent beings, the lairs of wild beasts, or no living thing
+at all? Could we breathe the air, would we choke for breath or be
+poisoned by the fumes of some noxious gas?
+
+To most of these questions science cannot as yet give a positive
+answer, except in the case of the moon. Our satellite is so near
+us that we can see it has no atmosphere and no water, and
+therefore cannot be the abode of life like ours. The contrast of
+its eternal deadness with the active life around us is great
+indeed. Here we have weather of so many kinds that we never tire
+of talking about it. But on the moon there is no weather at all.
+On our globe so many things are constantly happening that our
+thousands of daily journals cannot begin to record them. But on
+the dreary, rocky wastes of the moon nothing ever happens. So far
+as we can determine, every stone that lies loose on its surface
+has lain there through untold ages, unchanged and unmoved.
+
+We cannot speak so confidently of the planets. The most powerful
+telescopes yet made, the most powerful we can ever hope to make,
+would scarcely shows us mountains, or lakes, rivers, or fields at
+a distance of fifty millions of miles. Much less would they show
+us any works of man. Pointed at the two nearest planets, Venus and
+Mars, they whet our curiosity more than they gratify it.
+Especially is this the case with Venus. Ever since the telescope
+was invented observers have tried to find the time of rotation of
+this planet on its axis. Some have reached one conclusion, some
+another, while the wisest have only doubted. The great Herschel
+claimed that the planet was so enveloped in vapor or clouds that
+no permanent features could be seen on its surface. The best
+equipped recent observers think they see faint, shadowy patches,
+which remain the same from day to day, and which show that the
+planet always presents the same face to the sun, as the moon does
+to the earth. Others do not accept this conclusion as proved,
+believing that these patches may be nothing more than variations
+of light, shade, and color caused by the reflection of the sun's
+light at various angles from different parts of the planet.
+
+There is also some mystery about the atmosphere of this planet.
+When Venus passes nearly between us and the sun, her dark
+hemisphere is turned towards us, her bright one being always
+towards the sun. But she is not exactly on a line with the sun
+except on the very rare occasions of a transit across the sun's
+disk. Hence, on ordinary occasions, when she seems very near on a
+line with the sun, we see a very small part of the illuminated
+hemisphere, which now presents the form of a very thin crescent
+like the new moon. And this crescent is supposed to be a little
+broader than it would be if only half the planet were illuminated,
+and to encircle rather more than half the planet. Now, this is
+just the effect that would be produced by an atmosphere refracting
+the sun's light around the edge of the illuminated hemisphere.
+
+The difficulty of observations of this kind is such that the
+conclusion may be open to doubt. What is seen during transits of
+Venus over the sun's disk leads to more certain, but yet very
+puzzling, conclusions. The writer will describe what he saw at the
+Cape of Good Hope during the transit of December 5, 1882. As the
+dark planet impinged on the bright sun, it of course cut out a
+round notch from the edge of the sun. At first, when this notch
+was small, nothing could be seen of the outline of that part of
+the planet which was outside the sun. But when half the planet was
+on the sun, the outline of the part still off the sun was marked
+by a slender arc of light. A curious fact was that this arc did
+not at first span the whole outline of the planet, but only showed
+at one or two points. In a few moments another part of the outline
+appeared, and then another, until, at last, the arc of light
+extended around the complete outline. All this seems to show that
+while the planet has an atmosphere, it is not transparent like
+ours, but is so filled with mist and clouds that the sun is seen
+through it only as if shining in a fog.
+
+Not many years ago the planet Mars, which is the next one outside
+of us, was supposed to have a surface like that of our earth. Some
+parts were of a dark greenish gray hue; these were supposed to be
+seas and oceans. Other parts had a bright, warm tint; these were
+supposed to be the continents. During the last twenty years much
+has been learned as to how this planet looks, and the details of
+its surface have been mapped by several observers, using the best
+telescopes under the most favorable conditions of air and climate.
+And yet it must be confessed that the result of this labor is not
+altogether satisfactory. It seems certain that the so-called seas
+are really land and not water. When it comes to comparing Mars
+with the earth, we cannot be certain of more than a single point
+of resemblance. This is that during the Martian winter a white
+cap, as of snow, is formed over the pole, which partially melts
+away during the summer. The conclusion that there are oceans whose
+evaporation forms clouds which give rise to this snow seems
+plausible. But the telescope shows no clouds, and nothing to make
+it certain that there is an atmosphere to sustain them. There is
+no certainty that the white deposit is what we call snow; perhaps
+it is not formed of water at all. The most careful studies of the
+surface of this planet, under the best conditions, are those made
+at the Lowell Observatory at Flagstaff, Arizona. Especially
+wonderful is the system of so-called canals, first seen by
+Schiaparelli, but mapped in great detail at Flagstaff. But the
+nature and meaning of these mysterious lines are still to be
+discovered. The result is that the question of the real nature of
+the surface of Mars and of what we should see around us could we
+land upon it and travel over it are still among the unsolved
+problems of astronomy.
+
+If this is the case with the nearest planets that we can study,
+how is it with more distant ones? Jupiter is the only one of these
+of the condition of whose surface we can claim to have definite
+knowledge. But even this knowledge is meagre. The substance of
+what we know is that its surface is surrounded by layers of what
+look like dense clouds, through which nothing can certainly be
+seen.
+
+I have already spoken of the heat of the sun and its probable
+origin. But the question of its heat, though the most important,
+is not the only one that the sun offers us. What is the sun? When
+we say that it is a very hot globe, more than a million times as
+large as the earth, and hotter than any furnace that man can make,
+so that literally "the elements melt with fervent heat" even at
+its surface, while inside they are all vaporized, we have told the
+most that we know as to what the sun really is. Of course we know
+a great deal about the spots, the rotation of the sun on its axis,
+the materials of which it is composed, and how its surroundings
+look during a total eclipse. But all this does not answer our
+question. There are several mysteries which ingenious men have
+tried to explain, but they cannot prove their explanations to be
+correct. One is the cause and nature of the spots. Another is that
+the shining surface of the sun, the "photosphere," as it is
+technically called, seems so calm and quiet while forces are
+acting within it of a magnitude quite beyond our conception.
+Flames in which our earth and everything on it would be engulfed
+like a boy's marble in a blacksmith's forge are continually
+shooting up to a height of tens of thousands of miles. One would
+suppose that internal forces capable of doing this would break the
+surface up into billows of fire a thousand miles high; but we see
+nothing of the kind. The surface of the sun seems almost as placid
+as a lake.
+
+Yet another mystery is the corona of the sun. This is something we
+should never have known to exist if the sun were not sometimes
+totally eclipsed by the dark body of the moon. On these rare
+occasions the sun is seen to be surrounded by a halo of soft,
+white light, sending out rays in various directions to great
+distances. This halo is called the corona, and has been most
+industriously studied and photographed during nearly every total
+eclipse for thirty years. Thus we have learned much about how it
+looks and what its shape is. It has a fibrous, woolly structure, a
+little like the loose end of a much-worn hempen rope. A certain
+resemblance has been seen between the form of these seeming fibres
+and that of the lines in which iron filings arrange themselves
+when sprinkled on paper over a magnet. It has hence been inferred
+that the sun has magnetic properties, a conclusion which, in a
+general way, is supported by many other facts. Yet the corona
+itself remains no less an unexplained phenomenon.
+
+[Illustration with caption: PHOTOGRAPH OF THE CORONA OF THE SUN,
+TAKEN IN TRIPOLI DURING TOTAL ECLIPSE OF AUGUST 30, 1905]
+
+A phenomenon almost as mysterious as the solar corona is the
+"zodiacal light," which any one can see rising from the western
+horizon just after the end of twilight on a clear winter or spring
+evening. The most plausible explanation is that it is due to a
+cloud of small meteoric bodies revolving round the sun. We should
+hardly doubt this explanation were it not that this light has a
+yet more mysterious appendage, commonly called the Gegenschein, or
+counter-glow. This is a patch of light in the sky in a direction
+exactly opposite that of the sun. It is so faint that it can be
+seen only by a practised eye under the most favorable conditions.
+But it is always there. The latest suggestion is that it is a tail
+of the earth, of the same kind as the tail of a comet!
+
+We know that the motions of the heavenly bodies are predicted with
+extraordinary exactness by the theory of gravitation. When one
+finds that the exact path of the moon's shadow on the earth during
+a total eclipse of the sun can be mapped out many years in
+advance, and that the planets follow the predictions of the
+astronomer so closely that, if you could see the predicted planet
+as a separate object, it would look, even in a good telescope, as
+if it exactly fitted over the real planet, one thinks that here at
+least is a branch of astronomy which is simply perfect. And yet
+the worlds themselves show slight deviations in their movements
+which the astronomer cannot always explain, and which may be due
+to some hidden cause that, when brought to light, shall lead to
+conclusions of the greatest importance to our race.
+
+One of these deviations is in the rotation of the earth.
+Sometimes, for several years at a time, it seems to revolve a
+little faster, and then again a little slower. The changes are
+very slight; they can be detected only by the most laborious and
+refined methods; yet they must have a cause, and we should like to
+know what that cause is.
+
+The moon shows a similar irregularity of motion. For half a
+century, perhaps through a whole century, she will go around the
+earth a little ahead of her regular rate, and then for another
+half-century or more she will fall behind. The changes are very
+small; they would never have been seen with the unaided eye, yet
+they exist. What is their cause? Mathematicians have vainly spent
+years of study in trying to answer this question.
+
+The orbit of Mercury is found by observations to have a slight
+motion which mathematicians have vainly tried to explain. For some
+time it was supposed to be caused by the attraction of an unknown
+planet between Mercury and the sun, and some were so sure of the
+existence of this planet that they gave it a name, calling it
+Vulcan. But of late years it has become reasonably certain that no
+planet large enough to produce the effect observed can be there.
+So thoroughly has every possible explanation been sifted out and
+found wanting, that some astronomers are now inquiring whether the
+law of gravitation itself may not be a little different from what
+has always been supposed. A very slight deviation, indeed, would
+account for the facts, but cautious astronomers want other proofs
+before regarding the deviation of gravitation as an established
+fact.
+
+Intelligent men have sometimes inquired how, after devoting so
+much work to the study of the heavens, anything can remain for
+astronomers to find out. It is a curious fact that, although they
+were never learning so fast as at the present day, yet there seems
+to be more to learn now than there ever was before. Great and
+numerous as are the unsolved problems of our science, knowledge is
+now advancing into regions which, a few years ago, seemed
+inaccessible. Where it will stop none can say.
+
+
+
+
+
+II
+
+THE NEW PROBLEMS OF THE UNIVERSE
+
+
+The achievements of the nineteenth century are still a theme of
+congratulation on the part of all who compare the present state of
+the world with that of one hundred years ago. And yet, if we
+should fancy the most sagacious prophet, endowed with a brilliant
+imagination, to have set forth in the year 1806 the problems that
+the century might solve and the things which it might do, we
+should be surprised to see how few of his predictions had come to
+pass. He might have fancied aerial navigation and a number of
+other triumphs of the same class, but he would hardly have had
+either steam navigation or the telegraph in his picture. In 1856
+an article appeared in Harper's Magazine depicting some
+anticipated features of life in A.D. 3000. We have since made
+great advances, but they bear little resemblance to what the
+writer imagined. He did not dream of the telephone, but did
+describe much that has not yet come to pass and probably never
+will.
+
+The fact is that, much as the nineteenth century has done, its
+last work was to amuse itself by setting forth more problems for
+this century to solve than it has ever itself succeeded in
+mastering. We should not be far wrong in saying that to-day there
+are more riddles in the universe than there were before men knew
+that it contained anything more than the objects they could see.
+
+So far as mere material progress is concerned, it may be doubtful
+whether anything so epoch-making as the steam-engine or the
+telegraph is held in store for us by the future. But in the field
+of purely scientific discovery we are finding a crowd of things of
+which our philosophy did not dream even ten years ago.
+
+The greatest riddles which the nineteenth century has bequeathed
+to us relate to subjects so widely separated as the structure of
+the universe and the structure of atoms of matter. We see more and
+more of these structures, and we see more and more of unity
+everywhere, and yet new facts difficult of explanation are being
+added more rapidly than old facts are being explained.
+
+We all know that the nineteenth century was marked by a separation
+of the sciences into a vast number of specialties, to the
+subdivisions of which one could see no end. But the great work of
+the twentieth century will be to combine many of these
+specialties. The physical philosopher of the present time is
+directing his thought to the demonstration of the unity of
+creation. Astronomical and physical researches are now being
+united in a way which is bringing the infinitely great and the
+infinitely small into one field of knowledge. Ten years ago the
+atoms of matter, of which it takes millions of millions to make a
+drop of water, were the minutest objects with which science could
+imagine itself to be concerned, Now a body of experimentalists,
+prominent among whom stand Professors J. J. Thompson, Becquerel,
+and Roentgen, have demonstrated the existence of objects so minute
+that they find their way among and between the atoms of matter as
+rain-drops do among the buildings of a city. More wonderful yet,
+it seems likely, although it has not been demonstrated, that these
+little things, called "corpuscles," play an important part in what
+is going on among the stars. Whether this be true or not, it is
+certain that there do exist in the universe emanations of some
+sort, producing visible effects, the investigation of which the
+nineteenth century has had to bequeath to the twentieth.
+
+For the purpose of the navigator, the direction of the magnetic
+needle is invariable in any one place, for months and even years;
+but when exact scientific observations on it are made, it is found
+subject to numerous slight changes. The most regular of these
+consists in a daily change of its direction. It moves one way from
+morning until noon, and then, late in the afternoon and during the
+night, turns back again to its original pointing. The laws of this
+change have been carefully studied from observations, which show
+that it is least at the equator and larger as we go north into
+middle latitudes; but no explanation of it resting on an
+indisputable basis has ever been offered.
+
+Besides these regular changes, there are others of a very
+irregular character. Every now and then the changes in the
+direction of the magnet are wider and more rapid than those which
+occur regularly every day. The needle may move back and forth in a
+way so fitful as to show the action of some unusual exciting
+cause. Such movements of the needle are commonly seen when there
+is a brilliant aurora. This connection shows that a magnetic storm
+and an aurora must be due to the same or some connected causes.
+
+Those of us who are acquainted with astronomical matters know that
+the number of spots on the sun goes through a regular cycle of
+change, having a period of eleven years and one or two months.
+Now, the curious fact is, when the number and violence of magnetic
+storms are recorded and compared, it is found that they correspond
+to the spots on the sun, and go through the same period of eleven
+years. The conclusion seems almost inevitable: magnetic storms are
+due to some emanation sent out by the sun, which arises from the
+same cause that produces the spots. This emanation does not go on
+incessantly, but only in an occasional way, as storms follow each
+other on the earth. What is it? Every attempt to detect it has
+been in vain. Professor Hale, at the Yerkes Observatory, has had
+in operation from time to time, for several years, his ingenious
+spectroheliograph, which photographs the sun by a single ray of
+the spectrum. This instrument shows that violent actions are going
+on in the sun, which ordinary observation would never lead us to
+suspect. But it has failed to show with certainty any peculiar
+emanation at the time of a magnetic storm or anything connected
+with such a storm.
+
+A mystery which seems yet more impenetrable is associated with the
+so-called new stars which blaze forth from time to time. These
+offer to our sight the most astounding phenomena ever presented to
+the physical philosopher. One hundred years ago such objects
+offered no mystery. There was no reason to suppose that the
+Creator of the universe had ceased His functions; and, continuing
+them, it was perfectly natural that He should be making continual
+additions to the universe of stars. But the idea that these
+objects are really new creations, made out of nothing, is contrary
+to all our modern ideas and not in accord with the observed facts.
+Granting the possibility of a really new star--if such an object
+were created, it would be destined to take its place among the
+other stars as a permanent member of the universe. Instead of
+this, such objects invariably fade away after a few months, and
+are changed into something very like an ordinary nebula. A
+question of transcendent interest is that of the cause of these
+outbursts. It cannot be said that science has, up to the present
+time, been able to offer any suggestion not open to question. The
+most definite one is the collision theory, according to which the
+outburst is due to the clashing together of two stars, one or both
+of which might previously have been dark, like a planet. The stars
+which may be actually photographed probably exceed one hundred
+millions in number, and those which give too little light to
+affect the photographic plate may be vastly more numerous than
+those which do. Dark stars revolve around bright ones in an
+infinite variety of ways, and complex systems of bodies, the
+members of which powerfully attract each other, are the rule
+throughout the universe. Moreover, we can set no limit to the
+possible number of dark or invisible stars that may be flying
+through the celestial spaces. While, therefore, we cannot regard
+the theory of collision as established, it seems to be the only
+one yet put forth which can lay any claim to a scientific basis.
+What gives most color to it is the extreme suddenness with which
+the new stars, so far as has yet been observed, invariably blaze
+forth. In almost every case it has been only two or three days
+from the time that the existence of such an object became known
+until it had attained nearly its full brightness. In fact, it
+would seem that in the case of the star in Perseus, as in most
+other cases, the greater part of the outburst took place within
+the space of twenty-four hours. This suddenness and rapidity is
+exactly what would be the result of a collision.
+
+The most inexplicable feature of all is the rapid formation of a
+nebula around this star. In the first photographs of the latter,
+the appearance presented is simply that of an ordinary star. But,
+in the course of three or four months, the delicate photographs
+taken at the Lick Observatory showed that a nebulous light
+surrounded the star, and was continually growing larger and
+larger. At first sight, there would seem to be nothing
+extraordinary in this fact. Great masses of intensely hot vapor,
+shining by their own light, would naturally be thrown out from the
+star. Or, if the star had originally been surrounded by a very
+rare nebulous fog or vapor, the latter would be seen by the
+brilliant light emitted by the star. On this was based an
+explanation offered by Kapteyn, which at first seemed very
+plausible. It was that the sudden wave of light thrown out by the
+star when it burst forth caused the illumination of the
+surrounding vapor, which, though really at rest, would seem to
+expand with the velocity of light, as the illumination reached
+more and more distant regions of the nebula. This result may be
+made the subject of exact calculation. The velocity of light is
+such as would make a circuit of the earth more than seven times in
+a second. It would, therefore, go out from the star at the rate of
+a million of miles in between five and six seconds. In the lapse
+of one of our days, the light would have filled a sphere around
+the star having a diameter more than one hundred and fifty times
+the distance of the sun from the earth, and more than five times
+the dimensions of the whole solar system. Continuing its course
+and enlarging its sphere day after day, the sight presented to us
+would have been that of a gradually expanding nebulous mass--a
+globe of faint light continually increasing in size with the
+velocity of light.
+
+The first sentiment the reader will feel on this subject is
+doubtless one of surprise that the distance of the star should be
+so great as this explanation would imply. Six months after the
+explosion, the globe of light, as actually photographed, was of a
+size which would have been visible to the naked eye only as a very
+minute object in the sky. Is it possible that this minute object
+could have been thousands of times the dimensions of our solar
+system?
+
+To see how the question stands from this point of view, we must
+have some idea of the possible distance of the new star. To gain
+this idea, we must find some way of estimating distances in the
+universe. For a reason which will soon be apparent, we begin with
+the greatest structure which nature offers to the view of man. We
+all know that the Milky Way is formed of countless stars, too
+minute to be individually visible to the naked eye. The more
+powerful the telescope through which we sweep the heavens, the
+greater the number of the stars that can be seen in it. With the
+powerful instruments which are now in use for photographing the
+sky, the number of stars brought to light must rise into the
+hundreds of millions, and the greater part of these belong to the
+Milky Way. The smaller the stars we count, the greater their
+comparative number in the region of the Milky Way. Of the stars
+visible through the telescope, more than one-half are found in the
+Milky Way, which may be regarded as a girdle spanning the entire
+visible universe.
+
+Of the diameter of this girdle we can say, almost with certainty,
+that it must be more than a thousand times as great as the
+distance of the nearest fixed star from us, and is probably two or
+three times greater. According to the best judgment we can form,
+our solar system is situate near the central region of the girdle,
+so that the latter must be distant from us by half its diameter.
+It follows that if we can imagine a gigantic pair of compasses, of
+which the points extend from us to Alpha Centauri, the nearest
+star, we should have to measure out at least five hundred spaces
+with the compass, and perhaps even one thousand or more, to reach
+the region of the Milky Way.
+
+With this we have to connect another curious fact. Of eighteen new
+stars which have been observed to blaze forth during the last four
+hundred years, all are in the region of the Milky Way. This seems
+to show that, as a rule, they belong to the Milky Way. Accepting
+this very plausible conclusion, the new star in Perseus must have
+been more than five hundred times as far as the nearest fixed
+star. We know that it takes light four years to reach us from
+Alpha Centauri. It follows that the new star was at a distance
+through which light would require more than two thousand years to
+travel, and quite likely a time two or three times this. It
+requires only the most elementary ideas of geometry to see that if
+we suppose a ray of light to shoot from a star at such a distance
+in a direction perpendicular to the line of sight from us to the
+star, we can compute how fast the ray would seem to us to travel.
+Granting the distance to be only two thousand light years, the
+apparent size of the sphere around the star which the light would
+fill at the end of one year after the explosion would be that of a
+coin seen at a distance of two thousand times its radius, or one
+thousand times its diameter--say, a five-cent piece at the
+distance of sixty feet. But, as a matter of fact, the nebulous
+illumination expanded with a velocity from ten to twenty times as
+great as this.
+
+The idea that the nebulosity around the new star was formed by the
+illumination caused by the light of the explosion spreading out on
+all sides therefore fails to satisfy us, not because the expansion
+of the nebula seemed to be so slow, but because it was many times
+as swift as the speed of light. Another reason for believing that
+it was not a mere wave of light is offered by the fact that it did
+not take place regularly in every direction from the star, but
+seemed to shoot off at various angles.
+
+Up to the present time, the speed of light has been to science, as
+well as to the intelligence of our race, almost a symbol of the
+greatest of possible speeds. The more carefully we reflect on the
+case, the more clearly we shall see the difficulty in supposing
+any agency to travel at the rate of the seeming emanations from
+the new star in Perseus.
+
+As the emanation is seen spreading day after day, the reader may
+inquire whether this is not an appearance due to some other cause
+than the mere motion of light. May not an explosion taking place
+in the centre of a star produce an effect which shall travel yet
+faster than light? We can only reply that no such agency is known
+to science.
+
+But is there really anything intrinsically improbable in an agency
+travelling with a speed many times that of light? In considering
+that there is, we may fall into an error very much like that into
+which our predecessors fell in thinking it entirely out of the
+range of reasonable probability that the stars should be placed at
+such distances as we now know them to be.
+
+Accepting it as a fact that agencies do exist which travel from
+sun to planet and from star to star with a speed which beggars all
+our previous ideas, the first question that arises is that of
+their nature and mode of action. This question is, up to the
+present time, one which we do not see any way of completely
+answering. The first difficulty is that we have no evidence of
+these agents except that afforded by their action. We see that the
+sun goes through a regular course of pulsations, each requiring
+eleven years for completion; and we see that, simultaneously with
+these, the earth's magnetism goes through a similar course of
+pulsations. The connection of the two, therefore, seems absolutely
+proven. But when we ask by what agency it is possible for the sun
+to affect the magnetism of the earth, and when we trace the
+passage of some agent between the two bodies, we find nothing to
+explain the action. To all appearance, the space between the earth
+and the sun is a perfect void. That electricity cannot of itself
+pass through a vacuum seems to be a well-established law of
+physics. It is true that electromagnetic waves, which are supposed
+to be of the same nature with those of light, and which are used
+in wireless telegraphy, do pass through a vacuum and may pass from
+the sun to the earth. But there is no way of explaining how such
+waves would either produce or affect the magnetism of the earth.
+
+The mysterious emanations from various substances, under certain
+conditions, may have an intimate relation with yet another of the
+mysteries of the universe. It is a fundamental law of the universe
+that when a body emits light or heat, or anything capable of being
+transformed into light or heat, it can do so only by the
+expenditure of force, limited in supply. The sun and stars are
+continually sending out a flood of heat. They are exhausting the
+internal supply of something which must be limited in extent.
+Whence comes the supply? How is the heat of the sun kept up? If it
+were a hot body cooling off, a very few years would suffice for it
+to cool off so far that its surface would become solid and very
+soon cold. In recent years, the theory universally accepted has
+been that the supply of heat is kept up by the continual
+contraction of the sun, by mutual gravitation of its parts as it
+cools off. This theory has the advantage of enabling us to
+calculate, with some approximation to exactness, at what rate the
+sun must be contracting in order to keep up the supply of heat
+which it radiates. On this theory, it must, ten millions of years
+ago, have had twice its present diameter, while less than twenty
+millions of years ago it could not have existed except as an
+immense nebula filling the whole solar system. We must bear in
+mind that this theory is the only one which accounts for the
+supply of heat, even through human history. If it be true, then
+the sun, earth, and solar system must be less than twenty million
+years old.
+
+Here the geologists step in and tell us that this conclusion is
+wholly inadmissible. The study of the strata of the earth and of
+many other geological phenomena, they assure us, makes it certain
+that the earth must have existed much in its present condition for
+hundreds of millions of years. During all that time there can have
+been no great diminution in the supply of heat radiated by the
+sun.
+
+The astronomer, in considering this argument, has to admit that he
+finds a similar difficulty in connection with the stars and
+nebulas. It is an impossibility to regard these objects as new;
+they must be as old as the universe itself. They radiate heat and
+light year after year. In all probability, they must have been
+doing so for millions of years. Whence comes the supply? The
+geologist may well claim that until the astronomer explains this
+mystery in his own domain, he cannot declare the conclusions of
+geology as to the age of the earth to be wholly inadmissible.
+
+Now, the scientific experiments of the last two years have brought
+this mystery of the celestial spaces right down into our earthly
+laboratories. M. and Madame Curie have discovered the singular
+metal radium, which seems to send out light, heat, and other rays
+incessantly, without, so far as has yet been determined, drawing
+the required energy from any outward source. As we have already
+pointed out, such an emanation must come from some storehouse of
+energy. Is the storehouse, then, in the medium itself, or does the
+latter draw it from surrounding objects? If it does, it must
+abstract heat from these objects. This question has been settled
+by Professor Dewar, at the Royal Institution, London, by placing
+the radium in a medium next to the coldest that art has yet
+produced--liquid air. The latter is surrounded by the only yet
+colder medium, liquid hydrogen, so that no heat can reach it.
+Under these circumstances, the radium still gives out heat,
+boiling away the liquid air until the latter has entirely
+disappeared. Instead of the radiation diminishing with time, it
+rather seems to increase.
+
+Called on to explain all this, science can only say that a
+molecular change must be going on in the radium, to correspond to
+the heat it gives out. What that change may be is still a complete
+mystery. It is a mystery which we find alike in those minute
+specimens of the rarest of substances under our microscopes, in
+the sun, and in the vast nebulous masses in the midst of which our
+whole solar system would be but a speck. The unravelling of this
+mystery must be the great work of science of the twentieth
+century. What results shall follow for mankind one cannot say, any
+more than he could have said two hundred years ago what modern
+science would bring forth. Perhaps, before future developments,
+all the boasted achievements of the nineteenth century may take
+the modest place which we now assign to the science of the
+eighteenth century--that of the infant which is to grow into a
+man.
+
+
+
+
+
+III
+
+THE STRUCTURE OF THE UNIVERSE
+
+
+The questions of the extent of the universe in space and of its
+duration in time, especially of its possible infinity in either
+space or time, are of the highest interest both in philosophy and
+science. The traditional philosophy had no means of attacking
+these questions except considerations suggested by pure reason,
+analogy, and that general fitness of things which was supposed to
+mark the order of nature. With modern science the questions belong
+to the realm of fact, and can be decided only by the results of
+observation and a study of the laws to which these results may
+lead.
+
+From the philosophic stand-point, a discussion of this subject
+which is of such weight that in the history of thought it must be
+assigned a place above all others, is that of Kant in his
+"Kritik." Here we find two opposing propositions--the thesis that
+the universe occupies only a finite space and is of finite
+duration; the antithesis that it is infinite both as regards
+extent in space and duration in time. Both of these opposing
+propositions are shown to admit of demonstration with equal force,
+not directly, but by the methods of reductio ad absurdum. The
+difficulty, discussed by Kant, was more tersely expressed by
+Hamilton in pointing out that we could neither conceive of
+infinite space nor of space as bounded. The methods and
+conclusions of modern astronomy are, however, in no way at
+variance with Kant's reasoning, so far as it extends. The fact is
+that the problem with which the philosopher of Konigsberg vainly
+grappled is one which our science cannot solve any more than could
+his logic. We may hope to gain complete information as to
+everything which lies within the range of the telescope, and to
+trace to its beginning every process which we can now see going on
+in space. But before questions of the absolute beginning of
+things, or of the boundary beyond which nothing exists, our means
+of inquiry are quite powerless.
+
+Another example of the ancient method is found in the great work
+of Copernicus. It is remarkable how completely the first expounder
+of the system of the world was dominated by the philosophy of his
+time, which he had inherited from his predecessors. This is seen
+not only in the general course of thought through the opening
+chapters of his work, but among his introductory propositions. The
+first of these is that the universe--mundus--as well as the earth,
+is spherical in form. His arguments for the sphericity of the
+earth, as derived from observation, are little more than a
+repetition of those of Ptolemy, and therefore not of special
+interest. His proposition that the universe is spherical is,
+however, not based on observation, but on considerations of the
+perfection of the spherical form, the general tendency of bodies--
+a drop of water, for example--to assume this form, and the
+sphericity of the sun and moon. The idea retained its place in his
+mind, although the fundamental conception of his system did away
+with the idea of the universe having any well-defined form.
+
+The question as attacked by modern astronomy is this: we see
+scattered through space in every direction many millions of stars
+of various orders of brightness and at distances so great as to
+defy exact measurement, except in the case of a few of the
+nearest. Has this collection of stars any well-defined boundary,
+or is what we see merely that part of an infinite mass which
+chances to lie within the range of our telescopes? If we were
+transported to the most distant star of which we have knowledge,
+should we there find ourselves still surrounded by stars on all
+sides, or would the space beyond be void? Granting that, in any or
+every direction, there is a limit to the universe, and that the
+space beyond is therefore void, what is the form of the whole
+system and the distance of its boundaries? Preliminary in some
+sort to these questions are the more approachable ones: Of what
+sort of matter is the universe formed? and into what sort of
+bodies is this matter collected?
+
+To the ancients the celestial sphere was a reality, instead of a
+mere effect of perspective, as we regard it. The stars were set on
+its surface, or at least at no great distance within its
+crystalline mass. Outside of it imagination placed the empyrean.
+When and how these conceptions vanished from the mind of man, it
+would be as hard to say as when and how Santa Claus gets
+transformed in the mind of the child. They are not treated as
+realities by any astronomical writer from Ptolemy down; yet, the
+impressions and forms of thought to which they gave rise are well
+marked in Copernicus and faintly evident in Kepler. The latter was
+perhaps the first to suggest that the sun might be one of the
+stars; yet, from defective knowledge of the relative brightness of
+the latter, he was led to the conclusion that their distances from
+each other were less than the distance which separated them from
+the sun. The latter he supposed to stand in the centre of a vast
+vacant region within the system of stars.
+
+For us the great collection of millions of stars which are made
+known to us by the telescope, together with all the invisible
+bodies which may be contained within the limits of the system,
+form the universe. Here the term "universe" is perhaps
+objectionable because there may be other systems than the one with
+which we are acquainted. The term stellar system is, therefore, a
+better one by which to designate the collection of stars in
+question.
+
+It is remarkable that the first known propounder of that theory of
+the form and arrangement of the system which has been most
+generally accepted seems to have been a writer otherwise unknown
+in science--Thomas Wright, of Durham, England. He is said to have
+published a book on the theory of the universe, about 1750. It
+does not appear that this work was of a very scientific character,
+and it was, perhaps, too much in the nature of a speculation to
+excite notice in scientific circles. One of the curious features
+of the history is that it was Kant who first cited Wright's
+theory, pointed out its accordance with the appearance of the
+Milky Way, and showed its general reasonableness. But, at the time
+in question, the work of the philosopher of Konigsberg seems to
+have excited no more notice among his scientific contemporaries
+than that of Wright.
+
+Kant's fame as a speculative philosopher has so eclipsed his
+scientific work that the latter has but recently been appraised at
+its true value. He was the originator of views which, though
+defective in detail, embodied a remarkable number of the results
+of recent research on the structure and form of the universe, and
+the changes taking place in it. The most curious illustration of
+the way in which he arrived at a correct conclusion by defective
+reasoning is found in his anticipation of the modern theory of a
+constant retardation of the velocity with which the earth revolves
+on its axis. He conceived that this effect must result from the
+force exerted by the tidal wave, as moving towards the west it
+strikes the eastern coasts of Asia and America. An opposite
+conclusion was reached by Laplace, who showed that the effect of
+this force was neutralized by forces producing the wave and acting
+in the opposite direction. And yet, nearly a century later, it was
+shown that while Laplace was quite correct as regards the general
+principles involved, the friction of the moving water must prevent
+the complete neutralization of the two opposing forces, and leave
+a small residual force acting towards the west and retarding the
+rotation. Kant's conclusion was established, but by an action
+different from that which he supposed.
+
+The theory of Wright and Kant, which was still further developed
+by Herschel, was that our stellar system has somewhat the form of
+a flattened cylinder, or perhaps that which the earth would assume
+if, in consequence of more rapid rotation, the bulging out at its
+equator and the flattening at its poles were carried to an extreme
+limit. This form has been correctly though satirically compared to
+that of a grindstone. It rests to a certain extent, but not
+entirely, on the idea that the stars are scattered through space
+with equal thickness in every direction, and that the appearance
+of the Milky Way is due to the fact that we, situated in the
+centre of this flattened system, see more stars in the direction
+of the circumference of the system than in that of its poles. The
+argument on which the view in question rests may be made clear in
+the following way.
+
+Let us chose for our observations that hour of the night at which
+the Milky Way skirts our horizon. This is nearly the case in the
+evenings of May and June, though the coincidence with the horizon
+can never be exact except to observers stationed near the tropics.
+Using the figure of the grindstone, we at its centre will then
+have its circumference around our horizon, while the axis will be
+nearly vertical. The points in which the latter intersects the
+celestial sphere are called the galactic poles. There will be two
+of these poles, the one at the hour in question near the zenith,
+the other in our nadir, and therefore invisible to us, though seen
+by our antipodes. Our horizon corresponds, as it were, to the
+central circle of the Milky Way, which now surrounds us on all
+sides in a horizontal direction, while the galactic poles are 90
+degrees distant from every part of it, as every point of the
+horizon is 90 degrees from the zenith.
+
+Let us next count the number of stars visible in a powerful
+telescope in the region of the heavens around the galactic pole,
+now our zenith, and find the average number per square degree.
+This will be the richness of the region in stars. Then we take
+regions nearer the horizontal Milky Way--say that contained
+between 10 degrees and 20 degrees from the zenith--and, by a
+similar count, find its richness in stars. We do the same for
+other regions, nearer and nearer to the horizon, till we reach the
+galaxy itself. The result of all the counts will be that the
+richness of the sky in stars is least around the galactic pole,
+and increases in every direction towards the Milky Way.
+
+Without such counts of the stars we might imagine our stellar
+system to be a globular collection of stars around which the
+object in question passed as a girdle; and we might take a globe
+with a chain passing around it as representative of the possible
+figure of the stellar system. But the actual increase in star-
+thickness which we have pointed out shows us that this view is
+incorrect. The nature and validity of the conclusions to be drawn
+can be best appreciated by a statement of some features of this
+tendency of the stars to crowd towards the galactic circle.
+
+Most remarkable is the fact that the tendency is seen even among
+the brighter stars. Without either telescope or technical
+knowledge, the careful observer of the stars will notice that the
+most brilliant constellations show this tendency. The glorious
+Orion, Canis Major containing the brightest star in the heavens,
+Cassiopeia, Perseus, Cygnus, and Lyra with its bright-blue Vega,
+not to mention such constellations as the Southern Cross, all lie
+in or near the Milky Way. Schiaparelli has extended the
+investigation to all the stars visible to the naked eye. He laid
+down on planispheres the number of such stars in each region of
+the heavens of 5 degrees square. Each region was then shaded with
+a tint that was darker as the region was richer in stars. The very
+existence of the Milky Way was ignored in this work, though his
+most darkly shaded regions lie along the course of this belt. By
+drawing a band around the sky so as to follow or cover his darkest
+regions, we shall rediscover the course of the Milky Way without
+any reference to the actual object. It is hardly necessary to add
+that this result would be reached with yet greater precision if we
+included the telescopic stars to any degree of magnitude--plotting
+them on a chart and shading the chart in the same way. What we
+learn from this is that the stellar system is not an irregular
+chaos; and that notwithstanding all its minor irregularities, it
+may be considered as built up with special reference to the Milky
+Way as a foundation.
+
+Another feature of the tendency in question is that it is more and
+more marked as we include fainter stars in our count. The galactic
+region is perhaps twice as rich in stars visible to the naked eye
+as the rest of the heavens. In telescopic stars to the ninth
+magnitude it is three or four times as rich. In the stars found on
+the photographs of the sky made at the Harvard and other
+observatories, and in the stargauges of the Herschels, it is from
+five to ten times as rich.
+
+Another feature showing the unity of the system is the symmetry of
+the heavens on the two sides of the galactic belt Let us return to
+our supposition of such a position of the celestial sphere, with
+respect to the horizon, that the latter coincides with the central
+line of this belt, one galactic pole being near our zenith. The
+celestial hemisphere which, being above our horizon, is visible to
+us, is the one to which we have hitherto directed our attention in
+describing the distribution of the stars. But below our horizon is
+another hemisphere, that of our antipodes, which is the
+counterpart of ours. The stars which it contains are in a
+different part of the universe from those which we see, and,
+without unity of plan, would not be subject to the same law. But
+the most accurate counts of stars that have been made fail to show
+any difference in their general arrangement in the two
+hemispheres. They are just as thick around the south galactic
+poles as around the north one. They show the same tendency to
+crowd towards the Milky Way in the hemisphere invisible to us as
+in the hemisphere which we see. Slight differences and
+irregularities, are, indeed, found in the enumeration, but they
+are no greater than must necessarily arise from the difficulty of
+stopping our count at a perfectly fixed magnitude. The aim of
+star-counts is not to estimate the total number of stars, for this
+is beyond our power, but the number visible with a given
+telescope. In such work different observers have explored
+different parts of the sky, and in a count of the same region by
+two observers we shall find that, although they attempt to stop at
+the same magnitude, each will include a great number of stars
+which the other omits. There is, therefore, room for considerable
+difference in the numbers of stars recorded, without there being
+any actual inequality between the two hemispheres.
+
+A corresponding similarity is found in the physical constitution
+of the stars as brought out by the spectroscope. The Milky Way is
+extremely rich in bluish stars, which make up a considerable
+majority of the cloudlike masses there seen. But when we recede
+from the galaxy on one side, we find the blue stars becoming
+thinner, while those having a yellow tinge become relatively more
+numerous. This difference of color also is the same on the two
+sides of the galactic plane. Nor can any systematic difference be
+detected between the proper motions of the stars in these two
+hemispheres. If the largest known proper motion is found in the
+one, the second largest is in the other. Counting all the known
+stars that have proper motions exceeding a given limit, we find
+about as many in one hemisphere as in the other. In this respect,
+also, the universe appears to be alike through its whole extent.
+It is the uniformity thus prevailing through the visible universe,
+as far as we can see, in two opposite directions, which inspires
+us with confidence in the possibility of ultimately reaching some
+well-founded conclusion as to the extent and structure of the
+system.
+
+All these facts concur in supporting the view of Wright, Kant, and
+Herschel as to the form of the universe. The farther out the stars
+extend in any direction, the more stars we may see in that
+direction. In the direction of the axis of the cylinder, the
+distances of the boundary are least, so that we see fewer stars.
+The farther we direct our attention towards the equatorial regions
+of the system, the greater the distance from us to the boundary,
+and hence the more stars we see. The fact that the increase in the
+number of stars seen towards the equatorial region of the system
+is greater, the smaller the stars, is the natural consequence of
+the fact that distant stars come within our view in greater
+numbers towards the equatorial than towards the polar regions.
+
+Objections have been raised to the Herschelian view on the ground
+that it assumes an approximately uniform distribution of the stars
+in space. It has been claimed that the fact of our seeing more
+stars in one direction than in another may not arise merely from
+our looking through a deeper stratum, as Herschel supposed, but
+may as well be due to the stars being more thinly scattered in the
+direction of the axis of the system than in that of its equatorial
+region. The great inequalities in the richness of neighboring
+regions in the Milky Way show that the hypothesis of uniform
+distribution does not apply to the equatorial region. The claim
+has therefore been made that there is no proof of the system
+extending out any farther in the equatorial than in the polar
+direction.
+
+The consideration of this objection requires a closer inquiry as
+to what we are to understand by the form of our system. We have
+already pointed out the impossibility of assigning any boundary
+beyond which we can say that nothing exists. And even as regards a
+boundary of our stellar system, it is impossible for us to assign
+any exact limit beyond which no star is visible to us. The analogy
+of collections of stars seen in various parts of the heavens leads
+us to suppose that there may be no well-defined form to our
+system, but that, as we go out farther and farther, we shall see
+occasional scattered stars to, possibly, an indefinite distance.
+The truth probably is that, as in ascending a mountain, we find
+the trees, which may be very dense at its base, thin out gradually
+as we approach the summit, where there may be few or none, so we
+might find the stars to thin out could we fly to the distant
+regions of space. The practical question is whether, in such a
+flight, we should find this sooner by going in the direction of
+the axis of our system than by directing our course towards the
+Milky Way. If a point is at length reached beyond which there are
+but few scattered stars, such a point would, for us, mark the
+boundary of our system. From this point of view the answer does
+not seem to admit of doubt. If, going in every direction, we mark
+the point, if any, at which the great mass of the stars are seen
+behind us, the totality of all these points will lie on a surface
+of the general form that Herschel supposed.
+
+There is still another direct indication of the finitude of our
+stellar system upon which we have not touched. If this system
+extended out without limit in any direction whatever, it is shown
+by a geometric process which it is not necessary to explain in the
+present connection, but which is of the character of mathematical
+demonstration, that the heavens would, in every direction where
+this was true, blaze with the light of the noonday sun. This would
+be very different from the blue-black sky which we actually see on
+a clear night, and which, with a reservation that we shall
+consider hereafter, shows that, how far so-ever our stellar
+system may extend, it is not infinite. Beyond this negative
+conclusion the fact does not teach us much. Vast, indeed, is the
+distance to which the system might extend without the sky
+appearing much brighter than it is, and we must have recourse to
+other considerations in seeking for indications of a boundary, or
+even of a well-marked thinning out, of stars.
+
+If, as was formerly supposed, the stars did not greatly differ in
+the amount of light emitted by each, and if their diversity of
+apparent magnitude were due principally to the greater distance of
+the fainter stars, then the brightness of a star would enable us
+to form a more or less approximate idea of its distance. But the
+accumulated researches of the past seventy years show that the
+stars differ so enormously in their actual luminosity that the
+apparent brightness of a star affords us only a very imperfect
+indication of its distance. While, in the general average, the
+brighter stars must be nearer to us than the fainter ones, it by
+no means follows that a very bright star, even of the first
+magnitude, is among the nearer to our system. Two stars are worthy
+of especial mention in this connection, Canopus and Rigel. The
+first is, with the single exception of Sirius, the brightest star
+in the heavens. The other is a star of the first magnitude in the
+southwest corner of Orion. The most long-continued and complete
+measures of parallax yet made are those carried on by Gill, at the
+Cape of Good Hope, on these two and some other bright stars. The
+results, published in 1901, show that neither of these bodies has
+any parallax that can be measured by the most refined instrumental
+means known to astronomy. In other words, the distance of these
+stars is immeasurably great. The actual amount of light emitted by
+each is certainly thousands and probably tens of thousands of
+times that of the sun.
+
+Notwithstanding the difficulties that surround the subject, we can
+at least say something of the distance of a considerable number of
+the stars. Two methods are available for our estimate--measures of
+parallax and determination of proper motions.
+
+The problem of stellar parallax, simple though it is in its
+conception, is the most delicate and difficult of all which the
+practical astronomer has to encounter. An idea of it may be gained
+by supposing a minute object on a mountain-top, we know not how
+many miles away, to be visible through a telescope. The observer
+is allowed to change the position of his instrument by two inches,
+but no more. He is required to determine the change in the
+direction of the object produced by this minute displacement with
+accuracy enough to determine the distance of the mountain. This is
+quite analogous to the determination of the change in the
+direction in which we see a star as the earth, moving through its
+vast circuit, passes from one extremity of its orbit to the other.
+Representing this motion on such a scale that the distance of our
+planet from the sun shall be one inch, we find that the nearest
+star, on the same scale, will be more than four miles away, and
+scarcely one out of a million will be at a less distance than ten
+miles. It is only by the most wonderful perfection both in the
+heliometer, the instrument principally used for these measures,
+and in methods of observation, that any displacement at all can be
+seen even among the nearest stars. The parallaxes of perhaps a
+hundred stars have been determined, with greater or less
+precision, and a few hundred more may be near enough for
+measurement. All the others are immeasurably distant; and it is
+only by statistical methods based on their proper motions and
+their probable near approach to equality in distribution that any
+idea can be gained of their distances.
+
+To form a conception of the stellar system, we must have a unit of
+measure not only exceeding any terrestrial standard, but even any
+distance in the solar system. For purely astronomical purposes the
+most convenient unit is the distance corresponding to a parallax
+of 1", which is a little more than 200,000 times the sun's
+distance. But for the purposes of all but the professional
+astronomer the most convenient unit will be the light-year--that
+is, the distance through which light would travel in one year.
+This is equal to the product of 186,000 miles, the distance
+travelled in one second, by 31,558,000, the number of seconds in a
+year. The reader who chooses to do so may perform the
+multiplication for himself. The product will amount to about
+63,000 times the distance of the sun.
+
+[Illustration with caption: A Typical Star Cluster--Centauri]
+
+The nearest star whose distance we know, Alpha Centauri, is
+distant from us more than four light-years. In all likelihood
+this is really the nearest star, and it is not at all probable
+that any other star lies within six light-years. Moreover, if we
+were transported to this star the probability seems to be that the
+sun would now be the nearest star to us. Flying to any other of
+the stars whose parallax has been measured, we should probably
+find that the average of the six or eight nearest stars around us
+ranges somewhere between five and seven light-years. We may, in a
+certain sense, call eight light-years a star-distance, meaning by
+this term the average of the nearest distances from one star to
+the surrounding ones.
+
+To put the result of measures of parallax into another form, let
+us suppose, described around our sun as a centre, a system of
+concentric spheres each of whose surfaces is at the distance of
+six light-years outside the sphere next within it. The inner is at
+the distance of six light-years around the sun. The surface of the
+second sphere will be twelve light-years away, that of the third
+eighteen, etc. The volumes of space within each of these spheres
+will be as the cubes of the diameters. The most likely conclusion
+we can draw from measures of parallax is that the first sphere
+will contain, beside the sun at its centre, only Alpha Centauri.
+The second, twelve light-years away, will probably contain,
+besides these two, six other stars, making eight in all. The third
+may contain twenty-one more, making twenty-seven stars within the
+third sphere, which is the cube of three. Within the fourth would
+probably be found sixty-four stars, this being the cube of four,
+and so on.
+
+Beyond this no measures of parallax yet made will give us much
+assistance. We can only infer that probably the same law holds for
+a large number of spheres, though it is quite certain that it does
+not hold indefinitely. For more light on the subject we must have
+recourse to the proper motions. The latest words of astronomy on
+this subject may be briefly summarized. As a rule, no star is at
+rest. Each is moving through space with a speed which differs
+greatly with different stars, but is nearly always swift, indeed,
+when measured by any standard to which we are accustomed. Slow and
+halting, indeed, is that star which does not make more than a mile
+a second. With two or three exceptions, where the attraction of a
+companion comes in, the motion of every star, so far as yet
+determined, takes place in a straight line. In its outward motion
+the flying body deviates neither to the right nor left. It is safe
+to say that, if any deviation is to take place, thousands of years
+will be required for our terrestrial observers to recognize it.
+
+Rapid as the course of these objects is, the distances which we
+have described are such that, in the great majority of cases, all
+the observations yet made on the positions of the stars fail to
+show any well-established motion. It is only in the case of the
+nearer of these objects that we can expect any motion to be
+perceptible during the period, in no case exceeding one hundred
+and fifty years, through which accurate observations extend. The
+efforts of all the observatories which engage in such work are, up
+to the present time, unequal to the task of grappling with the
+motions of all the stars that can be seen with the instruments,
+and reaching a decision as to the proper motion in each particular
+case. As the question now stands, the aim of the astronomer is to
+determine what stars have proper motions large enough to be well
+established. To make our statement on this subject clear, it must
+be understood that by this term the astronomer does not mean the
+speed of a star in space, but its angular motion as he observes it
+on the celestial sphere. A star moving forward with a given speed
+will have a greater proper motion according as it is nearer to us.
+To avoid all ambiguity, we shall use the term "speed" to express
+the velocity in miles per second with which such a body moves
+through space, and the term "proper motion" to express the
+apparent angular motion which the astronomer measures upon the
+celestial sphere.
+
+Up to the present time, two stars have been found whose proper
+motions are so large that, if continued, the bodies would make a
+complete circuit of the heavens in less than 200,000 years. One of
+these would require about 160,000; the other about 180,000 years
+for the circuit. Of other stars having a rapid motion only about
+one hundred would complete their course in less than a million of
+years.
+
+Quite recently a system of observations upon stars to the ninth
+magnitude has been nearly carried through by an international
+combination of observatories. The most important conclusion from
+these observations relates to the distribution of the stars with
+reference to the Milky Way, which we have already described. We
+have shown that stars of every magnitude, bright and faint, show a
+tendency to crowd towards this belt. It is, therefore, remarkable
+that no such tendency is seen in the case of those stars which
+have proper motions large enough to be accurately determined. So
+far as yet appears, such stars are equally scattered over the
+heavens, without reference to the course of the Milky Way. The
+conclusion is obvious. These stars are all inside the girdle of
+the Milky Way, and within the sphere which contains them the
+distribution in space is approximately uniform. At least there is
+no well-marked condensation in the direction of the galaxy nor any
+marked thinning out towards its poles. What can we say as to the
+extent of this sphere?
+
+To answer this question, we have to consider whether there is any
+average or ordinary speed that a star has in space. A great number
+of motions in the line of sight--that is to say, in the direction
+of the line from us to the star--have been measured with great
+precision by Campbell at the Lick Observatory, and by other
+astronomers. The statistical investigations of Kaptoyn also throw
+much light on the subject. The results of these investigators
+agree well in showing an average speed in space--a straight-ahead
+motion we may call it--of twenty-one miles per second. Some stars
+may move more slowly than this to any extent; others more rapidly.
+In two or three cases the speed exceeds one hundred miles per
+second, but these are quite exceptional. By taking several
+thousand stars having a given proper motion, we may form a general
+idea of their average distance, though a great number of them will
+exceed this average to a considerable extent. The conclusion drawn
+in this way would be that the stars having an apparent proper
+motion of 10" per century or more are mostly contained within, or
+lie not far outside of a sphere whose surface is at a distance
+from us of 200 light-years. Granting the volume of space which we
+have shown that nature seems to allow to each star, this sphere
+should contain 27,000 stars in all. There are about 10,000 stars
+known to have so large a proper motion as 10". But there is no
+actual discordance between these results, because not only are
+there, in all probability, great numbers of stars of which the
+proper motion is not yet recognized, but there are within the
+sphere a great number of stars whose motion is less than the
+average. On the other hand, it is probable that a considerable
+number of the 10,000 stars lie at a distance at least one-half
+greater than that of the radius of the sphere.
+
+On the whole, it seems likely that, out to a distance of 300 or
+even 400 light-years, there is no marked inequality in star
+distribution. If we should explore the heavens to this distance,
+we should neither find the beginning of the Milky Way in one
+direction nor a very marked thinning out in the other. This
+conclusion is quite accordant with the probabilities of the case.
+If all the stars which form the groundwork of the Milky Way should
+be blotted out, we should probably find 100,000,000, perhaps even
+more, remaining. Assigning to each star the space already shown to
+be its quota, we should require a sphere of about 3000 light-years
+radius to contain such a number of stars. At some such distance as
+this, we might find a thinning out of the stars in the direction
+of the galactic poles, or the commencement of the Milky Way in the
+direction of this stream.
+
+Even if this were not found at the distance which we have
+supposed, it is quite certain that, at some greater distance, we
+should at least find that the region of the Milky Way is richer in
+stars than the region near the galactic poles. There is strong
+reason, based on the appearance of the stars of the Milky Way,
+their physical constitution, and their magnitudes as seen in the
+telescope, to believe that, were we placed on one of these stars,
+we should find the stars around us to be more thickly strewn than
+they are around our system. In other words, the quota of space
+filled by each star is probably less in the region of the Milky
+Way than it is near the centre where we seem to be situated.
+
+We are, therefore, presented with what seems to be the most
+extraordinary spectacle that the universe can offer, a ring of
+stars spanning it, and including within its limits by far the
+great majority of the stars within our system. We have in this
+spectacle another example of the unity which seems to pervade the
+system. We might imagine the latter so arranged as to show
+diversity to any extent. We might have agglomerations of stars
+like those of the Milky Way situated in some corner of the system,
+or at its centre, or scattered through it here and there in every
+direction. But such is not the case. There are, indeed, a few
+star-clusters scattered here and there through the system; but
+they are essentially different from the clusters of the Milky Way,
+and cannot be regarded as forming an important part of the general
+plan. In the case of the galaxy we have no such scattering, but
+find the stars built, as it were, into this enormous ring, having
+similar characteristics throughout nearly its whole extent, and
+having within it a nearly uniform scattering of stars, with here
+and there some collected into clusters. Such, to our limited
+vision, now appears the universe as a whole.
+
+We have already alluded to the conclusion that an absolutely
+infinite system of stars would cause the entire heavens to be
+filled with a blaze of light as bright as the sun. It is also true
+that the attractive force within such a universe would be
+infinitely great in some direction or another. But neither of
+these considerations enables us to set a limit to the extent of
+our system. In two remarkable papers by Lord Kelvin which have
+recently appeared, the one being an address before the British
+Association at its Glasgow meeting, in 1901, are given the results
+of some numerical computations pertaining to this subject.
+Granting that the stars are scattered promiscuously through space
+with some approach to uniformity in thickness, and are of a known
+degree of brilliancy, it is easy to compute how far out the system
+must extend in order that, looking up at the sky, we shall see a
+certain amount of light coming from the invisible stars. Granting
+that, in the general average, each star is as bright as the sun,
+and that their thickness is such that within a sphere of 3300
+light-years there are 1,000,000,000 stars, if we inquire how far
+out such a system must be continued in order that the sky shall
+shine with even four per cent of the light of the sun, we shall
+find the distance of its boundary so great that millions of
+millions of years would be required for the light of the outer
+stars to reach the centre of the system. In view of the fact that
+this duration in time far exceeds what seems to be the possible
+life duration of a star, so far as our knowledge of it can extend,
+the mere fact that the sky does not glow with any such brightness
+proves little or nothing as to the extent of the system.
+
+We may, however, replace these purely negative considerations by
+inquiring how much light we actually get from the invisible stars
+of our system. Here we can make a definite statement. Mark out a
+small circle in the sky 1 degree in diameter. The quantity of
+light which we receive on a cloudless and moonless night from the
+sky within this circle admits of actual determination. From the
+measures so far available it would seem that, in the general
+average, this quantity of light is not very different from that of
+a star of the fifth magnitude. This is something very different
+from a blaze of light. A star of the fifth magnitude is scarcely
+more than plainly visible to ordinary vision. The area of the
+whole sky is, in round numbers, about 50,000 times that of the
+circle we have described. It follows that the total quantity of
+light which we receive from all the stars is about equal to that
+of 50,000 stars of the fifth magnitude--somewhat more than 1000 of
+the first magnitude. This whole amount of light would have to be
+multiplied by 90,000,000 to make a light equal to that of the sun.
+It is, therefore, not at all necessary to consider how far the
+system must extend in order that the heavens should blaze like the
+sun. Adopting Lord Kelvin's hypothesis, we shall find that, in
+order that we may receive from the stars the amount of light we
+have designated, this system need not extend beyond some 5000
+light-years. But this hypothesis probably overestimates the
+thickness of the stars in space. It does not seem probable that
+there are as many as 1,000,000,000 stars within the sphere of 3300
+light-years. Nor is it at all certain that the light of the
+average star is equal to that of the sun. It is impossible, in the
+present state of our knowledge, to assign any definite value to
+this average. To do so is a problem similar to that of assigning
+an average weight to each component of the animal creation, from
+the microscopic insects which destroy our plants up to the
+elephant. What we can say with a fair approximation to confidence
+is that, if we could fly out in any direction to a distance of
+20,000, perhaps even of 10,000, light-years, we should find that
+we had left a large fraction of our system behind us. We should
+see its boundary in the direction in which we had travelled much
+more certainly than we see it from our stand-point.
+
+We should not dismiss this branch of the subject without saying
+that considerations are frequently adduced by eminent authorities
+which tend to impair our confidence in almost any conclusion as to
+the limits of the stellar system. The main argument is based on
+the possibility that light is extinguished in its passage through
+space; that beyond a certain distance we cannot see a star,
+however bright, because its light is entirely lost before reaching
+us. That there could be any loss of light in passing through an
+absolute vacuum of any extent cannot be admitted by the physicist
+of to-day without impairing what he considers the fundamental
+principles of the vibration of light. But the possibility that the
+celestial spaces are pervaded by matter which might obstruct the
+passage of light is to be considered. We know that minute meteoric
+particles are flying through our system in such numbers that the
+earth encounters several millions of them every day, which appear
+to us in the familiar phenomena of shooting-stars. If such
+particles are scattered through all space, they must ultimately
+obstruct the passage of light. We know little of the size of these
+bodies, but, from the amount of energy contained in their light as
+they are consumed in the passage through our atmosphere, it does
+not seem at all likely that they are larger than grains of sand
+or, perhaps, minute pebbles. They are probably vastly more
+numerous in the vicinity of the sun than in the interstellar
+spaces, since they would naturally tend to be collected by the
+sun's attraction. In fact there are some reasons for believing
+that most of these bodies are the debris of comets; and the latter
+are now known to belong to the solar system, and not to the
+universe at large.
+
+But whatever view we take of these possibilities, they cannot
+invalidate our conclusion as to the general structure of the
+stellar system as we know it. Were meteors so numerous as to cut
+off a large fraction of the light from the more distant stars, we
+should see no Milky Way, but the apparent thickness of the stars
+in every direction would be nearly the same. The fact that so many
+more of these objects are seen around the galactic belt than in
+the direction of its poles shows that, whatever extinction light
+may suffer in going through the greatest distances, we see nearly
+all that comes from stars not more distant than the Milky Way
+itself.
+
+Intimately connected with the subject we have discussed is the
+question of the age of our system, if age it can be said to have.
+In considering this question, the simplest hypothesis to suggest
+itself is that the universe has existed forever in some such form
+as we now see it; that it is a self-sustaining system, able to go
+on forever with only such cycles of transformation as may repeat
+themselves indefinitely, and may, therefore, have repeated
+themselves indefinitely in the past. Ordinary observation does not
+make anything known to us which would seem to invalidate this
+hypothesis. In looking upon the operations of the universe, we may
+liken ourselves to a visitor to the earth from another sphere who
+has to draw conclusions about the life of an individual man from
+observations extending through a few days. During that time, he
+would see no reason why the life of the man should have either a
+beginning or an end. He sees a daily round of change, activity and
+rest, nutrition and waste; but, at the end of the round, the
+individual is seemingly restored to his state of the day before.
+Why may not this round have been going on forever, and continue in
+the future without end? It would take a profounder course of
+observation and a longer time to show that, notwithstanding this
+seeming restoration, an imperceptible residual of vital energy,
+necessary to the continuance of life, has not been restored, and
+that the loss of this residuum day by day must finally result in
+death.
+
+The case is much the same with the great bodies of the universe.
+Although, to superficial observation, it might seem that they
+could radiate their light forever, the modern generalizations of
+physics show that such cannot be the case. The radiation of light
+necessarily involves a corresponding loss of heat and with it the
+expenditure of some form of energy. The amount of energy within
+any body is necessarily limited. The supply must be exhausted
+unless the energy of the light sent out into infinite space is, in
+some way, restored to the body which expended it. The possibility
+of such a restoration completely transcends our science. How can
+the little vibration which strikes our eye from some distant star,
+and which has been perhaps thousands of years in reaching us, find
+its way back to its origin? The light emitted by the sun 10,000
+years ago is to-day pursuing its way in a sphere whose surface is
+10,000 light-years distant on all sides. Science has nothing even
+to suggest the possibility of its restoration, and the most
+delicate observations fail to show any return from the
+unfathomable abyss.
+
+Up to the time when radium was discovered, the most careful
+investigations of all conceivable sources of supply had shown only
+one which could possibly be of long duration. This is the
+contraction which is produced in the great incandescent bodies of
+the universe by the loss of the heat which they radiate. As
+remarked in the preceding essay, the energy generated by the sun's
+contraction could not have kept up its present supply of heat for
+much more than twenty or thirty millions of years, while the study
+of earth and ocean shows evidence of the action of a series of
+causes which must have been going on for hundreds of millions of
+years.
+
+The antagonism between the two conclusions is even more marked
+than would appear from this statement. The period of the sun's
+heat set by the astronomical physicist is that during which our
+luminary could possibly have existed in its present form. The
+period set by the geologist is not merely that of the sun's
+existence, but that during which the causes effecting geological
+changes have not undergone any complete revolution. If, at any
+time, the sun radiated much less than its present amount of heat,
+no water could have existed on the earth's surface except in the
+form of ice; there would have been scarcely any evaporation, and
+the geological changes due to erosion could not have taken place.
+Moreover, the commencement of the geological operations of which
+we speak is by no means the commencement of the earth's existence.
+The theories of both parties agree that, for untold aeons before
+the geological changes now visible commenced, our planet was a
+molten mass, perhaps even an incandescent globe like the sun.
+During all those aeons the sun must have been in existence as a
+vast nebulous mass, first reaching as far as the earth's orbit,
+and slowly contracting its dimensions. And these aeons are to be
+included in any estimate of the age of the sun.
+
+The doctrine of cosmic evolution--the theory which in former times
+was generally known as the nebular hypothesis--that the heavenly
+bodies were formed by the slow contraction of heated nebulous
+masses, is indicated by so many facts that it seems scarcely
+possible to doubt it except on the theory that the laws of nature
+were, at some former time, different from those which we now see
+in operation. Granting the evolutionary hypothesis, every star has
+its lifetime. We can even lay down the law by which it passes from
+infancy to old age. All stars do not have the same length of life;
+the rule is that the larger the star, or the greater the mass of
+matter which composes it, the longer will it endure. Up to the
+present time, science can do nothing more than point out these
+indications of a beginning, and their inevitable consequence, that
+there is to be an end to the light and heat of every heavenly
+body. But no cautious thinker can treat such a subject with the
+ease of ordinary demonstration. The investigator may even be
+excused if he stands dumb with awe before the creation of his own
+intellect. Our accurate records of the operations of nature extend
+through only two or three centuries, and do not reach a
+satisfactory standard until within a single century. The
+experience of the individual is limited to a few years, and beyond
+this period he must depend upon the records of his ancestors. All
+his knowledge of the laws of nature is derived from this very
+limited experience. How can he essay to describe what may have
+been going on hundreds of millions of years in the past? Can he
+dare to say that nature was the same then as now?
+
+It is a fundamental principle of the theory of evolution, as
+developed by its greatest recent expounder, that matter itself is
+eternal, and that all the changes which have taken place in the
+universe, so far as made up of matter, are in the nature of
+transformations of this eternal substance. But we doubt whether
+any physical philosopher of the present day would be satisfied to
+accept any demonstration of the eternity of matter. All he would
+admit is that, so far as his observation goes, no change in the
+quantity of matter can be produced by the action of any known
+cause. It seems to be equally uncreatable and indestructible. But
+he would, at the same time, admit that his experience no more
+sufficed to settle the question than the observation of an animal
+for a single day would settle the question of the duration of its
+life, or prove that it had neither beginning nor end. He would
+probably admit that even matter itself may be a product of
+evolution. The astronomer finds it difficult to conceive that the
+great nebulous masses which he sees in the celestial spaces--
+millions of times larger than the whole solar system, yet so
+tenuous that they offer not the slightest obstruction to the
+passage of a ray of light through their whole length--situated in
+what seems to be a region of eternal cold, below anything that we
+can produce on the earth's surface, yet radiating light, and with
+it heat, like an incandescent body--can be made up of the same
+kind of substance that we have around us on the earth's surface.
+Who knows but that the radiant property that Becquerel has found
+in certain forms of matter may be a residuum of some original form
+of energy which is inherent in great cosmical masses, and has fed
+our sun during all the ages required by the geologist for the
+structure of the earth's crusts? It may be that in this phenomenon
+we have the key to the great riddle of the universe, with which
+profounder secrets of matter than any we have penetrated will be
+opened to the eyes of our successors.
+
+
+
+
+
+IV
+
+THE EXTENT OF THE UNIVERSE
+
+
+We cannot expect that the wisest men of our remotest posterity,
+who can base their conclusions upon thousands of years of accurate
+observation, will reach a decision on this subject without some
+measure of reserve. Such being the case, it might appear the
+dictate of wisdom to leave its consideration to some future age,
+when it may be taken up with better means of information than we
+now possess. But the question is one which will refuse to be
+postponed so long as the propensity to think of the possibilities
+of creation is characteristic of our race. The issue is not
+whether we shall ignore the question altogether, like Eve in the
+presence of Raphael; but whether in studying it we shall confine
+our speculations within the limits set by sound scientific
+reasoning. Essaying to do this, I invite the reader's attention to
+what science may suggest, admitting in advance that the sphere of
+exact knowledge is small compared with the possibilities of
+creation, and that outside this sphere we can state only more or
+less probable conclusions.
+
+The reader who desires to approach this subject in the most
+receptive spirit should begin his study by betaking himself on a
+clear, moonless evening, when he has no earthly concern to disturb
+the serenity of his thoughts, to some point where he can lie on
+his back on bench or roof, and scan the whole vault of heaven at
+one view. He can do this with the greatest pleasure and profit in
+late summer or autumn--winter would do equally well were it
+possible for the mind to rise so far above bodily conditions that
+the question of temperature should not enter. The thinking man who
+does this under circumstances most favorable for calm thought will
+form a new conception of the wonder of the universe. If summer or
+autumn be chosen, the stupendous arch of the Milky Way will pass
+near the zenith, and the constellation Lyra, led by its beautiful
+blue Vega of the first magnitude, may be not very far from that
+point. South of it will be seen the constellation Aquila, marked
+by the bright Altair, between two smaller but conspicuous stars.
+The bright Arcturus will be somewhere in the west, and, if the
+observation is not made too early in the season, Aldebaran will be
+seen somewhere in the east. When attention is concentrated on the
+scene the thousands of stars on each side of the Milky Way will
+fill the mind with the consciousness of a stupendous and all-
+embracing frame, beside which all human affairs sink into
+insignificance. A new idea will be formed of such a well-known
+fact of astronomy as the motion of the solar system in space, by
+reflecting that, during all human history, the sun, carrying the
+earth with it, has been flying towards a region in or just south
+of the constellation Lyra, with a speed beyond all that art can
+produce on earth, without producing any change apparent to
+ordinary vision in the aspect of the constellation. Not only Lyra
+and Aquila, but every one of the thousand stars which form the
+framework of the sky, were seen by our earliest ancestors just as
+we see them now. Bodily rest may be obtained at any time by
+ceasing from our labors, and weary systems may find nerve rest at
+any summer resort; but I know of no way in which complete rest can
+be obtained for the weary soul--in which the mind can be so
+entirely relieved of the burden of all human anxiety--as by the
+contemplation of the spectacle presented by the starry heavens
+under the conditions just described. As we make a feeble attempt
+to learn what science can tell us about the structure of this
+starry frame, I hope the reader will allow me to at least fancy
+him contemplating it in this way.
+
+The first question which may suggest itself to the inquiring
+reader is: How is it possible by any methods of observation yet
+known to the astronomer to learn anything about the universe as a
+whole? We may commence by answering this question in a somewhat
+comprehensive way. It is possible only because the universe, vast
+though it is, shows certain characteristics of a unified and
+bounded whole. It is not a chaos, it is not even a collection of
+things, each of which came into existence in its own separate way.
+If it were, there would be nothing in common between two widely
+separate regions of the universe. But, as a matter of fact,
+science shows unity in the whole structure, and diversity only in
+details. The Milky Way itself will be seen by the most ordinary
+observer to form a single structure. This structure is, in some
+sort, the foundation on which the universe is built. It is a
+girdle which seems to span the whole of creation, so far as our
+telescopes have yet enabled us to determine what creation is; and
+yet it has elements of similarity in all its parts. What has yet
+more significance, it is in some respects unlike those parts of
+the universe which lie without it, and even unlike those which lie
+in that central region within it where our system is now situated.
+The minute stars, individually far beyond the limit of visibility
+to the naked eye, which form its cloudlike agglomerations, are
+found to be mostly bluer in color, from one extreme to the other,
+than the general average of the stars which make up the rest of
+the universe.
+
+In the preceding essay on the structure of the universe, we have
+pointed out several features of the universe showing the unity of
+the whole. We shall now bring together these and other features
+with a view of showing their relation to the question of the
+extent of the universe.
+
+The Milky Way being in a certain sense the foundation on which the
+whole system is constructed, we have first to notice the symmetry
+of the whole. This is seen in the fact that a certain resemblance
+is found in any two opposite regions of the sky, no matter where
+we choose them. If we take them in the Milky Way, the stars are
+more numerous than elsewhere; if we take opposite regions in or
+near the Milky Way, we shall find more stars in both of them than
+elsewhere; if we take them in the region anywhere around the poles
+of the Milky Way, we shall find fewer stars, but they will be
+equally numerous in each of the two regions. We infer from this
+that whatever cause determined the number of the stars in space
+was of the same nature in every two antipodal regions of the
+heavens.
+
+Another unity marked with yet more precision is seen in the
+chemical elements of which stars are composed. We know that the
+sun is composed of the same elements which we find on the earth
+and into which we resolve compounds in our laboratories. These
+same elements are found in the most distant stars. It is true that
+some of these bodies seem to contain elements which we do not find
+on earth. But as these unknown elements are scattered from one
+extreme of the universe to the other, they only serve still
+further to enforce the unity which runs through the whole. The
+nebulae are composed, in part at least, of forms of matter
+dissimilar to any with which we are acquainted. But, different
+though they may be, they are alike in their general character
+throughout the whole field we are considering. Even in such a
+feature as the proper motions of the stars, the same unity is
+seen. The reader doubtless knows that each of these objects is
+flying through space on its own course with a speed comparable
+with that of the earth around the sun. These speeds range from the
+smallest limit up to more than one hundred miles a second. Such
+diversity might seem to detract from the unity of the whole; but
+when we seek to learn something definite by taking their average,
+we find this average to be, so far as can yet be determined, much
+the same in opposite regions of the universe. Quite recently it
+has become probable that a certain class of very bright stars
+known as Orion stars--because there are many of them in the most
+brilliant of our constellations--which are scattered along the
+whole course of the Milky Way, have one and all, in the general
+average, slower motions than other stars. Here again we have a
+definable characteristic extending through the universe. In
+drawing attention to these points of similarity throughout the
+whole universe, it must not be supposed that we base our
+conclusions directly upon them. The point they bring out is that
+the universe is in the nature of an organized system; and it is
+upon the fact of its being such a system that we are able, by
+other facts, to reach conclusions as to its structure, extent, and
+other characteristics.
+
+One of the great problems connected with the universe is that of
+its possible extent. How far away are the stars? One of the
+unities which we have described leads at once to the conclusion
+that the stars must be at very different distances from us;
+probably the more distant ones are a thousand times as far as the
+nearest; possibly even farther than this. This conclusion may, in
+the first place, be based on the fact that the stars seem to be
+scattered equally throughout those regions of the universe which
+are not connected with the Milky Way. To illustrate the principle,
+suppose a farmer to sow a wheat-field of entirely unknown extent
+with ten bushels of wheat. We visit the field and wish to have
+some idea of its acreage. We may do this if we know how many
+grains of wheat there are in the ten bushels. Then we examine a
+space two or three feet square in any part of the field and count
+the number of grains in that space. If the wheat is equally
+scattered over the whole field, we find its extent by the simple
+rule that the size of the field bears the same proportion to the
+size of the space in which the count was made that the whole
+number of grains in the ten bushels sown bears to the number of
+grains counted. If we find ten grains in a square foot, we know
+that the number of square feet in the whole field is one-tenth
+that of the number of grains sown. So it is with the universe of
+stars. If the latter are sown equally through space, the extent of
+the space occupied must be proportional to the number of stars
+which it contains.
+
+But this consideration does not tell us anything about the actual
+distance of the stars or how thickly they may be scattered. To do
+this we must be able to determine the distance of a certain number
+of stars, just as we suppose the farmer to count the grains in a
+certain small extent of his wheat-field. There is only one way in
+which we can make a definite measure of the distance of any one
+star. As the earth swings through its vast annual circuit round
+the sun, the direction of the stars must appear to be a little
+different when seen from one extremity of the circuit than when
+seen from the other. This difference is called the parallax of the
+stars; and the problem of measuring it is one of the most delicate
+and difficult in the whole field of practical astronomy.
+
+The nineteenth century was well on its way before the instruments
+of the astronomer were brought to such perfection as to admit of
+the measurement. From the time of Copernicus to that of Bessel
+many attempts had been made to measure the parallax of the stars,
+and more than once had some eager astronomer thought himself
+successful. But subsequent investigation always showed that he had
+been mistaken, and that what he thought was the effect of parallax
+was due to some other cause, perhaps the imperfections of his
+instrument, perhaps the effect of heat and cold upon it or upon
+the atmosphere through which he was obliged to observe the star,
+or upon the going of his clock. Thus things went on until 1837,
+when Bessel announced that measures with a heliometer--the most
+refined instrument that has ever been used in measurement--showed
+that a certain star in the constellation Cygnus had a parallax of
+one-third of a second. It may be interesting to give an idea of
+this quantity. Suppose one's self in a house on top of a mountain
+looking out of a window one foot square, at a house on another
+mountain one hundred miles away. One is allowed to look at that
+distant house through one edge of the pane of glass and then
+through the opposite edge; and he has to determine the change in
+the direction of the distant house produced by this change of one
+foot in his own position. From this he is to estimate how far off
+the other mountain is. To do this, one would have to measure just
+about the amount of parallax that Bessel found in his star. And
+yet this star is among the few nearest to our system. The nearest
+star of all, Alpha Centauri, visible only in latitudes south of
+our middle ones, is perhaps half as far as Bessel's star, while
+Sirius and one or two others are nearly at the same distance.
+About 100 stars, all told, have had their parallax measured with a
+greater or less degree of probability. The work is going on from
+year to year, each successive astronomer who takes it up being
+able, as a general rule, to avail himself of better instruments or
+to use a better method. But, after all, the distances of even some
+of the 100 stars carefully measured must still remain quite
+doubtful.
+
+Let us now return to the idea of dividing the space in which the
+universe is situated into concentric spheres drawn at various
+distances around our system as a centre. Here we shall take as our
+standard a distance 400,000 times that of the sun from the earth.
+Regarding this as a unit, we imagine ourselves to measure out in
+any direction a distance twice as great as this--then another
+equal distance, making one three times as great, and so
+indefinitely. We then have successive spheres of which we take the
+nearer one as the unit. The total space filled by the second
+sphere will be 8 times the unit; that of the third space 27 times,
+and so on, as the cube of each distance. Since each sphere
+includes all those within it, the volume of space between each two
+spheres will be proportional to the difference of these numbers--
+that is, to 1, 7, 19, etc. Comparing these volumes with the number
+of stars probably within them, the general result up to the
+present time is that the number of stars in any of these spheres
+will be about equal to the units of volume which they comprise,
+when we take for this unit the smallest and innermost of the
+spheres, having a radius 400,000 times the sun's distance. We are
+thus enabled to form some general idea of how thickly the stars
+are sown through space. We cannot claim any numerical exactness
+for this idea, but in the absence of better methods it does afford
+us some basis for reasoning.
+
+Now we can carry on our computation as we supposed the farmer to
+measure the extent of his wheat-field. Let us suppose that there
+are 125,000,000 stars in the heavens. This is an exceedingly rough
+estimate, but let us make the supposition for the time being.
+Accepting the view that they are nearly equally scattered
+throughout space, it will follow that they must be contained
+within a volume equal to 125,000,000 times the sphere we have
+taken as our unit. We find the distance of the surface of this
+sphere by extracting the cube root of this number, which gives us
+500. We may, therefore, say, as the result of a very rough
+estimate, that the number of stars we have supposed would be
+contained within a distance found by multiplying 400,000 times the
+distance of the sun by 500; that is, that they are contained
+within a region whose boundary is 200,000,000 times the distance
+of the sun. This is a distance through which light would travel in
+about 3300 years.
+
+It is not impossible that the number of stars is much greater than
+that we have supposed. Let us grant that there are eight times as
+many, or 1,000,000,000. Then we should have to extend the boundary
+of our universe twice as far, carrying it to a distance which
+light would require 6600 years to travel.
+
+There is another method of estimating the thickness with which
+stars are sown through space, and hence the extent of the
+universe, the result of which will be of interest. It is based on
+the proper motion of the stars. One of the greatest triumphs of
+astronomy of our time has been the measurement of the actual speed
+at which many of the stars are moving to or from us in space.
+These measures are made with the spectroscope. Unfortunately, they
+can be best made only on the brighter stars--becoming very
+difficult in the case of stars not plainly visible to the naked
+eye. Still the motions of several hundreds have been measured and
+the number is constantly increasing.
+
+A general result of all these measures and of other estimates may
+be summed up by saying that there is a certain average speed with
+which the individual stars move in space; and that this average is
+about twenty miles per second. We are also able to form an
+estimate as to what proportion of the stars move with each rate of
+speed from the lowest up to a limit which is probably as high as
+150 miles per second. Knowing these proportions we have, by
+observation of the proper motions of the stars, another method of
+estimating how thickly they are scattered in space; in other
+words, what is the volume of space which, on the average, contains
+a single star. This method gives a thickness of the stars greater
+by about twenty-five per cent, than that derived from the measures
+of parallax. That is to say, a sphere like the second we have
+proposed, having a radius 800,000 times the distance of the sun,
+and therefore a diameter 1,600,000 times this distance, would,
+judging by the proper motions, have ten or twelve stars contained
+within it, while the measures of parallax only show eight stars
+within the sphere of this diameter having the sun as its centre.
+The probabilities are in favor of the result giving the greater
+thickness of the stars. But, after all, the discrepancy does not
+change the general conclusion as to the limits of the visible
+universe. If we cannot estimate its extent with the same certainty
+that we can determine the size of the earth, we can still form a
+general idea of it.
+
+The estimates we have made are based on the supposition that the
+stars are equally scattered in space. We have good reason to
+believe that this is true of all the stars except those of the
+Milky Way. But, after all, the latter probably includes half the
+whole number of stars visible with a telescope, and the question
+may arise whether our results are seriously wrong from this cause.
+This question can best be solved by yet another method of
+estimating the average distance of certain classes of stars.
+
+The parallaxes of which we have heretofore spoken consist in the
+change in the direction of a star produced by the swing of the
+earth from one side of its orbit to the other. But we have already
+remarked that our solar system, with the earth as one of its
+bodies, has been journeying straightforward through space during
+all historic times. It follows, therefore, that we are continually
+changing the position from which we view the stars, and that, if
+the latter were at rest, we could, by measuring the apparent speed
+with which they are moving in the opposite direction from that of
+the earth, determine their distance. But since every star has its
+own motion, it is impossible, in any one case, to determine how
+much of the apparent motion is due to the star itself, and how
+much to the motion of the solar system through space. Yet, by
+taking general averages among groups of stars, most of which are
+probably near each other, it is possible to estimate the average
+distance by this method. When an attempt is made to apply it, so
+as to obtain a definite result, the astronomer finds that the data
+now available for the purpose are very deficient. The proper
+motion of a star can be determined only by comparing its observed
+position in the heavens at two widely separate epochs.
+Observations of sufficient precision for this purpose were
+commenced about 1750 at the Greenwich Observatory, by Bradley,
+then Astronomer Royal of England. But out of 3000 stars which he
+determined, only a few are available for the purpose. Even since
+his time, the determinations made by each generation of
+astronomers have not been sufficiently complete and systematic to
+furnish the material for anything like a precise determination of
+the proper motions of stars. To determine a single position of any
+one star involves a good deal of computation, and if we reflect
+that, in order to attack the problem in question in a satisfactory
+way, we should have observations of 1,000,000 of these bodies made
+at intervals of at least a considerable fraction of a century, we
+see what an enormous task the astronomers dealing with this
+problem have before them, and how imperfect must be any
+determination of the distance of the stars based on our motion
+through space. So far as an estimate can be made, it seems to
+agree fairly well with the results obtained by the other methods.
+Speaking roughly, we have reason, from the data so far available,
+to believe that the stars of the Milky Way are situated at a
+distance between 100,000,000 and 200,000,000 times the distance of
+the sun. At distances less than this it seems likely that the
+stars are distributed through space with some approach to
+uniformity. We may state as a general conclusion, indicated by
+several methods of making the estimate, that nearly all the stars
+which we can see with our telescopes are contained within a sphere
+not likely to be much more than 200,000,000 times the distance of
+the sun.
+
+The inquiring reader may here ask another question. Granting that
+all the stars we can see are contained within this limit, may
+there not be any number of stars outside the limit which are
+invisible only because they are too far away to be seen?
+
+This question may be answered quite definitely if we grant that
+light from the most distant stars meets with no obstruction in
+reaching us. The most conclusive answer is afforded by the measure
+of starlight. If the stars extended out indefinitely, then the
+number of those of each order of magnitude would be nearly four
+times that of the magnitude next brighter. For example, we should
+have nearly four times as many stars of the sixth magnitude as of
+the fifth; nearly four times as many of the seventh as of the
+sixth, and so on indefinitely. Now, it is actually found that
+while this ratio of increase is true for the brighter stars, it is
+not so for the fainter ones, and that the increase in the number
+of the latter rapidly falls off when we make counts of the fainter
+telescopic stars. In fact, it has long been known that, were the
+universe infinite in extent, and the stars equally scattered
+through all space, the whole heavens would blaze with the light of
+countless millions of distant stars separately invisible even with
+the telescope.
+
+The only way in which this conclusion can be invalidated is by the
+possibility that the light of the stars is in some way
+extinguished or obstructed in its passage through space. A theory
+to this effect was propounded by Struve nearly a century ago, but
+it has since been found that the facts as he set them forth do not
+justify the conclusion, which was, in fact, rather hypothetical.
+The theories of modern science converge towards the view that, in
+the pure ether of space, no single ray of light can ever be lost,
+no matter how far it may travel. But there is another possible
+cause for the extinction of light. During the last few years
+discoveries of dark and therefore invisible stars have been made
+by means of the spectroscope with a success which would have been
+quite incredible a very few years ago, and which, even to-day,
+must excite wonder and admiration. The general conclusion is that,
+besides the shining stars which exist in space, there may be any
+number of dark ones, forever invisible in our telescopes. May it
+not be that these bodies are so numerous as to cut off the light
+which we would otherwise receive from the more distant bodies of
+the universe? It is, of course, impossible to answer this question
+in a positive way, but the probable conclusion is a negative one.
+We may say with certainty that dark stars are not so numerous as
+to cut off any important part of the light from the stars of the
+Milky Way, because, if they did, the latter would not be so
+clearly seen as it is. Since we have reason to believe that the
+Milky Way comprises the more distant stars of our system, we may
+feel fairly confident that not much light can be cut off by dark
+bodies from the most distant region to which our telescopes can
+penetrate. Up to this distance we see the stars just as they are.
+Even within the limit of the universe as we understand it, it is
+likely that more than one-half the stars which actually exist are
+too faint to be seen by human vision, even when armed with the
+most powerful telescopes. But their invisibility is due only to
+their distance and the faintness of their intrinsic light, and not
+to any obstructing agency.
+
+The possibility of dark stars, therefore, does not invalidate the
+general conclusions at which our survey of the subject points. The
+universe, so far as we can see it, is a bounded whole. It is
+surrounded by an immense girdle of stars, which, to our vision,
+appears as the Milky Way. While we cannot set exact limits to its
+distance, we may yet confidently say that it is bounded. It has
+uniformities running through its vast extent. Could we fly out to
+distances equal to that of the Milky Way, we should find
+comparatively few stars beyond the limits of that girdle. It is
+true that we cannot set any definite limit and say that beyond
+this nothing exists. What we can say is that the region containing
+the visible stars has some approximation to a boundary. We may
+fairly anticipate that each successive generation of astronomers,
+through coming centuries, will obtain a little more light on the
+subject--will be enabled to make more definite the boundaries of
+our system of stars, and to draw more and more probable
+conclusions as to the existence or non-existence of any object
+outside of it. The wise investigator of to-day will leave to them
+the task of putting the problem into a more positive shape.
+
+
+
+
+
+V
+
+MAKING AND USING A TELESCOPE
+
+
+The impression is quite common that satisfactory views of the
+heavenly bodies can be obtained only with very large telescopes,
+and that the owner of a small one must stand at a great
+disadvantage alongside of the fortunate possessor of a great one.
+This is not true to the extent commonly supposed. Sir William
+Herschel would have been delighted to view the moon through what
+we should now consider a very modest instrument; and there are
+some objects, especially the moon, which commonly present a more
+pleasing aspect through a small telescope than through a large
+one. The numerous owners of small telescopes throughout the
+country might find their instruments much more interesting than
+they do if they only knew what objects were best suited to
+examination with the means at their command. There are many
+others, not possessors of telescopes, who would like to know how
+one can be acquired, and to whom hints in this direction will be
+valuable. We shall therefore give such information as we are able
+respecting the construction of a telescope, and the more
+interesting celestial objects to which it may be applied.
+
+Whether the reader does or does not feel competent to undertake
+the making of a telescope, it may be of interest to him to know
+how it is done. First, as to the general principles involved, it
+is generally known that the really vital parts of the telescope,
+which by their combined action perform the office of magnifying
+the object looked at, are two in number, the OBJECTIVE and the
+EYE-PIECE. The former brings the rays of light which emanate from
+the object to the focus where the image of the object is formed.
+The eye-piece enables the observer to see this image to the best
+advantage.
+
+The functions of the objective as well as those of the eye-piece
+may, to a certain extent, each be performed by a single lens.
+Galileo and his contemporaries made their telescopes in this way,
+because they knew of no way in which two lenses could be made to
+do better than one. But every one who has studied optics knows
+that white light passing through a single lens is not all brought
+to the same focus, but that the blue light will come to a focus
+nearer the objective than the red light. There will, in fact, be a
+succession of images, blue, green, yellow, and red, corresponding
+to the colors of the spectrum. It is impossible to see these
+different images clearly at the same time, because each of them
+will render all the others indistinct.
+
+The achromatic object-glass, invented by Dollond, about 1750,
+obviates this difficulty, and brings all the rays to nearly the
+same focus. Nearly every one interested in the subject is aware
+that this object-glass is composed of two lenses--a concave one of
+flint-glass and a convex one of crown-glass, the latter being on
+the side towards the object. This is the one vital part of the
+telescope, the construction of which involves the greatest
+difficulty. Once in possession of a perfect object-glass, the rest
+of the telescope is a matter of little more than constructive
+skill which there is no difficulty in commanding.
+
+The construction of the object-glass requires two completely
+distinct processes: the making of the rough glass, which is the
+work of the glass-maker; and the grinding and polishing into
+shape, which is the work of the optician. The ordinary glass of
+commerce will not answer the purpose of the telescope at all,
+because it is not sufficiently clear and homogeneous. OPTICAL
+GLASS, as it is called, must be made of materials selected and
+purified with the greatest care, and worked in a more elaborate
+manner than is necessary in any other kind of glass. In the time
+of Dollond it was found scarcely possible to make good disks of
+flint-glass more than three or four inches in diameter. Early in
+the present century, Guinand, of Switzerland, invented a process
+by which disks of much larger size could be produced. In
+conjunction with the celebrated Fraunhofer he made disks of nine
+or ten inches in diameter, which were employed by his colaborer in
+constructing the telescopes which were so famous in their time. He
+was long supposed to be in possession of some secret method of
+avoiding the difficulties which his predecessors had met. It is
+now believed that this secret, if one it was, consisted
+principally in the constant stirring of the molten glass during
+the process of manufacture. However this may be, it is a curious
+historical fact that the most successful makers of these great
+disks of glass have either been of the family of Guinand, or
+successors, in the management of the family firm. It was Feil, a
+son-in-law or near relative, who made the glass from which Clark
+fabricated the lenses of the great telescope of the Lick
+Observatory. His successor, Mantois, of Paris, carried the art to
+a point of perfection never before approached. The transparency
+and uniformity of his disks as well as the great size to which he
+was able to carry them would suggest that he and his successors
+have out-distanced all competitors in the process. He it was who
+made the great 40-inch lens for the Yerkes Observatory.
+
+As optical glass is now made, the material is constantly stirred
+with an iron rod during all the time it is melting in the furnace,
+and after it has begun to cool, until it becomes so stiff that the
+stirring has to cease. It is then placed, pot and all, in the
+annealing furnace, where it is kept nearly at a melting heat for
+three weeks or more, according to the size of the pot. When the
+furnace has cooled off, the glass is taken out, and the pot is
+broken from around it, leaving only the central mass of glass.
+Having such a mass, there is no trouble in breaking it up into
+pieces of all desirable purity, and sufficiently large for
+moderate-sized telescopes. But when a great telescope of two feet
+aperture or upward is to be constructed, very delicate and
+laborious operations have to be undertaken. The outside of the
+glass has first to be chipped off, because it is filled with
+impurities from the material of the pot itself. But this is not
+all. Veins of unequal density are always found extending through
+the interior of the mass, no way of avoiding them having yet been
+discovered. They are supposed to arise from the materials of the
+pot and stirring rod, which become mixed in with the glass in
+consequence of the intense heat to which all are subjected. These
+veins must, so far as possible, be ground or chipped out with the
+greatest care. The glass is then melted again, pressed into a flat
+disk, and once more put into the annealing oven. In fact, the
+operation of annealing must be repeated every time the glass is
+melted. When cooled, it is again examined for veins, of which
+great numbers are sure to be found. The problem now is to remove
+these by cutting and grinding without either breaking the glass in
+two or cutting a hole through it. If the parts of the glass are
+once separated, they can never be joined without producing a bad
+scar at the point of junction. So long, however, as the surface is
+unbroken, the interior parts of the glass can be changed in form
+to any extent. Having ground out the veins as far as possible, the
+glass is to be again melted, and moulded into proper shape. In
+this mould great care must be taken to have no folding of the
+surface. Imagining the latter to be a sort of skin enclosing the
+melted glass inside, it must be raised up wherever the glass is
+thinnest, and the latter allowed to slowly run together beneath
+it.
+
+[Illustration with caption: THE GLASS DISK.]
+
+If the disk is of flint, all the veins must be ground out on the
+first or second trial, because after two or three mouldings the
+glass will lose its transparency. A crown disk may, however, be
+melted a number of times without serious injury. In many cases--
+perhaps the majority--the artisan finds that after all his months
+of labor he cannot perfectly clear his glass of the noxious veins,
+and he has to break it up into smaller pieces. When he finally
+succeeds, the disk has the form of a thin grindstone two feet or
+upward in diameter, according to the size of the telescope to be
+made, and from two to three inches in thickness. The glass is then
+ready for the optician.
+
+[Illustration with caption: THE OPTICIAN'S TOOL.]
+
+The first process to be performed by the optician is to grind the
+glass into the shape of a lens with perfectly spherical surfaces.
+The convex surface must be ground in a saucer-shaped tool of
+corresponding form. It is impossible to make a tool perfectly
+spherical in the first place, but success may be secured on the
+geometrical principle that two surfaces cannot fit each other in
+all positions unless both are perfectly spherical. The tool of the
+optician is a very simple affair, being nothing more than a plate
+of iron somewhat larger, perhaps a fourth, than the lens to be
+ground to the corresponding curvature. In order to insure its
+changing to fit the glass, it is covered on the interior with a
+coating of pitch from an eighth to a quarter of an inch thick.
+This material is admirably adapted to the purpose because it gives
+way certainly, though very slowly, to the pressure of the glass.
+In order that it may have room to change its form, grooves are cut
+through it in both directions, so as to leave it in the form of
+squares, like those on a chess-board.
+
+[Illustration with caption: THE OPTICIAN'S TOOL.]
+
+It is then sprinkled over with rouge, moistened with water, and
+gently warmed. The roughly ground lens is then placed upon it, and
+moved from side to side. The direction of the motion is slightly
+changed with every stroke, so that after a dozen or so of strokes
+the lines of motion will lie in every direction on the tool. This
+change of direction is most readily and easily effected by the
+operator slowly walking around as he polishes, at the same time
+the lens is to be slowly turned around either in the opposite
+direction or more rapidly yet in the same direction, so that the
+strokes of the polisher shall cross the lens in all directions.
+This double motion insures every part of the lens coming into
+contact with every part of the polisher, and moving over it in
+every direction.
+
+Then whatever parts either of the lens or of the polisher may be
+too high to form a spherical surface will be gradually worn down,
+thus securing the perfect sphericity of both.
+
+[Illustration with caption: GRINDING A LARGE LENS.]
+
+When the polishing is done by machinery, which is the custom in
+Europe, with large lenses, the polisher is slid back and forth
+over the lens by means of a crank attached to a revolving wheel.
+The polisher is at the same time slowly revolving around a pivot
+at its centre, which pivot the crank works into, and the glass
+below it is slowly turned in an opposite direction. Thus the same
+effect is produced as in the other system. Those who practice this
+method claim that by thus using machinery the conditions of a
+uniform polish for every part of the surface can be more perfectly
+fulfilled than by a hand motion. The results, however, do not
+support this view. No European optician will claim to do better
+than the American firm of Alvan Clark & Sons in producing
+uniformly good object-glasses, and this firm always does the work
+by hand, moving the glass over the polisher, and not the polisher
+over the glass.
+
+Having brought both flint and crown glasses into proper figure by
+this process, they are joined together, and tested by observations
+either upon a star in the heavens, or some illuminated point at a
+little distance on the ground. The reflection of the sun from a
+drop of quicksilver, a thermometer bulb, or even a piece of broken
+bottle, makes an excellent artificial star. The very best optician
+will always find that on a first trial his glass is not perfect.
+He will find that he has not given exactly the proper curves to
+secure achromatism. He must then change the figure of one or both
+the glasses by polishing it upon a tool of slightly different
+curvature. He may also find that there is some spherical
+aberration outstanding. He must then alter his curve so as to
+correct this. The correction of these little imperfections in the
+figures of the lenses so as to secure perfect vision through them
+is the most difficult branch of the art of the optician, and upon
+his skill in practising it will depend more than upon anything
+else his ultimate success and reputation. The shaping of a pair of
+lenses in the way we have described is not beyond the power of any
+person of ordinary mechanical ingenuity, possessing the necessary
+delicacy of touch and appreciation of the problem he is attacking.
+But to make a perfect objective of considerable size, which shall
+satisfy all the wants of the astronomer, is an undertaking
+requiring such accuracy of eyesight, and judgment in determining
+where the error lies, and such skill in manipulating so as to
+remove the defects, that the successful men in any one generation
+can be counted on one's fingers.
+
+In order that the telescope may finally perform satisfactorily it
+is not sufficient that the lenses should both be of proper figure;
+they must also both be properly centred in their cells. If either
+lens is tipped aside, or slid out from its proper central line,
+the definition will be injured. As this is liable to happen with
+almost any telescope, we shall explain how the proper adjustment
+is to be made.
+
+The easiest way to test this adjustment is to set the cell with
+the two glasses of the objective in it against a wall at night,
+and going to a short distance, observe the reflection in the glass
+of the flame of a candle held in the hand. Three or four
+reflections will be seen from the different surfaces. The
+observer, holding the candle before his eye, and having his line
+of sight as close as possible to the flame, must then move until
+the different images of the flame coincide with each other. If he
+cannot bring them into coincidence, owing to different pairs
+coinciding on different sides of the flame, the glasses are not
+perfectly centred upon each other. When the centring is perfect,
+the observer having the light in the line of the axes of the
+lenses, and (if it were possible to do so) looking through the
+centre of the flame, would see the three or four images all in
+coincidence. As he cannot see through the flame itself, he must
+look first on one side and then on the other, and see if the
+arrangement of the images seen in the lenses is symmetrical. If,
+going to different distances, he finds no deviation from symmetry,
+in this respect the adjustment is near enough for all practical
+purposes.
+
+A more artistic instrument than a simple candle is a small concave
+reflector pierced through its centre, such as is used by
+physicians in examining the throat.
+
+[Illustration with caption: IMAGE OF CANDLE-FLAME IN OBJECT-
+GLASS.]
+
+[Illustration with caption: TESTING ADJUSTMENT OF OBJECT-GLASS.]
+
+Place this reflector in the prolongation of the optical axis, set
+the candle so that the light from the reflector shall be shown
+through the glass, and look through the opening. Images of the
+reflector itself will then be seen in the object-glass, and if the
+adjustment is perfect, the reflector can be moved so that they
+will all come into coincidence together.
+
+When the objective is in the tube of the telescope, it is always
+well to examine this adjustment from time to time, holding the
+candle so that its light shall shine through the opening
+perpendicularly upon the object-glass. The observer looks upon one
+side of the flame, and then upon the other, to see if the images
+are symmetrical in the different positions. If in order to see
+them in this way the candle has to be moved to one side of the
+central line of the tube, the whole objective must be adjusted. If
+two images coincide in one position of the candle-flame, and two
+in another position, so that they cannot all be brought together
+in any position, it shows that the glasses are not properly
+adjusted in their cell. It may be remarked that this last
+adjustment is the proper work of the optician, since it is so
+difficult that the user of the telescope cannot ordinarily effect
+it. But the perpendicularity of the whole objective to the tube of
+the telescope is liable to be deranged in use, and every one who
+uses such an instrument should be able to rectify an error of this
+kind.
+
+The question may be asked, How much of a telescope can an amateur
+observer, under any circumstances, make for himself? As a general
+rule, his work in this direction must be confined to the tube and
+the mounting. We should not, it is true, dare to assert that any
+ingenious young man, with a clear appreciation of optical
+principles, could not soon learn to grind and polish an object-
+glass for himself by the method we have described, and thus obtain
+a much better instrument than Galileo ever had at his command. But
+it would be a wonderful success if his home-made telescope was
+equal to the most indifferent one which can be bought at an
+optician's. The objective, complete in itself, can be purchased at
+prices depending upon the size.
+
+[Footnote: The following is a rough rule for getting an idea of
+the price of an achromatic objective, made to order, of the finest
+quality. Take the cube of the diameter in inches, or, which is the
+same thing, calculate the contents of a cubical box which would
+hold a sphere of the same diameter as the clear aperture of the
+glass. The price of the glass will then range from $1 to $1.75 for
+each cubic inch in this box. For example, the price of a four-inch
+objective will probably range from $64 to $112. Very small object-
+glasses of one or two inches may be a little higher than would be
+given by this rule. Instruments which are not first-class, but
+will answer most of the purposes of the amateur, are much
+cheaper.]
+
+[Illustration with caption: A VERY PRIMITIVE MOUNTING FOR A
+TELESCOPE.]
+
+The tube for the telescope may be made of paper, by pasting a
+great number of thicknesses around a long wooden cylinder. A yet
+better tube is made of a simple wooden box. The best material,
+however, is metal, because wood and pasteboard are liable both to
+get out of shape, and to swell under the influence of moisture.
+Tin, if it be of sufficient thickness, would be a very good
+material. The brighter it is kept, the better. The work of fitting
+the objective into one end of a tin tube of double thickness, and
+properly adjusting it, will probably be quite within the powers of
+the ordinary amateur. The fitting of the eye-piece into the other
+end of the tube will require some skill and care both on his own
+part and that of his tinsmith.
+
+Although the construction of the eye-piece is much easier than
+that of the objective, since the same accuracy in adjusting the
+curves is not necessary, yet the price is lower in a yet greater
+degree, so that the amateur will find it better to buy than to
+make his eye-piece, unless he is anxious to test his mechanical
+powers. For a telescope which has no micrometer, the Huyghenian or
+negative eye-piece, as it is commonly called, is the best. As made
+by Huyghens, it consists of two plano-convex lenses, with their
+plane sides next the eye, as shown in the figure.
+
+[Illustration with caption: THE HUYGHENIAN EYE-PIECE.]
+
+So far as we have yet described our telescope it is optically
+complete. If it could be used as a spy-glass by simply holding it
+in the hand, and pointing at the object we wish to observe, there
+would be little need of any very elaborate support. But if a
+telescope, even of the smallest size, is to be used with
+regularity, a proper "mounting" is as essential as a good
+instrument. Persons unpractised in the use of such instruments are
+very apt to underrate the importance of those accessories which
+merely enable us to point the telescope. An idea of what is wanted
+in the mounting may readily be formed if the reader will try to
+look at a star with an ordinary good-sized spy-glass held in the
+hand, and then imagine the difficulties he meets with multiplied
+by fifty.
+
+The smaller and cheaper telescopes, as commonly sold, are mounted
+on a simple little stand, on which the instrument admits of a
+horizontal and vertical motion. If one only wants to get a few
+glimpses of a celestial object, this mounting will answer his
+purpose. But to make anything like a study of a celestial body,
+the mounting must be an equatorial one; that is, one of the axes
+around which the telescope moves must be inclined so as to point
+towards the pole of the heavens, which is near the polar star.
+This axis will then make an angle with the horizon equal to the
+latitude of the place. The telescope cannot, however, be mounted
+directly on this axis, but must be attached to a second one,
+itself fastened to this one.
+
+[Illustration with caption: SECTION OF THE PRIMITIVE MOUNTING. P
+P. Polar axis, bearing a fork at the upper end A. Declination axis
+passing through the fork E. Section of telescope tube C. Weight to
+balance the tube.]
+
+When mounted in this way, an object can be followed in its diurnal
+motion from east to west by turning on the polar axis alone. But
+if the greatest facility in use is required, this motion must be
+performed by clock-work. A telescope with this appendage will
+commonly cost one thousand dollars and upward, so that it is not
+usually applied to very small ones.
+
+We will now suppose that the reader wishes to purchase a telescope
+or an object-glass for himself, and to be able to judge of its
+performance. He must have the object-glass properly adjusted in
+its tube, and must use the highest power; that is, the smallest
+eye-piece, which he intends to use in the instrument. Of course he
+understands that in looking directly at a star or a celestial
+object it must appear sharp in outline and well defined. But
+without long practice with good instruments, this will not give
+him a very definite idea. If the person who selects the telescope
+is quite unpractised, it is possible that he can make the best
+test by ascertaining at what distance he can read ordinary print.
+To do this he should have an eye-piece magnifying about fifty
+times for each inch of aperture of the telescope. For instance, if
+his telescope is three inches clear aperture, then his eye-piece
+should magnify one hundred and fifty times; if the aperture is
+four inches, one magnifying two hundred times may be used. This
+magnifying power is, as a general rule, about the highest that can
+be advantageously used with any telescope. Supposing this
+magnifying power to be used, this page should be legible at a
+distance of four feet for every unit of magnifying power of the
+telescope. For example, with a power of 100, it should be legible
+at a distance of 400 feet; with a power of 200, at 800 feet, and
+so on. To put the condition into another shape: if the telescope
+will read the print at a distance of 150 feet for each inch of
+aperture with the best magnifying power, its performance is at
+least not very bad. If the magnifying power is less than would be
+given by this rule, the telescope should perform a little better;
+for instance, a three-inch telescope with a power of 60 should
+make this page legible at a distance of 300 feet, or four feet for
+each unit of power.
+
+The test applied by the optician is much more exact, and also more
+easy. He points the instrument at a star, or at the reflection of
+the sun's rays from a small round piece of glass or a globule of
+quicksilver several hundred yards away, and ascertains whether the
+rays are all brought to a focus. This is not done by simply
+looking at the star, but by alternately pushing the eye-piece in
+beyond the point of distinct vision and drawing it out past the
+point. In this way the image of the star will appear, not as a
+point, but as a round disk of light. If the telescope is perfect,
+this disk will appear round and of uniform brightness in either
+position of the eye-piece. But if there is any spherical
+aberration or differences of density in different parts of the
+glass, the image will appear distorted in various ways. If the
+spherical aberration is not correct, the outer rim of the disk
+will be brighter than the centre when the eye-piece is pushed in,
+and the centre will be the brighter when it is drawn out. If the
+curves of the glass are not even all around, the image will appear
+oval in one or the other position. If there are large veins of
+unequal density, wings or notches will be seen on the image. If
+the atmosphere is steady, the image, when the eye-piece is pushed
+in, will be formed of a great number of minute rings of light. If
+the glass is good, these rings will be round, unbroken, and
+equally bright. We present several figures showing how these
+spectral images, as they are sometimes called, will appear; first,
+when the eye-piece is pushed in, and secondly, when it is drawn
+out, with telescopes of different qualities.
+
+We have thus far spoken only of the refracting telescope, because
+it is the kind with which an observer would naturally seek to
+supply himself. At the same time there is little doubt that the
+construction of a reflector of moderate size is easier than that
+of a corresponding refractor. The essential part of the reflector
+is a slightly concave mirror of any metal which will bear a high
+polish. This mirror may be ground and polished in the same way as
+a lens, only the tool must be convex.
+
+[Illustration with caption: SPECTRAL IMAGES OF STARS; THE UPPER
+LINE SHOWING HOW THEY APPEAR WITH THE EYE-PIECE PUSHED IN, THE
+LOWER WITH THE EYE-PIECE DRAWN OUT.
+
+A The telescope is all right
+B Spherical aberration shown by the light and dark centre
+C The objective is not spherical but elliptical
+D The glass not uniform--a very bad and incurable case
+E One side of the objective nearer than the other. Adjust it]
+
+Of late years it has become very common to make the mirror of
+glass and to cover the reflecting face with an exceedingly thin
+film of silver, which can be polished by hand in a few minutes.
+Such a mirror differs from our ordinary looking-glass in that the
+coating of silver is put on the front surface, so that the light
+does not pass through the glass. Moreover, the coating of silver
+is so thin as to be almost transparent: in fact, the sun may be
+seen through it by direct vision as a faint blue object. Silvered
+glass reflectors made in this way are extensively manufactured in
+London, and are far cheaper than refracting telescopes of
+corresponding size. Their great drawback is the want of permanence
+in the silver film. In the city the film will ordinarily tarnish
+in a few months from the sulphurous vapors arising from gaslights
+and other sources, and even in the country it is very difficult to
+preserve the mirror from the contact of everything that will
+injure it. In consequence, the possessor of such a telescope, if
+he wishes to keep it in order, must always be prepared to resilver
+and repolish it. To do this requires such careful manipulation and
+management of the chemicals that it is hardly to be expected that
+an amateur will take the trouble to keep his telescope in order,
+unless he has a taste for chemistry as well as for astronomy.
+
+The curiosity to see the heavenly bodies through great telescopes
+is so wide-spread that we are apt to forget how much can be seen
+and done with small ones. The fact is that a large proportion of
+the astronomical observations of past times have been made with
+what we should now regard as very small instruments, and a good
+deal of the solid astronomical work of the present time is done
+with meridian circles the apertures of which ordinarily range from
+four to eight inches. One of the most conspicuous examples in
+recent times of how a moderate-sized instrument may be utilized is
+afforded by the discoveries of double stars made by Mr. S. W.
+Burnham, of Chicago. Provided with a little six-inch telescope,
+procured at his own expense from the Messrs. Clark, he has
+discovered many hundred double stars so difficult that they had
+escaped the scrutiny of Maedler and the Struves, and gained for
+himself one of the highest positions among the astronomers of the
+day engaged in the observation of these objects. It was with this
+little instrument that on Mount Hamilton, California--afterward
+the site of the great Lick Observatory--he discovered forty-eight
+new double stars, which had remained unnoticed by all previous
+observers. First among the objects which show beautifully through
+moderate instruments stands the moon. People who want to see the
+moon at an observatory generally make the mistake of looking when
+the moon is full, and asking to see it through the largest
+telescope. Nothing can then be made out but a brilliant blaze of
+light, mottled with dark spots, and crossed by irregular bright
+lines. The best time to view the moon is near or before the first
+quarter, or when she is from three to eight days old. The last
+quarter is of course equally favorable, so far as seeing is
+concerned, only one must be up after midnight to see her in that
+position. Seen through a three or four inch telescope, a day or
+two before the first quarter, about half an hour after sunset, and
+with a magnifying power between fifty and one hundred, the moon is
+one of the most beautiful objects in the heavens. Twilight softens
+her radiance so that the eye is not dazzled as it will be when the
+sky is entirely dark. The general aspect she then presents is that
+of a hemisphere of beautiful chased silver carved out in curious
+round patterns with a more than human skill. If, however, one
+wishes to see the minute details of the lunar surface, in which
+many of our astronomers are now so deeply interested, he must use
+a higher magnifying power. The general beautiful effect is then
+lessened, but more details are seen. Still, it is hardly necessary
+to seek for a very large telescope for any investigation of the
+lunar surface. I very much doubt whether any one has ever seen
+anything on the moon which could not be made out in a clear,
+steady atmosphere with a six-inch telescope of the first class.
+
+Next to the moon, Saturn is among the most beautiful of celestial
+objects. Its aspect, however, varies with its position in its
+orbit. Twice in the course of a revolution, which occupies nearly
+thirty years, the rings are seen edgewise, and for a few days are
+invisible even in a powerful telescope. For an entire year their
+form may be difficult to make out with a small telescope. These
+unfavorable conditions occur in 1907 and 1921. Between these
+dates, especially for some years after 1910, the position of the
+planet in the sky will be the most favorable, being in northern
+declination, near its perihelion, and having its rings widely
+open. We all know that Saturn is plainly visible to the naked eye,
+shining almost like a star of the first magnitude, so that there
+is no difficulty in finding it if one knows when and where to
+look. In 1906-1908 its oppositions occur in the month of
+September. In subsequent years, it will occur a month later every
+two and a half years. The ring can be seen with a common, good
+spy-glass fastened to a post so as to be steady. A four or five-
+inch telescope will show most of the satellites, the division in
+the ring, and, when the ring is well opened, the curious dusky
+ring discovered by Bond. This "crape ring," as it is commonly
+called, is one of the most singular phenomena presented by that
+planet.
+
+It might be interesting to the amateur astronomer with a keen eye
+and a telescope of four inches aperture or upward to frequently
+scrutinize Saturn, with a view of detecting any extraordinary
+eruptions upon his surface, like that seen by Professor Hall in
+1876. On December 7th of that year a bright spot was seen upon
+Saturn's equator. It elongated itself from day to day, and
+remained visible for several weeks. Such a thing had never before
+been known upon this planet, and had it not been that Professor
+Hall was engaged in observations upon the satellites, it would not
+have been seen then. A similar spot on the planet was recorded in
+1902, and much more extensively noticed. On this occasion the spot
+appeared in a higher latitude from the planet's equator than did
+Professor Hall's. At this appearance the time of the planet's
+revolution on its axis was found to be somewhat greater than in
+1876, in accordance with the general law exhibited in the
+rotations of the sun and of Jupiter. Notwithstanding their
+transient character, these two spots have afforded the only
+determination of the time of revolution of Saturn which has been
+made since Herschel the elder.
+
+[Illustration with caption: THE GREAT REFRACTOR OF THE NATIONAL
+OBSERVATORY AT WASHINGTON]
+
+Of the satellites of Saturn the brightest is Titan, which can be
+seen with the smallest telescope, and revolves around the planet
+in fifteen days. Iapetus, the outer satellite, is remarkable for
+varying greatly in brilliancy during its revolution around the
+planet. Any one having the means and ability to make accurate
+photometrical estimates of the light of this satellite in all
+points of its orbit, can thereby render a valuable service to
+astronomy.
+
+The observations of Venus, by which the astronomers of the last
+century supposed themselves to have discovered its time of
+rotation on its axis, were made with telescopes much inferior to
+ours. Although their observations have not been confirmed, some
+astronomers are still inclined to think that their results have
+not been refuted by the failure of recent observers to detect
+those changes which the older ones describe on the surface of the
+planet. With a six-inch telescope of the best quality, and with
+time to choose the most favorable moment, one will be as well
+equipped to settle the question of the rotation of Venus as the
+best observer. The few days near each inferior conjunction are
+especially to be taken advantage of.
+
+The questions to be settled are two: first, are there any dark
+spots or other markings on the disk? second, are there any
+irregularities in the form of the sharp cusps? The central
+portions of the disk are much darker than the outline, and it is
+probably this fact which has given rise to the impression of dark
+spots. Unless this apparent darkness changes from time to time, or
+shows some irregularity in its outline, it cannot indicate any
+rotation of the planet. The best time to scrutinize the sharp
+cusps will be when the planet is nearly on the line from the earth
+to the sun. The best hour of the day is near sunset, the half-hour
+following sunset being the best of all. But if Venus is near the
+sun, she will after sunset be too low down to be well seen, and
+must be looked at late in the afternoon.
+
+The planet Mars must always be an object of great interest,
+because of all the heavenly bodies it is that which appears to
+bear the greatest resemblance to the earth. It comes into
+opposition at intervals of a little more than two years, and can
+be well seen only for a month or two before and after each
+opposition. It is hopeless to look for the satellites of Mars with
+any but the greatest telescopes of the world. But the markings on
+the surface, from which the time of rotation has been determined,
+and which indicate a resemblance to the surface of our own planet,
+can be well seen with telescopes of six inches aperture and
+upward. One or both of the bright polar spots, which are supposed
+to be due to deposits of snow, can be seen with smaller telescopes
+when the situation of the planet is favorable.
+
+The case is different with the so-called canals discovered by
+Schiaparelli in 1877, which have ever since excited so much
+interest, and given rise to so much discussion as to their nature.
+The astronomer who has had the best opportunities for studying
+them is Mr. Percival Lowell, whose observatory at Flaggstaff,
+Arizona, is finely situated for the purpose, while he also has one
+of the best if not the largest of telescopes. There the canals are
+seen as fine dark lines; but, even then, they must be fifty miles
+in breadth, so that the word "canal" may be regarded as a
+misnomer.
+
+Although the planet Jupiter does not present such striking
+features as Saturn, it is of even more interest to the amateur
+astronomer, because he can study it with less optical power, and
+see more of the changes upon its surface. Every work on astronomy
+tells in a general way of the belts of Jupiter, and many speculate
+upon their causes. The reader of recent works knows that Jupiter
+is supposed to be not a solid mass like the earth, but a great
+globe of molten and vaporous matter, intermediate in constitution
+between the earth and the sun. The outer surface which we see is
+probably a hot mass of vapor hundreds of miles deep, thrown up
+from the heated interior. The belts are probably cloudlike forms
+in this vaporous mass. Certain it is that they are continually
+changing, so that the planet seldom looks exactly the same on two
+successive evenings. The rotation of the planet can be very well
+seen by an hour's watching. In two hours an object at the centre
+of the disk will move off to near the margin.
+
+The satellites of this planet, in their ever-varying phases, are
+objects of perennial interest. Their eclipses may be observed with
+a very small telescope, if one knows when to look for them. To do
+this successfully, and without waste of time, it is necessary to
+have an astronomical ephemeris for the year. All the observable
+phenomena are there predicted for the convenience of observers.
+Perhaps the most curious observation to be made is that of the
+shadow of the satellite crossing the disk of Jupiter. The writer
+has seen this perfectly with a six-inch telescope, and a much
+smaller one would probably show it well. With a telescope of this
+size, or a little larger, the satellites can be seen between us
+and Jupiter. Sometimes they appear a little brighter than the
+planet, and sometimes a little fainter.
+
+Of the remaining large planets, Mercury, the inner one, and Uranus
+and Neptune, the two outer ones, are of less interest than the
+others to an amateur with a small telescope, because they are more
+difficult to see. Mercury can, indeed, be observed with the
+smallest instrument, but no physical configurations or changes
+have ever been made out upon his surface. The question whether any
+such can be observed is still an open one, which can be settled
+only by long and careful scrutiny. A small telescope is almost as
+good for this purpose as a large one, because the atmospheric
+difficulties in the way of getting a good view of the planet
+cannot be lessened by an increase of telescopic power.
+
+Uranus and Neptune are so distant that telescopes of considerable
+size and high magnifying power are necessary to show their disks.
+In small telescopes they have the appearance of stars, and the
+observer has no way of distinguishing them from the surrounding
+stars unless he can command the best astronomical appliances, such
+as star maps, circles on his instrument, etc. It is, however, to
+be remarked, as a fact not generally known, that Uranus can be
+well seen with the naked eye if one knows where to look for it. To
+recognize it, it is necessary to have an astronomical ephemeris
+showing its right ascension and declination, and star maps showing
+where the parallels of right ascension and declination lie among
+the stars. When once found by the naked eye, there will, of
+course, be no difficulty in pointing the telescope upon it.
+
+Of celestial objects which it is well to keep a watch upon, and
+which can be seen to good advantage with inexpensive instruments,
+the sun may be considered as holding the first place. Astronomers
+who make a specialty of solar physics have, especially in this
+country, so many other duties, and their view is so often
+interrupted by clouds, that a continuous record of the spots on
+the sun and the changes they undergo is hardly possible. Perhaps
+one of the most interesting and useful pieces of astronomical work
+which an amateur can perform will consist of a record of the
+origin and changes of form of the solar spots and faculae. What
+does a spot look like when it first comes into sight? Does it
+immediately burst forth with considerable magnitude, or does it
+begin as the smallest visible speck, and gradually grow? When
+several spots coalesce into one, how do they do it? When a spot
+breaks up into several pieces, what is the seeming nature of the
+process? How do the groups of brilliant points called faculae
+come, change, and grow? All these questions must no doubt be
+answered in various ways, according to the behavior of the
+particular spot, but the record is rather meagre, and the
+conscientious and industrious amateur will be able to amuse
+himself by adding to it, and possibly may make valuable
+contributions to science in the same way.
+
+Still another branch of astronomical observation, in which
+industry and skill count for more than expensive instruments, is
+the search for new comets. This requires a very practised eye, in
+order that the comet may be caught among the crowd of stars which
+flit across the field of view as the telescope is moved. It is
+also necessary to be well acquainted with a number of nebulae
+which look very much like comets. The search can be made with
+almost any small telescope, if one is careful to use a very low
+power. With a four-inch telescope a power not exceeding twenty
+should be employed. To search with ease, and in the best manner,
+the observer should have what among astronomers is familiarly
+known as a "broken-backed telescope." This instrument has the eye-
+piece on the end of the axis, where one would never think of
+looking for it. By turning the instrument on this axis, it sweeps
+from one horizon through the zenith and over to the other horizon
+without the observer having to move his head. This is effected by
+having a reflector in the central part of the instrument, which
+throws the rays of light at right angles through the axis.
+
+[Illustration: THE "BROKEN-BACKED COMET-SEEKER"]
+
+How well this search can be conducted by observers with limited
+means at their disposal is shown by the success of several
+American observers, among whom Messrs. W. R. Brooks, E. E.
+Barnard, and Lewis Swift are well known. The cometary discoveries
+of these men afford an excellent illustration of how much can be
+done with the smallest means when one sets to work in the right
+spirit.
+
+The larger number of wonderful telescopic objects are to be sought
+for far beyond the confines of the solar system, in regions from
+which light requires years to reach us. On account of their great
+distance, these objects generally require the most powerful
+telescopes to be seen in the best manner; but there are quite a
+number within the range of the amateur. Looking at the Milky Way,
+especially its southern part, on a clear winter or summer evening,
+tufts of light will be seen here and there. On examining these
+tufts with a telescope, they will be found to consist of congeries
+of stars. Many of these groups are of the greatest beauty, with
+only a moderate optical power. Of all the groups in the Milky Way
+the best known is that in the sword-handle of Perseus, which may
+be seen during the greater part of the year, and is distinctly
+visible to the naked eye as a patch of diffused light. With the
+telescope there are seen in this patch two closely connected
+clusters of stars, or perhaps we ought rather to say two centres
+of condensation.
+
+Another object of the same class is Proesepe in the constellation
+Cancer. This can be very distinctly seen by the naked eye on a
+clear moonless night in winter or spring as a faint nebulous
+object, surrounded by three small stars. The smallest telescope
+shows it as a group of stars.
+
+Of all stellar objects, the great nebula of Orion is that which
+has most fascinated the astronomers of two centuries. It is
+distinctly visible to the naked eye, and may be found without
+difficulty on any winter night. The three bright stars forming the
+sword-belt of Orion are known to every one who has noticed that
+constellation. Below this belt is seen another triplet of stars,
+not so bright, and lying in a north and south direction. The
+middle star of this triplet is the great nebula. At first the
+naked eye sees nothing to distinguish it from other stars, but if
+closely scanned it will be seen to have a hazy aspect. A four-inch
+telescope will show its curious form. Not the least interesting of
+its features are the four stars known as the "Trapezium," which
+are located in a dark region near its centre. In fact, the whole
+nebula is dotted with stars, which add greatly to the effect
+produced by its mysterious aspect.
+
+The great nebula of Andromeda is second only to that of Orion in
+interest. Like the former, it is distinctly visible to the naked
+eye, having the aspect of a faint comet. The most curious feature
+of this object is that although the most powerful telescopes do
+not resolve it into stars, it appears in the spectroscope as if it
+were solid matter shining by its own light.
+
+The above are merely selections from the countless number of
+objects which the heavens offer to telescopic study. Many such are
+described in astronomical works, but the amateur can gratify his
+curiosity to almost any extent by searching them out for himself.
+
+[Illustration with caption: NEBULA IN ORION]
+
+Ever since 1878 a red spot, unlike any before noticed, has
+generally been visible on Jupiter. At first it was for several
+years a very conspicuous object, but gradually faded away, so that
+since 1890 it has been made out only with difficulty. But it is
+now regarded as a permanent feature of the planet. There is some
+reason to believe it was occasionally seen long before attention
+was first attracted to it. Doubtless, when it can be seen at all,
+practice in observing such objects is more important than size of
+telescope.
+
+
+
+
+
+VI
+
+WHAT THE ASTRONOMERS ARE DOING
+
+
+In no field of science has human knowledge been more extended in
+our time than in that of astronomy. Forty years ago astronomical
+research seemed quite barren of results of great interest or value
+to our race. The observers of the world were working on a
+traditional system, grinding out results in an endless course,
+without seeing any prospect of the great generalizations to which
+they might ultimately lead. Now this is all changed. A new
+instrument, the spectroscope, has been developed, the extent of
+whose revelations we are just beginning to learn, although it has
+been more than thirty years in use. The application of photography
+has been so extended that, in some important branches of
+astronomical work, the observer simply photographs the phenomenon
+which he is to study, and then makes his observation on the
+developed negative.
+
+The world of astronomy is one of the busiest that can be found to-
+day, and the writer proposes, with the reader's courteous consent,
+to take him on a stroll through it and see what is going on. We
+may begin our inspection with a body which is, for us, next to the
+earth, the most important in the universe. I mean the sun. At the
+Greenwich Observatory the sun has for more than twenty years been
+regularly photographed on every clear day, with the view of
+determining the changes going on in its spots. In recent years
+these observations have been supplemented by others, made at
+stations in India and Mauritius, so that by the combination of all
+it is quite exceptional to have an entire day pass without at
+least one photograph being taken. On these observations must
+mainly rest our knowledge of the curious cycle of change in the
+solar spots, which goes through a period of about eleven years,
+but of which no one has as yet been able to establish the cause.
+
+This Greenwich system has been extended and improved by an
+American. Professor George E. Hale, formerly Director of the
+Yerkes Observatory, has devised an instrument for taking
+photographs of the sun by a single ray of the spectrum. The light
+emitted by calcium, the base of lime, and one of the substances
+most abundant in the sun, is often selected to impress the plate.
+
+The Carnegie Institution has recently organized an enterprise for
+carrying on the study of the sun under a combination of better
+conditions than were ever before enjoyed. The first requirement in
+such a case is the ablest and most enthusiastic worker in the
+field, ready to devote all his energies to its cultivation. This
+requirement is found in the person of Professor Hale himself. The
+next requirement is an atmosphere of the greatest transparency,
+and a situation at a high elevation above sea-level, so that the
+passage of light from the sun to the observer shall be obstructed
+as little as possible by the mists and vapors near the earth's
+surface. This requirement is reached by placing the observatory on
+Mount Wilson, near Pasadena, California, where the climate is
+found to be the best of any in the United States, and probably not
+exceeded by that of any other attainable point in the world. The
+third requirement is the best of instruments, specially devised to
+meet the requirements. In this respect we may be sure that nothing
+attainable by human ingenuity will be found wanting.
+
+Thus provided, Professor Hale has entered upon the task of
+studying the sun, and recording from day to day all the changes
+going on in it, using specially devised instruments for each
+purpose in view. Photography is made use of through almost the
+entire investigation. A full description of the work would require
+an enumeration of technical details, into which we need not enter
+at present. Let it, therefore, suffice to say in a general way
+that the study of the sun is being carried on on a scale, and with
+an energy worthy of the most important subject that presents
+itself to the astronomer. Closely associated with this work is
+that of Professor Langley and Dr. Abbot, at the Astro-Physical
+Observatory of the Smithsonian Institution, who have recently
+completed one of the most important works ever carried out on the
+light of the sun. They have for years been analyzing those of its
+rays which, although entirely invisible to our eyes, are of the
+same nature as those of light, and are felt by us as heat. To do
+this, Langley invented a sort of artificial eye, which he called a
+bolometer, in which the optic nerve is made of an extremely thin
+strip of metal, so slight that one can hardly see it, which is
+traversed by an electric current. This eye would be so dazzled by
+the heat radiated from one's body that, when in use, it must be
+protected from all such heat by being enclosed in a case kept at a
+constant temperature by being immersed in water. With this eye the
+two observers have mapped the heat rays of the sun down to an
+extent and with a precision which were before entirely unknown.
+
+The question of possible changes in the sun's radiation, and of
+the relation of those changes to human welfare, still eludes our
+scrutiny. With all the efforts that have been made, the physicist
+of to-day has not yet been able to make anything like an exact
+determination of the total amount of heat received from the sun.
+The largest measurements are almost double the smallest. This is
+partly due to the atmosphere absorbing an unknown and variable
+fraction of the sun's rays which pass through it, and partly to
+the difficulty of distinguishing the heat radiated by the sun from
+that radiated by terrestrial objects.
+
+In one recent instance, a change in the sun's radiation has been
+noticed in various parts of the world, and is of especial interest
+because there seems to be little doubt as to its origin. In the
+latter part of 1902 an extraordinary diminution was found in the
+intensity of the sun's heat, as measured by the bolometer and
+other instruments. This continued through the first part of 1903,
+with wide variations at different places, and it was more than a
+year after the first diminution before the sun's rays again
+assumed their ordinary intensity.
+
+This result is now attributed to the eruption of Mount Pelee,
+during which an enormous mass of volcanic dust and vapor was
+projected into the higher regions of the air, and gradually
+carried over the entire earth by winds and currents. Many of our
+readers may remember that something yet more striking occurred
+after the great cataclasm at Krakatoa in 1883, when, for more than
+a year, red sunsets and red twilights of a depth of shade never
+before observed were seen in every part of the world.
+
+What we call universology--the knowledge of the structure and
+extent of the universe--must begin with a study of the starry
+heavens as we see them. There are perhaps one hundred million
+stars in the sky within the reach of telescopic vision. This
+number is too great to allow of all the stars being studied
+individually; yet, to form the basis for any conclusion, we must
+know the positions and arrangement of as many of them as we can
+determine.
+
+To do this the first want is a catalogue giving very precise
+positions of as many of the brighter stars as possible. The
+principal national observatories, as well as some others, are
+engaged in supplying this want. Up to the present time about
+200,000 stars visible in our latitudes have been catalogued on
+this precise plan, and the work is still going on. In that part of
+the sky which we never see, because it is only visible from the
+southern hemisphere, the corresponding work is far from being as
+extensive. Sir David Gill, astronomer at the Cape of Good Hope,
+and also the directors of other southern observatories, are
+engaged in pushing it forward as rapidly as the limited facilities
+at their disposal will allow.
+
+Next in order comes the work of simply listing as many stars as
+possible. Here the most exact positions are not required. It is
+only necessary to lay down the position of each star with
+sufficient exactness to distinguish it from all its neighbors.
+About 400,000 stars were during the last half-century listed in
+this way at the observatory of Bonn by Argelander, Schonfeld, and
+their assistants. This work is now being carried through the
+southern hemisphere on a large scale by Thome, Director of the
+Cordoba Observatory, in the Argentine Republic. This was founded
+thirty years ago by our Dr. B. A. Gould, who turned it over to Dr.
+Thome in 1886. The latter has, up to the present time, fixed and
+published the positions of nearly half a million stars. This work
+of Thome extends to fainter stars than any other yet attempted, so
+that, as it goes on, we have more stars listed in a region
+invisible in middle northern latitudes than we have for that part
+of the sky we can see. Up to the present time three quarto volumes
+giving the positions and magnitudes of the stars have appeared.
+Two or three volumes more, and, perhaps, ten or fifteen years,
+will be required to complete the work.
+
+About twenty years ago it was discovered that, by means of a
+telescope especially adapted to this purpose, it was possible to
+photograph many more stars than an instrument of the same size
+would show to the eye. This discovery was soon applied in various
+quarters. Sir David Gill, with characteristic energy, photographed
+the stars of the southern sky to the number of nearly half a
+million. As it was beyond his power to measure off and compute the
+positions of the stars from his plates, the latter were sent to
+Professor J. C. Kapteyn, of Holland, who undertook the enormous
+labor of collecting them into a catalogue, the last volume of
+which was published in 1899. One curious result of this enterprise
+is that the work of listing the stars is more complete for the
+southern hemisphere than for the northern.
+
+Another great photographic work now in progress has to do with the
+millions of stars which it is impossible to handle individually.
+Fifteen years ago an association of observatories in both
+hemispheres undertook to make a photographic chart of the sky on
+the largest scale. Some portions of this work are now approaching
+completion, but in others it is still in a backward state, owing
+to the failure of several South American observatories to carry
+out their part of the programme. When it is all done we shall have
+a picture of the sky, the study of which may require the labor of
+a whole generation of astronomers.
+
+Quite independently of this work, the Harvard University, under
+the direction of Professor Pickering, keeps up the work of
+photographing the sky on a surprising scale. On this plan we do
+not have to leave it to posterity to learn whether there is any
+change in the heavens, for one result of the enterprise has been
+the discovery of thirteen of the new stars which now and then
+blaze out in the heavens at points where none were before known.
+Professor Pickering's work has been continually enlarged and
+improved until about 150,000 photographic plates, showing from
+time to time the places of countless millions of stars among their
+fellows are now stored at the Harvard Observatory. Not less
+remarkable than this wealth of material has been the development
+of skill in working it up. Some idea of the work will be obtained
+by reflecting that, thirty years ago, careful study of the heavens
+by astronomers devoting their lives to the task had resulted in
+the discovery of some two or three hundred stars, varying in their
+light. Now, at Harvard, through keen eyes studying and comparing
+successive photographs not only of isolated stars, but of clusters
+and agglomerations of stars in the Milky Way and elsewhere,
+discoveries of such objects numbering hundreds have been made, and
+the work is going on with ever-increasing speed. Indeed, the
+number of variable stars now known is such that their study as
+individual objects no longer suffices, and they must hereafter be
+treated statistically with reference to their distribution in
+space, and their relations to one another, as a census classifies
+the entire population without taking any account of individuals.
+
+The works just mentioned are concerned with the stars. But the
+heavenly spaces contain nebulae as well as stars; and photography
+can now be even more successful in picturing them than the stars.
+A few years ago the late lamented Keeler, at the Lick Observatory,
+undertook to see what could be done by pointing the Crossley
+reflecting telescope at the sky and putting a sensitive
+photographic plate in the focus. He was surprised to find that a
+great number of nebulae, the existence of which had never before
+been suspected, were impressed on the plate. Up to the present
+time the positions of about 8000 of these objects have been
+listed. Keeler found that there were probably 200,000 nebulae in
+the heavens capable of being photographed with the Crossley
+reflector. But the work of taking these photographs is so great,
+and the number of reflecting telescopes which can be applied to it
+so small, that no one has ventured to seriously commence it. It is
+worthy of remark that only a very small fraction of these objects
+which can be photographed are visible to the eye, even with the
+most powerful telescope.
+
+This demonstration of what the reflecting telescope can do may be
+regarded as one of the most important discoveries of our time as
+to the capabilities of astronomical instruments. It has long been
+known that the image formed in the focus of the best refracting
+telescope is affected by an imperfection arising from the
+different action of the glasses on rays of light of different
+colors. Hence, the image of a star can never be seen or
+photographed with such an instrument, as an actual point, but only
+as a small, diffused mass. This difficulty is avoided in the
+reflecting telescope; but a new difficulty is found in the bending
+of the mirror under the influence of its own weight. Devices for
+overcoming this had been so far from successful that, when Mr.
+Crossley presented his instrument to the Lick Observatory, it was
+feared that little of importance could be done with it. But as
+often happens in human affairs outside the field of astronomy,
+when ingenious and able men devote their attention to the careful
+study of a problem, it was found that new results could be
+reached. Thus it was that, before a great while, what was supposed
+to be an inferior instrument proved not only to have qualities not
+before suspected, but to be the means of making an important
+addition to the methods of astronomical investigation.
+
+In order that our knowledge of the position of a star may be
+complete, we must know its distance. This can be measured only
+through the star's parallax--that is to say, the slight change in
+its direction produced by the swing of our earth around its orbit.
+But so vast is the distance in question that this change is
+immeasurably small, except for, perhaps, a few hundred stars, and
+even for these few its measurement almost baffles the skill of the
+most expert astronomer. Progress in this direction is therefore
+very slow, and there are probably not yet a hundred stars of which
+the parallax has been ascertained with any approach to certainty.
+Dr. Chase is now completing an important work of this kind at the
+Yale Observatory.
+
+To the most refined telescopic observations, as well as to the
+naked eye, the stars seem all alike, except that they differ
+greatly in brightness, and somewhat in color. But when their light
+is analyzed by the spectroscope, it is found that scarcely any two
+are exactly alike. An important part of the work of the astro-
+physical observatories, especially that of Harvard, consists in
+photographing the spectra of thousands of stars, and studying the
+peculiarities thus brought out. At Harvard a large portion of this
+work is done as part of the work of the Henry Draper Memorial,
+established by his widow in memory of the eminent investigator of
+New York, who died twenty years ago.
+
+By a comparison of the spectra of stars Sir William Huggins has
+developed the idea that these bodies, like human beings, have a
+life history. They are nebulae in infancy, while the progress to
+old age is marked by a constant increase in the density of their
+substance. Their temperature also changes in a way analogous to
+the vigor of the human being. During a certain time the star
+continually grows hotter and hotter. But an end to this must come,
+and it cools off in old age. What the age of a star may be is hard
+even to guess. It is many millions of years, perhaps hundreds,
+possibly even thousands, of millions.
+
+Some attempt at giving the magnitude is included in every
+considerable list of stars. The work of determining the magnitudes
+with the greatest precision is so laborious that it must go on
+rather slowly. It is being pursued on a large scale at the Harvard
+Observatory, as well as in that of Potsdam, Germany.
+
+We come now to the question of changes in the appearance of bright
+stars. It seems pretty certain that more than one per cent of
+these bodies fluctuate to a greater or less extent in their light.
+Observations of these fluctuations, in the case of at least the
+brighter stars, may be carried on without any instrument more
+expensive than a good opera-glass--in fact, in the case of stars
+visible to the naked eye, with no instrument at all.
+
+As a general rule, the light of these stars goes through its
+changes in a regular period, which is sometimes as short as a few
+hours, but generally several days, frequently a large fraction of
+a year or even eighteen months. Observations of these stars are
+made to determine the length of the period and the law of
+variation of the brightness. Any person with a good eye and skill
+in making estimates can make the observations if he will devote
+sufficient pains to training himself; but they require a degree of
+care and assiduity which is not to be expected of any one but an
+enthusiast on the subject. One of the most successful observers of
+the present time is Mr. W. A. Roberts, a resident of South Africa,
+whom the Boer war did not prevent from keeping up a watch of the
+southern sky, which has resulted in greatly increasing our
+knowledge of variable stars. There are also quite a number of
+astronomers in Europe and America who make this particular study
+their specialty.
+
+During the past fifteen years the art of measuring the speed with
+which a star is approaching us or receding from us has been
+brought to a wonderful degree of perfection. The instrument with
+which this was first done was the spectroscope; it is now replaced
+with another of the same general kind, called the spectrograph.
+The latter differs from the other only in that the spectrum of the
+star is photographed, and the observer makes his measures on the
+negative. This method was first extensively applied at the Potsdam
+Observatory in Germany, and has lately become one of the
+specialties of the Lick Observatory, where Professor Campbell has
+brought it to its present degree of perfection. The Yerkes
+Observatory is also beginning work in the same line, where
+Professor Frost is already rivalling the Lick Observatory in the
+precision of his measures.
+
+Let us now go back to our own little colony and see what is being
+done to advance our knowledge of the solar system. This consists
+of planets, on one of which we dwell, moons revolving around them,
+comets, and meteoric bodies. The principal national observatories
+keep up a more or less orderly system of observations of the
+positions of the planets and their satellites in order to
+determine the laws of their motion. As in the case of the stars,
+it is necessary to continue these observations through long
+periods of time in order that everything possible to learn may be
+discovered.
+
+Our own moon is one of the enigmas of the mathematical astronomer.
+Observations show that she is deviating from her predicted place,
+and that this deviation continues to increase. True, it is not
+very great when measured by an ordinary standard. The time at
+which the moon's shadow passed a given point near Norfolk during
+the total eclipse of May 29, 1900, was only about seven seconds
+different from the time given in the Astronomical Ephemeris. The
+path of the shadow along the earth was not out of place by more
+than one or two miles But, small though these deviations are, they
+show that something is wrong, and no one has as yet found out what
+it is. Worse yet, the deviation is increasing rapidly. The
+observers of the total eclipse in August, 1905, were surprised to
+find that it began twenty seconds before the predicted time. The
+mathematical problems involved in correcting this error are of
+such complexity that it is only now and then that a mathematician
+turns up anywhere in the world who is both able and bold enough to
+attack them.
+
+There now seems little doubt that Jupiter is a miniature sun, only
+not hot enough at its surface to shine by its own light The point
+in which it most resembles the sun is that its equatorial regions
+rotate in less time than do the regions near the poles. This shows
+that what we see is not a solid body. But none of the careful
+observers have yet succeeded in determining the law of this
+difference of rotation.
+
+Twelve years ago a suspicion which had long been entertained that
+the earth's axis of rotation varied a little from time to time was
+verified by Chandler. The result of this is a slight change in the
+latitude of all places on the earth's surface, which admits of
+being determined by precise observations. The National Geodetic
+Association has established four observatories on the same
+parallel of latitude--one at Gaithersburg, Maryland, another on
+the Pacific coast, a third in Japan, and a fourth in Italy--to
+study these variations by continuous observations from night to
+night. This work is now going forward on a well-devised plan.
+
+A fact which will appeal to our readers on this side of the
+Atlantic is the success of American astronomers. Sixty years ago
+it could not be said that there was a well-known observatory on
+the American continent. The cultivation of astronomy was confined
+to a professor here and there, who seldom had anything better than
+a little telescope with which he showed the heavenly bodies to his
+students. But during the past thirty years all this has been
+changed. The total quantity of published research is still less
+among us than on the continent of Europe, but the number of men
+who have reached the highest success among us may be judged by one
+fact. The Royal Astronomical Society of England awards an annual
+medal to the English or foreign astronomer deemed most worthy of
+it. The number of these medals awarded to Americans within twenty-
+five years is about equal to the number awarded to the astronomers
+of all other nations foreign to the English. That this
+preponderance is not growing less is shown by the award of medals
+to Americans in three consecutive years--1904, 1905, and 1906.
+The recipients were Hale, Boss, and Campbell. Of the fifty foreign
+associates chosen by this society for their eminence in
+astronomical research, no less than eighteen--more than one-third
+--are Americans.
+
+
+
+
+
+VII
+
+LIFE IN THE UNIVERSE
+
+
+So far as we can judge from what we see on our globe, the
+production of life is one of the greatest and most incessant
+purposes of nature. Life is absent only in regions of perpetual
+frost, where it never has an opportunity to begin; in places where
+the temperature is near the boiling-point, which is found to be
+destructive to it; and beneath the earth's surface, where none of
+the changes essential to it can come about. Within the limits
+imposed by these prohibitory conditions--that is to say, within
+the range of temperature at which water retains its liquid state,
+and in regions where the sun's rays can penetrate and where wind
+can blow and water exist in a liquid form--life is the universal
+rule. How prodigal nature seems to be in its production is too
+trite a fact to be dwelt upon. We have all read of the millions of
+germs which are destroyed for every one that comes to maturity.
+Even the higher forms of life are found almost everywhere. Only
+small islands have ever been discovered which were uninhabited,
+and animals of a higher grade are as widely diffused as man.
+
+If it would be going too far to claim that all conditions may have
+forms of life appropriate to them, it would be going as much too
+far in the other direction to claim that life can exist only with
+the precise surroundings which nurture it on this planet. It is
+very remarkable in this connection that while in one direction we
+see life coming to an end, in the other direction we see it
+flourishing more and more up to the limit. These two directions
+are those of heat and cold. We cannot suppose that life would
+develop in any important degree in a region of perpetual frost,
+such as the polar regions of our globe. But we do not find any end
+to it as the climate becomes warmer. On the contrary, every one
+knows that the tropics are the most fertile regions of the globe
+in its production. The luxuriance of the vegetation and the number
+of the animals continually increase the more tropical the climate
+becomes. Where the limit may be set no one can say. But it would
+doubtless be far above the present temperature of the equatorial
+regions.
+
+It has often been said that this does not apply to the human race,
+that men lack vigor in the tropics. But human vigor depends on so
+many conditions, hereditary and otherwise, that we cannot regard
+the inferior development of humanity in the tropics as due solely
+to temperature. Physically considered, no men attain a better
+development than many tribes who inhabit the warmer regions of the
+globe. The inferiority of the inhabitants of these regions in
+intellectual power is more likely the result of race heredity than
+of temperature.
+
+We all know that this earth on which we dwell is only one of
+countless millions of globes scattered through the wilds of
+infinite space. So far as we know, most of these globes are wholly
+unlike the earth, being at a temperature so high that, like our
+sun, they shine by their own light. In such worlds we may regard
+it as quite certain that no organized life could exist. But
+evidence is continually increasing that dark and opaque worlds
+like ours exist and revolve around their suns, as the earth on
+which we dwell revolves around its central luminary. Although the
+number of such globes yet discovered is not great, the
+circumstances under which they are found lead us to believe that
+the actual number may be as great as that of the visible stars
+which stud the sky. If so, the probabilities are that millions of
+them are essentially similar to our own globe. Have we any reason
+to believe that life exists on these other worlds?
+
+The reader will not expect me to answer this question positively.
+It must be admitted that, scientifically, we have no light upon
+the question, and therefore no positive grounds for reaching a
+conclusion. We can only reason by analogy and by what we know of
+the origin and conditions of life around us, and assume that the
+same agencies which are at play here would be found at play under
+similar conditions in other parts of the universe.
+
+If we ask what the opinion of men has been, we know historically
+that our race has, in all periods of its history, peopled other
+regions with beings even higher in the scale of development than
+we are ourselves. The gods and demons of an earlier age all
+wielded powers greater than those granted to man--powers which
+they could use to determine human destiny. But, up to the time
+that Copernicus showed that the planets were other worlds, the
+location of these imaginary beings was rather indefinite. It was
+therefore quite natural that when the moon and planets were found
+to be dark globes of a size comparable with that of the earth
+itself, they were made the habitations of beings like unto
+ourselves.
+
+The trend of modern discovery has been against carrying this view
+to its extreme, as will be presently shown. Before considering the
+difficulties in the way of accepting it to the widest extent, let
+us enter upon some preliminary considerations as to the origin and
+prevalence of life, so far as we have any sound basis to go upon.
+
+A generation ago the origin of life upon our planet was one of the
+great mysteries of science. All the facts brought out by
+investigation into the past history of our earth seemed to show,
+with hardly the possibility of a doubt, that there was a time when
+it was a fiery mass, no more capable of serving as the abode of a
+living being than the interior of a Bessemer steel furnace. There
+must therefore have been, within a certain period, a beginning of
+life upon its surface. But, so far as investigation had gone--
+indeed, so far as it has gone to the present time--no life has
+been found to originate of itself. The living germ seems to be
+necessary to the beginning of any living form. Whence, then, came
+the first germ? Many of our readers may remember a suggestion by
+Sir William Thomson, now Lord Kelvin, made twenty or thirty years
+ago, that life may have been brought to our planet by the falling
+of a meteor from space. This does not, however, solve the
+difficulty--indeed, it would only make it greater. It still
+leaves open the question how life began on the meteor; and
+granting this, why it was not destroyed by the heat generated as
+the meteor passed through the air. The popular view that life
+began through a special act of creative power seemed to be almost
+forced upon man by the failure of science to discover any other
+beginning for it. It cannot be said that even to-day anything
+definite has been actually discovered to refute this view. All we
+can say about it is that it does not run in with the general views
+of modern science as to the beginning of things, and that those
+who refuse to accept it must hold that, under certain conditions
+which prevail, life begins by a very gradual process, similar to
+that by which forms suggesting growth seem to originate even under
+conditions so unfavorable as those existing in a bottle of acid.
+
+But it is not at all necessary for our purpose to decide this
+question. If life existed through a creative act, it is absurd to
+suppose that that act was confined to one of the countless
+millions of worlds scattered through space. If it began at a
+certain stage of evolution by a natural process, the question will
+arise, what conditions are favorable to the commencement of this
+process? Here we are quite justified in reasoning from what,
+granting this process, has taken place upon our globe during its
+past history. One of the most elementary principles accepted by
+the human mind is that like causes produce like effects. The
+special conditions under which we find life to develop around us
+may be comprehensively summed up as the existence of water in the
+liquid form, and the presence of nitrogen, free perhaps in the
+first place, but accompanied by substances with which it may form
+combinations. Oxygen, hydrogen, and nitrogen are, then, the
+fundamental requirements. The addition of calcium or other forms
+of matter necessary to the existence of a solid world goes without
+saying. The question now is whether these necessary conditions
+exist in other parts of the universe.
+
+The spectroscope shows that, so far as the chemical elements go,
+other worlds are composed of the same elements as ours. Hydrogen
+especially exists everywhere, and we have reason to believe that
+the same is true of oxygen and nitrogen. Calcium, the base of
+lime, is almost universal. So far as chemical elements go, we may
+therefore take it for granted that the conditions under which life
+begins are very widely diffused in the universe. It is, therefore,
+contrary to all the analogies of nature to suppose that life began
+only on a single world.
+
+It is a scientific inference, based on facts so numerous as not to
+admit of serious question, that during the history of our globe
+there has been a continually improving development of life. As
+ages upon ages pass, new forms are generated, higher in the scale
+than those which preceded them, until at length reason appears and
+asserts its sway. In a recent well-known work Alfred Russel
+Wallace has argued that this development of life required the
+presence of such a rare combination of conditions that there is no
+reason to suppose that it prevailed anywhere except on our earth.
+It is quite impossible in the present discussion to follow his
+reasoning in detail; but it seems to me altogether inconclusive.
+Not only does life, but intelligence, flourish on this globe under
+a great variety of conditions as regards temperature and
+surroundings, and no sound reason can be shown why under certain
+conditions, which are frequent in the universe, intelligent beings
+should not acquire the highest development.
+
+Now let us look at the subject from the view of the mathematical
+theory of probabilities. A fundamental tenet of this theory is
+that no matter how improbable a result may be on a single trial,
+supposing it at all possible, it is sure to occur after a
+sufficient number of trials--and over and over again if the trials
+are repeated often enough. For example, if a million grains of
+corn, of which a single one was red, were all placed in a pile,
+and a blindfolded person were required to grope in the pile,
+select a grain, and then put it back again, the chances would be a
+million to one against his drawing out the red grain. If drawing
+it meant he should die, a sensible person would give himself no
+concern at having to draw the grain. The probability of his death
+would not be so great as the actual probability that he will
+really die within the next twenty-four hours. And yet if the whole
+human race were required to run this chance, it is certain that
+about fifteen hundred, or one out of a million, of the whole human
+family would draw the red grain and meet his death.
+
+Now apply this principle to the universe. Let us suppose, to fix
+the ideas, that there are a hundred million worlds, but that the
+chances are one thousand to one against any one of these taken at
+random being fitted for the highest development of life or for the
+evolution of reason. The chances would still be that one hundred
+thousand of them would be inhabited by rational beings whom we
+call human. But where are we to look for these worlds? This no man
+can tell. We only infer from the statistics of the stars--and this
+inference is fairly well grounded--that the number of worlds
+which, so far as we know, may be inhabited, are to be counted by
+thousands, and perhaps by millions.
+
+In a number of bodies so vast we should expect every variety of
+conditions as regards temperature and surroundings. If we suppose
+that the special conditions which prevail on our planet are
+necessary to the highest forms of life, we still have reason to
+believe that these same conditions prevail on thousands of other
+worlds. The fact that we might find the conditions in millions of
+other worlds unfavorable to life would not disprove the existence
+of the latter on countless worlds differently situated.
+
+Coming down now from the general question to the specific one, we
+all know that the only worlds the conditions of which can be made
+the subject of observation are the planets which revolve around
+the sun, and their satellites. The question whether these bodies
+are inhabited is one which, of course, completely transcends not
+only our powers of observation at present, but every appliance of
+research that we can conceive of men devising. If Mars is
+inhabited, and if the people of that planet have equal powers with
+ourselves, the problem of merely producing an illumination which
+could be seen in our most powerful telescope would be beyond all
+the ordinary efforts of an entire nation. An unbroken square mile
+of flame would be invisible in our telescopes, but a hundred
+square miles might be seen. We cannot, therefore, expect to see
+any signs of the works of inhabitants even on Mars. All that we
+can do is to ascertain with greater or less probability whether
+the conditions necessary to life exist on the other planets of the
+system.
+
+The moon being much the nearest to us of all the heavenly bodies,
+we can pronounce more definitely in its case than in any other. We
+know that neither air nor water exists on the moon in quantities
+sufficient to be perceived by the most delicate tests at our
+command. It is certain that the moon's atmosphere, if any exists,
+is less than the thousandth part of the density of that around us.
+The vacuum is greater than any ordinary air-pump is capable of
+producing. We can hardly suppose that so small a quantity of air
+could be of any benefit whatever in sustaining life; an animal
+that could get along on so little could get along on none at all.
+
+But the proof of the absence of life is yet stronger when we
+consider the results of actual telescopic observation. An object
+such as an ordinary city block could be detected on the moon. If
+anything like vegetation were present on its surface, we should
+see the changes which it would undergo in the course of a month,
+during one portion of which it would be exposed to the rays of the
+unclouded sun, and during another to the intense cold of space. If
+men built cities, or even separate buildings the size of the
+larger ones on our earth, we might see some signs of them.
+
+In recent times we not only observe the moon with the telescope,
+but get still more definite information by photography. The whole
+visible surface has been repeatedly photographed under the best
+conditions. But no change has been established beyond question,
+nor does the photograph show the slightest difference of structure
+or shade which could be attributed to cities or other works of
+man. To all appearances the whole surface of our satellite is as
+completely devoid of life as the lava newly thrown from Vesuvius.
+We next pass to the planets. Mercury, the nearest to the sun, is
+in a position very unfavorable for observation from the earth,
+because when nearest to us it is between us and the sun, so that
+its dark hemisphere is presented to us. Nothing satisfactory has
+yet been made out as to its condition. We cannot say with
+certainty whether it has an atmosphere or not. What seems very
+probable is that the temperature on its surface is higher than any
+of our earthly animals could sustain. But this proves nothing.
+
+We know that Venus has an atmosphere. This was very conclusively
+shown during the transits of Venus in 1874 and 1882. But this
+atmosphere is so filled with clouds or vapor that it does not seem
+likely that we ever get a view of the solid body of the planet
+through it. Some observers have thought they could see spots on
+Venus day after day, while others have disputed this view. On the
+whole, if intelligent inhabitants live there, it is not likely
+that they ever see sun or stars. Instead of the sun they see only
+an effulgence in the vapory sky which disappears and reappears at
+regular intervals.
+
+When we come to Mars, we have more definite knowledge, and there
+seems to be greater possibilities for life there than in the case
+of any other planet besides the earth. The main reason for denying
+that life such as ours could exist there is that the atmosphere of
+Mars is so rare that, in the light of the most recent researches,
+we cannot be fully assured that it exists at all. The very careful
+comparisons of the spectra of Mars and of the moon made by
+Campbell at the Lick Observatory failed to show the slightest
+difference in the two. If Mars had an atmosphere as dense as ours,
+the result could be seen in the darkening of the lines of the
+spectrum produced by the double passage of the light through it.
+There were no lines in the spectrum of Mars that were not seen
+with equal distinctness in that of the moon. But this does not
+prove the entire absence of an atmosphere. It only shows a limit
+to its density. It may be one-fifth or one-fourth the density of
+that on the earth, but probably no more.
+
+That there must be something in the nature of vapor at least seems
+to be shown by the formation and disappearance of the white polar
+caps of this planet. Every reader of astronomy at the present time
+knows that, during the Martian winter, white caps form around the
+pole of the planet which is turned away from the sun, and grow
+larger and larger until the sun begins to shine upon them, when
+they gradually grow smaller, and perhaps nearly disappear. It
+seems, therefore, fairly well proved that, under the influence of
+cold, some white substance forms around the polar regions of Mars
+which evaporates under the influence of the sun's rays. It has
+been supposed that this substance is snow, produced in the same
+way that snow is produced on the earth, by the evaporation of
+water.
+
+But there are difficulties in the way of this explanation. The sun
+sends less than half as much heat to Mars as to the earth, and it
+does not seem likely that the polar regions can ever receive
+enough of heat to melt any considerable quantity of snow. Nor does
+it seem likely that any clouds from which snow could fall ever
+obscure the surface of Mars.
+
+But a very slight change in the explanation will make it tenable.
+Quite possibly the white deposits may be due to something like
+hoar-frost condensed from slightly moist air, without the actual
+production of snow. This would produce the effect that we see.
+Even this explanation implies that Mars has air and water, rare
+though the former may be. It is quite possible that air as thin as
+that of Mars would sustain life in some form. Life not totally
+unlike that on the earth may therefore exist upon this planet for
+anything that we know to the contrary. More than this we cannot
+say.
+
+In the case of the outer planets the answer to our question must
+be in the negative. It now seems likely that Jupiter is a body
+very much like our sun, only that the dark portion is too cool to
+emit much, if any, light. It is doubtful whether Jupiter has
+anything in the nature of a solid surface. Its interior is in all
+likelihood a mass of molten matter far above a red heat, which is
+surrounded by a comparatively cool, yet, to our measure, extremely
+hot, vapor. The belt-like clouds which surround the planet are due
+to this vapor combined with the rapid rotation. If there is any
+solid surface below the atmosphere that we can see, it is swept by
+winds such that nothing we have on earth could withstand them.
+But, as we have said, the probabilities are very much against
+there being anything like such a surface. At some great depth in
+the fiery vapor there is a solid nucleus; that is all we can say.
+
+The planet Saturn seems to be very much like that of Jupiter in
+its composition. It receives so little heat from the sun that,
+unless it is a mass of fiery vapor like Jupiter, the surface must
+be far below the freezing-point.
+
+We cannot speak with such certainty of Uranus and Neptune; yet the
+probability seems to be that they are in much the same condition
+as Saturn. They are known to have very dense atmospheres, which
+are made known to us only by their absorbing some of the light of
+the sun. But nothing is known of the composition of these
+atmospheres.
+
+To sum up our argument: the fact that, so far as we have yet been
+able to learn, only a very small proportion of the visible worlds
+scattered through space are fitted to be the abode of life does
+not preclude the probability that among hundreds of millions of
+such worlds a vast number are so fitted. Such being the case, all
+the analogies of nature lead us to believe that, whatever the
+process which led to life upon this earth--whether a special act
+of creative power or a gradual course of development--through that
+same process does life begin in every part of the universe fitted
+to sustain it. The course of development involves a gradual
+improvement in living forms, which by irregular steps rise higher
+and higher in the scale of being. We have every reason to believe
+that this is the case wherever life exists. It is, therefore,
+perfectly reasonable to suppose that beings, not only animated,
+but endowed with reason, inhabit countless worlds in space. It
+would, indeed, be very inspiring could we learn by actual
+observation what forms of society exist throughout space, and see
+the members of such societies enjoying themselves by their warm
+firesides. But this, so far as we can now see, is entirely beyond
+the possible reach of our race, so long as it is confined to a
+single world.
+
+
+
+
+
+VIII
+
+HOW THE PLANETS ARE WEIGHED
+
+
+You ask me how the planets are weighed? I reply, on the same
+principle by which a butcher weighs a ham in a spring-balance.
+When he picks the ham up, he feels a pull of the ham towards the
+earth. When he hangs it on the hook, this pull is transferred from
+his hand to the spring of the balance. The stronger the pull, the
+farther the spring is pulled down. What he reads on the scale is
+the strength of the pull. You know that this pull is simply the
+attraction of the earth on the ham. But, by a universal law of
+force, the ham attracts the earth exactly as much as the earth
+does the ham. So what the butcher really does is to find how much
+or how strongly the ham attracts the earth, and he calls that pull
+the weight of the ham. On the same principle, the astronomer finds
+the weight of a body by finding how strong is its attractive pull
+on some other body. If the butcher, with his spring-balance and a
+ham, could fly to all the planets, one after the other, weigh the
+ham on each, and come back to report the results to an astronomer,
+the latter could immediately compute the weight of each planet of
+known diameter, as compared with that of the earth. In applying
+this principle to the heavenly bodies, we at once meet a
+difficulty that looks insurmountable. You cannot get up to the
+heavenly bodies to do your weighing; how then will you measure
+their pull? I must begin the answer to this question by explaining
+a nice point in exact science. Astronomers distinguish between the
+weight of a body and its mass. The weight of objects is not the
+same all over the world; a thing which weighs thirty pounds in New
+York would weigh an ounce more than thirty pounds in a spring-
+balance in Greenland, and nearly an ounce less at the equator.
+This is because the earth is not a perfect sphere, but a little
+flattened. Thus weight varies with the place. If a ham weighing
+thirty pounds were taken up to the moon and weighed there, the
+pull would only be five pounds, because the moon is so much
+smaller and lighter than the earth. There would be another weight
+of the ham for the planet Mars, and yet another on the sun, where
+it would weigh some eight hundred pounds. Hence the astronomer
+does not speak of the weight of a planet, because that would
+depend on the place where it was weighed; but he speaks of the
+mass of the planet, which means how much planet there is, no
+matter where you might weigh it.
+
+At the same time, we might, without any inexactness, agree that
+the mass of a heavenly body should be fixed by the weight it would
+have in New York. As we could not even imagine a planet at New
+York, because it may be larger than the earth itself, what we are
+to imagine is this: Suppose the planet could be divided into a
+million million million equal parts, and one of these parts
+brought to New York and weighed. We could easily find its weight
+in pounds or tons. Then multiply this weight by a million million
+million, and we shall have a weight of the planet. This would be
+what the astronomers might take as the mass of the planet.
+
+With these explanations, let us see how the weight of the earth is
+found. The principle we apply is that round bodies of the same
+specific gravity attract small objects on their surface with a
+force proportional to the diameter of the attracting body. For
+example, a body two feet in diameter attracts twice as strongly as
+one of a foot, one of three feet three times as strongly, and so
+on. Now, our earth is about 40,000,000 feet in diameter; that is
+10,000,000 times four feet. It follows that if we made a little
+model of the earth four feet in diameter, having the average
+specific gravity of the earth, it would attract a particle with
+one ten-millionth part of the attraction of the earth. The
+attraction of such a model has actually been measured. Since we do
+not know the average specific gravity of the earth--that being in
+fact what we want to find out--we take a globe of lead, four feet
+in diameter, let us suppose. By means of a balance of the most
+exquisite construction it is found that such a globe does exert a
+minute attraction on small bodies around it, and that this
+attraction is a little more than the ten-millionth part of that of
+the earth. This shows that the specific gravity of the lead is a
+little greater than that of the average of the whole earth. All
+the minute calculations made, it is found that the earth, in order
+to attract with the force it does, must be about five and one-half
+times as heavy as its bulk of water, or perhaps a little more.
+Different experimenters find different results; the best between
+5.5 and 5.6, so that 5.5 is, perhaps, as near the number as we can
+now get. This is much more than the average specific gravity of
+the materials which compose that part of the earth which we can
+reach by digging mines. The difference arises from the fact that,
+at the depth of many miles, the matter composing the earth is
+compressed into a smaller space by the enormous weight of the
+portions lying above it. Thus, at the depth of 1000 miles, the
+pressure on every cubic inch is more than 2000 tons, a weight
+which would greatly condense the hardest metal.
+
+We come now to the planets. I have said that the mass or weight of
+a heavenly body is determined by its attraction on some other
+body. There are two ways in which the attraction of a planet may
+be measured. One is by its attraction on the planets next to it.
+If these bodies did not attract one another at all, but only moved
+under the influence of the sun, they would move in orbits having
+the form of ellipses. They are found to move very nearly in such
+orbits, only the actual path deviates from an ellipse, now in one
+direction and then in another, and it slowly changes its position
+from year to year. These deviations are due to the pull of the
+other planets, and by measuring the deviations we can determine
+the amount of the pull, and hence the mass of the planet.
+
+The reader will readily understand that the mathematical processes
+necessary to get a result in this way must be very delicate and
+complicated. A much simpler method can be used in the case of
+those planets which have satellites revolving round them, because
+the attraction of the planet can be determined by the motions of
+the satellite. The first law of motion teaches us that a body in
+motion, if acted on by no force, will move in a straight line.
+Hence, if we see a body moving in a curve, we know that it is
+acted on by a force in the direction towards which the motion
+curves. A familiar example is that of a stone thrown from the
+hand. If the stone were not attracted by the earth, it would go on
+forever in the line of throw, and leave the earth entirely. But
+under the attraction of the earth, it is drawn down and down, as
+it travels onward, until finally it reaches the ground. The faster
+the stone is thrown, of course, the farther it will go, and the
+greater will be the sweep of the curve of its path. If it were a
+cannon-ball, the first part of the curve would be nearly a right
+line. If we could fire a cannon-ball horizontally from the top of
+a high mountain with a velocity of five miles a second, and if it
+were not resisted by the air, the curvature of the path would be
+equal to that of the surface of our earth, and so the ball would
+never reach the earth, but would revolve round it like a little
+satellite in an orbit of its own. Could this be done, the
+astronomer would be able, knowing the velocity of the ball, to
+calculate the attraction of the earth as well as we determine it
+by actually observing the motion of falling bodies around us.
+
+Thus it is that when a planet, like Mars or Jupiter, has
+satellites revolving round it, astronomers on the earth can
+observe the attraction of the planet on its satellites and thus
+determine its mass. The rule for doing this is very simple. The
+cube of the distance between the planet and satellite is divided
+by the square of the time of revolution of the satellite. The
+quotient is a number which is proportional to the mass of the
+planet. The rule applies to the motion of the moon round the earth
+and of the planets round the sun. If we divide the cube of the
+earth's distance from the sun, say 93,000,000 miles, by the square
+of 365 1/4, the days in a year, we shall get a certain quotient.
+Let us call this number the sun-quotient. Then, if we divide the
+cube of the moon's distance from the earth by the square of its
+time of revolution, we shall get another quotient, which we may
+call the earth-quotient. The sun-quotient will come out about
+330,000 times as large as the earth-quotient. Hence it is
+concluded that the mass of the sun is 330,000 times that of the
+earth; that it would take this number of earths to make a body as
+heavy as the sun.
+
+I give this calculation to illustrate the principle; it must not
+be supposed that the astronomer proceeds exactly in this way and
+has only this simple calculation to make. In the case of the moon
+and earth, the motion and distance of the former vary in
+consequence of the attraction of the sun, so that their actual
+distance apart is a changing quantity. So what the astronomer
+actually does is to find the attraction of the earth by observing
+the length of a pendulum which beats seconds in various latitudes.
+Then, by very delicate mathematical processes, he can find with
+great exactness what would be the time of revolution of a small
+satellite at any given distance from the earth, and thus can get
+the earth-quotient.
+
+But, as I have already pointed out, we must, in the case of the
+planets, find the quotient in question by means of the satellites;
+and it happens, fortunately, that the motions of these bodies are
+much less changed by the attraction of the sun than is the motion
+of the moon. Thus, when we make the computation for the outer
+satellite of Mars, we find the quotient to be 1/3093500 that of
+the sun-quotient. Hence we conclude that the mass of Mars is
+1/3093500 that of the sun. By the corresponding quotient, the mass
+of Jupiter is found to be about 1/1047 that of the sun, Saturn
+1/3500, Uranus 1/22700, Neptune 1/19500.
+
+We have set forth only the great principle on which the astronomer
+has proceeded for the purpose in question. The law of gravitation
+is at the bottom of all his work. The effects of this law require
+mathematical processes which it has taken two hundred years to
+bring to their present state, and which are still far from
+perfect. The measurement of the distance of a satellite is not a
+job to be done in an evening; it requires patient labor extending
+through months and years, and then is not as exact as the
+astronomer would wish. He does the best he can, and must be
+satisfied with that.
+
+
+
+
+
+IX
+
+THE MARINER'S COMPASS
+
+
+Among those provisions of Nature which seem to us as especially
+designed for the use of man, none is more striking than the
+seeming magnetism of the earth. What would our civilization have
+been if the mariner's compass had never been known? That Columbus
+could never have crossed the Atlantic is certain; in what
+generation since his time our continent would have been discovered
+is doubtful. Did the reader ever reflect what a problem the
+captain of the finest ocean liner of our day would face if he had
+to cross the ocean without this little instrument? With the aid of
+a pilot he gets his ship outside of Sandy Hook without much
+difficulty. Even later, so long as the sun is visible and the air
+is clear, he will have some apparatus for sailing by the direction
+of the sun. But after a few hours clouds cover the sky. From that
+moment he has not the slightest idea of east, west, north, or
+south, except so far as he may infer it from the direction in
+which he notices the wind to blow. For a few hours he may be
+guided by the wind, provided he is sure he is not going ashore on
+Long Island. Thus, in time, he feels his way out into the open
+sea. By day he has some idea of direction with the aid of the sun;
+by night, when the sky is clear he can steer by the Great Bear, or
+"Cynosure," the compass of his ancient predecessors on the
+Mediterranean. But when it is cloudy, if he persists in steaming
+ahead, he may be running towards the Azores or towards Greenland,
+or he may be making his way back to New York without knowing it.
+So, keeping up steam only when sun or star is visible, he at
+length finds that he is approaching the coast of Ireland. Then he
+has to grope along much like a blind man with his staff, feeling
+his way along the edge of a precipice. He can determine the
+latitude at noon if the sky is clear, and his longitude in the
+morning or evening in the same conditions. In this way he will get
+a general idea of his whereabouts. But if he ventures to make
+headway in a fog, he may find himself on the rocks at any moment.
+He reaches his haven only after many spells of patient waiting for
+favoring skies.
+
+The fact that the earth acts like a magnet, that the needle points
+to the north, has been generally known to navigators for nearly a
+thousand years, and is said to have been known to the Chinese at a
+yet earlier period. And yet, to-day, if any professor of physical
+science is asked to explain the magnetic property of the earth, he
+will acknowledge his inability to do so to his own satisfaction.
+Happily this does not hinder us from finding out by what law these
+forces act, and how they enable us to navigate the ocean. I
+therefore hope the reader will be interested in a short exposition
+of the very curious and interesting laws on which the science of
+magnetism is based, and which are applied in the use of the
+compass.
+
+The force known as magnetic, on which the compass depends, is
+different from all other natural forces with which we are
+familiar. It is very remarkable that iron is the only substance
+which can become magnetic in any considerable degree. Nickel and
+one or two other metals have the same property, but in a very
+slight degree. It is also remarkable that, however powerfully a
+bar of steel may be magnetized, not the slightest effect of the
+magnetism can be seen by its action on other than magnetic
+substances. It is no heavier than before. Its magnetism does not
+produce the slightest influence upon the human body. No one would
+know that it was magnetic until something containing iron was
+brought into its immediate neighborhood; then the attraction is
+set up. The most important principle of magnetic science is that
+there are two opposite kinds of magnetism, which are, in a certain
+sense, contrary in their manifestations. The difference is seen in
+the behavior of the magnet itself. One particular end points
+north, and the other end south. What is it that distinguishes
+these two ends? The answer is that one end has what we call north
+magnetism, while the other has south magnetism. Every magnetic bar
+has two poles, one near one end, one near the other. The north
+pole is drawn towards the north pole of the earth, the south pole
+towards the south pole, and thus it is that the direction of the
+magnet is determined. Now, when we bring two magnets near each
+other we find another curious phenomenon. If the two like poles
+are brought together, they do not attract but repel each other.
+But the two opposite poles attract each other. The attraction and
+repulsion are exactly equal under the same conditions. There is no
+more attraction than repulsion. If we seal one magnet up in a
+paper or a box, and then suspend another over the box, the north
+pole of the one outside will tend to the south pole of the one in
+the box, and vice versa.
+
+Our next discovery is, that whenever a magnet attracts a piece of
+iron it makes that iron into a magnet, at least for the time
+being. In the case of ordinary soft or untempered iron the
+magnetism disappears instantly when the magnet is removed. But if
+the magnet be made to attract a piece of hardened steel, the
+latter will retain the magnetism produced in it and become itself
+a permanent magnet.
+
+This fact must have been known from the time that the compass came
+into use. To make this instrument it was necessary to magnetize a
+small bar or needle by passing a natural magnet over it.
+
+In our times the magnetization is effected by an electric current.
+The latter has curious magnetic properties; a magnetic needle
+brought alongside of it will be found placing itself at right
+angles to the wire bearing the current. On this principle is made
+the galvanometer for measuring the intensity of a current.
+Moreover, if a piece of wire is coiled round a bar of steel, and a
+powerful electric current pass through the coil, the bar will
+become a magnet.
+
+Another curious property of magnetism is that we cannot develop
+north magnetism in a bar without developing south magnetism at the
+same time. If it were otherwise, important consequences would
+result. A separate north pole of a magnet would, if attached to a
+floating object and thrown into the ocean, start on a journey
+towards the north all by itself. A possible method of bringing
+this result about may suggest itself. Let us take an ordinary bar
+magnet, with a pole at each end, and break it in the middle; then
+would not the north end be all ready to start on its voyage north,
+and the south end to make its way south? But, alas! when this
+experiment is tried it is found that a south pole instantly
+develops itself on one side of the break, and a north pole on the
+other side, so that the two pieces will simply form two magnets,
+each with its north and south pole. There is no possibility of
+making a magnet with only one pole.
+
+It was formerly supposed that the central portions of the earth
+consisted of an immense magnet directed north and south. Although
+this view is found, for reasons which need not be set forth in
+detail, to be untenable, it gives us a good general idea of the
+nature of terrestrial magnetism. One result that follows from the
+law of poles already mentioned is that the magnetism which seems
+to belong to the north pole of the earth is what we call south on
+the magnet, and vice versa.
+
+Careful experiment shows us that the region around every magnet is
+filled with magnetic force, strongest near the poles of the
+magnet, but diminishing as the inverse square of the distance from
+the pole. This force, at each point, acts along a certain line,
+called a line of force. These lines are very prettily shown by the
+familiar experiment of placing a sheet of paper over a magnet, and
+then scattering iron filings on the surface of the paper. It will
+be noticed that the filings arrange themselves along a series of
+curved lines, diverging in every direction from each pole, but
+always passing from one pole to the other. It is a universal law
+that whenever a magnet is brought into a region where this force
+acts, it is attracted into such a position that it shall have the
+same direction as the lines of force. Its north pole will take the
+direction of the curve leading to the south pole of the other
+magnet, and its south pole the opposite one.
+
+The fact of terrestrial magnetism may be expressed by saying that
+the space within and around the whole earth is filled by lines of
+magnetic force, which we know nothing about until we suspend a
+magnet so perfectly balanced that it may point in any direction
+whatever. Then it turns and points in the direction of the lines
+of force, which may thus be mapped out for all points of the
+earth.
+
+We commonly say that the pole of the needle points towards the
+north. The poets tell us how the needle is true to the pole. Every
+reader, however, is now familiar with the general fact of a
+variation of the compass. On our eastern seaboard, and all the way
+across the Atlantic, the north pointing of the compass varies so
+far to the west that a ship going to Europe and making no
+allowance for this deviation would find herself making more nearly
+for the North Cape than for her destination. The "declination," as
+it is termed in scientific language, varies from one region of the
+earth to another. In some places it is towards the west, in others
+towards the east.
+
+The pointing of the needle in various regions of the world is
+shown by means of magnetic maps. Such maps are published by the
+United States Coast Survey, whose experts make a careful study of
+the magnetic force all over the country. It is found that there is
+a line running nearly north and south through the Middle States
+along which there is no variation of the compass. To the east of
+it the variation of the north pole of the magnet is west; to the
+west of it, east. The most rapid changes in the pointing of the
+needle are towards the northeast and northwest regions. When we
+travel to the northeastern boundary of Maine the westerly
+variation has risen to 20 degrees. Towards the northwest the
+easterly variation continually increases, until, in the northern
+part of the State of Washington, it amounts to 23 degrees.
+
+When we cross the Atlantic into Europe we find the west variation
+diminishing until we reach a certain line passing through central
+Russia and western Asia. This is again a line of no variation.
+Crossing it, the variation is once more towards the east. This
+direction continues over most of the continent of Asia, but varies
+in a somewhat irregular manner from one part of the continent to
+another.
+
+As a general rule, the lines of the earth's magnetic force are not
+horizontal, and therefore one end or the other of a perfectly
+suspended magnet will dip below the horizontal position. This is
+called the "dip of the needle." It is observed by means of a brass
+circle, of which the circumference is marked off in degrees. A
+magnet is attached to this circle so as to form a diameter, and
+suspended on a horizontal axis passing through the centre of
+gravity, so that the magnet shall be free to point in the
+direction indicated by the earth's lines of magnetic force. Armed
+with this apparatus, scientific travellers and navigators have
+visited various points of the earth in order to determine the dip.
+It is thus found that there is a belt passing around the earth
+near the equator, but sometimes deviating several degrees from it,
+in which there is no dip; that is to say, the lines of magnetic
+force are horizontal. Taking any point on this belt and going
+north, it will be found that the north pole of the magnet
+gradually tends downward, the dip constantly increasing as we go
+farther north. In the southern part of the United States the dip
+is about 60 degrees, and the direction of the needle is nearly
+perpendicular to the earth's axis. In the northern part of the
+country, including the region of the Great Lakes, the dip
+increases to 75 degrees. Noticing that a dip of 90 degrees would
+mean that the north end of the magnet points straight downward, it
+follows that it would be more nearly correct to say that,
+throughout the United States, the magnetic needle points up and
+down than that it points north and south.
+
+Going yet farther north, we find the dip still increasing, until
+at a certain point in the arctic regions the north pole of the
+needle points downward. In this region the compass is of no use to
+the traveller or the navigator. The point is called the Magnetic
+Pole. Its position has been located several times by scientific
+observers. The best determinations made during the last eighty
+years agree fairly well in placing it near 70 degrees north
+latitude and 97 degrees longitude west from Greenwich. This point
+is situated on the west shore of the Boothian Peninsula, which is
+bounded on the south end by McClintock Channel. It is about five
+hundred miles north of the northwest part of Hudson Bay. There is
+a corresponding magnetic pole in the Antarctic Ocean, or rather on
+Victoria Land, nearly south of Australia. Its position has not
+been so exactly located as in the north, but it is supposed to be
+at about 74 degrees of south latitude and 147 degrees of east
+longitude from Greenwich.
+
+The magnetic poles used to be looked upon as the points towards
+which the respective ends of the needle were attracted. And, as a
+matter of fact, the magnetic force is stronger near the poles than
+elsewhere. When located in this way by strength of force, it is
+found that there is a second north pole in northern Siberia. Its
+location has not, however, been so well determined as in the case
+of the American pole, and it is not yet satisfactorily shown that
+there is any one point in Siberia where the direction of the force
+is exactly downward.
+
+[Illustration with caption: DIP OF THE MAGNETIC NEEDLE IN VARIOUS
+LATITUDES. The arrow points show the direction of the north end of
+the magnetic needle, which dips downward in north latitudes, while
+the south end dips in south latitudes.]
+
+The declination and dip, taken together, show the exact direction
+of the magnetic force at any place. But in order to complete the
+statement of the force, one more element must be given--its
+amount. The intensity of the magnetic force is determined by
+suspending a magnet in a horizontal position, and then allowing it
+to oscillate back and forth around the suspension. The stronger
+the force, the less the time it will take to oscillate. Thus, by
+carrying a magnet to various parts of the world, the magnetic
+force can be determined at every point where a proper support for
+the magnet is obtainable. The intensity thus found is called the
+horizontal force. This is not really the total force, because the
+latter depends upon the dip; the greater the dip, the less will be
+the horizontal force which corresponds to a certain total force.
+But a very simple computation enables the one to be determined
+when the value of the other is known. In this way it is found
+that, as a general rule, the magnetic force is least in the
+earth's equatorial regions and increases as we approach either of
+the magnetic poles.
+
+When the most exact observations on the direction of the needle
+are made, it is found that it never remains at rest. Beginning
+with the changes of shortest duration, we have a change which
+takes place every day, and is therefore called diurnal. In our
+northern latitudes it is found that during the six hours from nine
+o'clock at night until three in the morning the direction of the
+magnet remains nearly the same. But between three and four A.M. it
+begins to deviate towards the east, going farther and farther east
+until about 8 A.M. Then, rather suddenly, it begins to swing
+towards the west with a much more rapid movement, which comes to
+an end between one and two o'clock in the afternoon. Then, more
+slowly, it returns in an easterly direction until about nine at
+night, when it becomes once more nearly quiescent. Happily, the
+amount of this change is so small that the navigator need not
+trouble himself with it. The entire range of movement rarely
+amounts to one-quarter of a degree.
+
+It is a curious fact that the amount of the change is twice as
+great in June as it is in December. This indicates that it is
+caused by the sun's radiation. But how or why this cause should
+produce such an effect no one has yet discovered.
+
+Another curious feature is that in the southern hemisphere the
+direction of the motion is reversed, although its general
+character remains the same. The pointing deviates towards the west
+in the morning, then rapidly moves towards the east until about
+two o'clock, after which it slowly returns to its original
+direction.
+
+The dip of the needle goes through a similar cycle of daily
+changes. In northern latitudes it is found that at about six in
+the morning the dip begins to increase, and continues to do so
+until noon, after which it diminishes until seven or eight o'clock
+in the evening, when it becomes nearly constant for the rest of
+the night. In the southern hemisphere the direction of the
+movement is reversed.
+
+When the pointing of the needle is compared with the direction of
+the moon, it is found that there is a similar change. But, instead
+of following the moon in its course, it goes through two periods
+in a day, like the tides. When the moon is on the meridian,
+whether above or below us, the effect is in one direction, while
+when it is rising or setting it is in the opposite direction. In
+other words, there is a complete swinging backward and forward
+twice in a lunar day. It might be supposed that such an effect
+would be due to the moon, like the earth, being a magnet. But were
+this the case there would be only one swing back and forth during
+the passage of the moon from the meridian until it came back to
+the meridian again. The effect would be opposite at the rising and
+setting of the moon, which we have seen is not the case. To make
+the explanation yet more difficult, it is found that, as in the
+case of the sun, the change is opposite in the northern and
+southern hemispheres and very small at the equator, where, by
+virtue of any action that we can conceive of, it ought to be
+greatest. The pointing is also found to change with the age of the
+moon and with the season of the year. But these motions are too
+small to be set forth in the present article.
+
+There is yet another class of changes much wider than these. The
+observations recorded since the time of Columbus show that, in the
+course of centuries, the variation of the compass, at any one
+point, changes very widely. It is well known that in 1490 the
+needle pointed east of north in the Mediterranean, as well as in
+those portions of the Atlantic which were then navigated. Columbus
+was therefore much astonished when, on his first voyage, in mid-
+ocean, he found that the deviation was reversed, and was now
+towards the west. It follows that a line of no variation then
+passed through the Atlantic Ocean. But this line has since been
+moving towards the east. About 1662 it passed the meridian of
+Paris. During the two hundred and forty years which have since
+elapsed, it has passed over Central Europe, and now, as we have
+already said, passes through European Russia.
+
+The existence of natural magnets composed of iron ore, and their
+property of attracting iron and making it magnetic, have been
+known from the remotest antiquity. But the question as to who
+first discovered the fact that a magnetized needle points north
+and south, and applied this discovery to navigation, has given
+rise to much discussion. That the property was known to the
+Chinese about the beginning of our era seems to be fairly well
+established, the statements to that effect being of a kind that
+could not well have been invented. Historical evidence of the use
+of the magnetic needle in navigation dates from the twelfth
+century. The earliest compass consisted simply of a splinter of
+wood or a piece of straw to which the magnetized needle was
+attached, and which was floated in water. A curious obstacle is
+said to have interfered with the first uses of this instrument.
+Jack is a superstitious fellow, and we may be sure that he was not
+less so in former times than he is today. From his point of view
+there was something uncanny in so very simple a contrivance as a
+floating straw persistently showing him the direction in which he
+must sail. It made him very uncomfortable to go to sea under the
+guidance of an invisible power. But with him, as with the rest of
+us, familiarity breeds contempt, and it did not take more than a
+generation to show that much good and no harm came to those who
+used the magic pointer.
+
+The modern compass, as made in the most approved form for naval
+and other large ships, is the liquid one. This does not mean that
+the card bearing the needle floats on the liquid, but only that a
+part of the force is taken off from the pivot on which it turns,
+so as to make the friction as small as possible, and to prevent
+the oscillation back and forth which would continually go on if
+the card were perfectly free to turn. The compass-card is marked
+not only with the thirty-two familiar points of the compass, but
+is also divided into degrees. In the most accurate navigation it
+is probable that very little use of the points is made, the ship
+being directed according to the degrees.
+
+A single needle is not relied upon to secure the direction of the
+card, the latter being attached to a system of four or even more
+magnets, all pointing in the same direction. The compass must have
+no iron in its construction or support, because the attraction of
+that substance on the needle would be fatal to its performance.
+
+From this cause the use of iron as ship-building material
+introduced a difficulty which it was feared would prove very
+serious. The thousands of tons of iron in a ship must exert a
+strong attraction on the magnetic needle. Another complication is
+introduced by the fact that the iron of the ship will always
+become more or less magnetic, and when the ship is built of steel,
+as modern ones are, this magnetism will be more or less permanent.
+
+We have already said that a magnet has the property of making
+steel or iron in its neighborhood into another magnet, with its
+poles pointing in the opposite direction. The consequence is that
+the magnetism of the earth itself will make iron or steel more or
+less magnetic. As a ship is built she thus becomes a great
+repository of magnetism, the direction of the force of which will
+depend upon the position in which she lay while building. If
+erected on the bank of an east and west stream, the north end of
+the ship will become the north pole of a magnet and the south end
+the south pole. Accordingly, when she is launched and proceeds to
+sea, the compass points not exactly according to the magnetism of
+the earth, but partly according to that of the ship also.
+
+The methods of obviating this difficulty have exercised the
+ingenuity of the ablest physicists from the beginning of iron ship
+building. One method is to place in the neighborhood of the
+compass, but not too near it, a steel bar magnetized in the
+opposite direction from that of the ship, so that the action of
+the latter shall be neutralized. But a perfect neutralization
+cannot be thus effected. It is all the more difficult to effect it
+because the magnetism of a ship is liable to change.
+
+The practical method therefore adopted is called "swinging the
+ship," an operation which passengers on ocean liners may have
+frequently noticed when approaching land. The ship is swung around
+so that her bow shall point in various directions. At each
+pointing the direction of the ship is noticed by sighting on the
+sun, and also the direction of the compass itself. In this way the
+error of the pointing of the compass as the ship swings around is
+found for every direction in which she may be sailing. A table can
+then be made showing what the pointing, according to the compass,
+should be in order that the ship may sail in any given direction.
+
+This, however, does not wholly avoid the danger. The tables thus
+made are good when the ship is on a level keel. If, from any cause
+whatever, she heels over to one side, the action will be
+different. Thus there is a "heeling error" which must be allowed
+for. It is supposed to have been from this source of error not
+having been sufficiently determined or appreciated that the
+lamentable wreck of the United States ship Huron off the coast of
+Hatteras occurred some twenty years ago.
+
+
+
+
+
+X
+
+THE FAIRYLAND OF GEOMETRY
+
+
+If the reader were asked in what branch of science the imagination
+is confined within the strictest limits, he would, I fancy, reply
+that it must be that of mathematics. The pursuer of this science
+deals only with problems requiring the most exact statements and
+the most rigorous reasoning. In all other fields of thought more
+or less room for play may be allowed to the imagination, but here
+it is fettered by iron rules, expressed in the most rigid logical
+form, from which no deviation can be allowed. We are told by
+philosophers that absolute certainty is unattainable in all
+ordinary human affairs, the only field in which it is reached
+being that of geometric demonstration.
+
+And yet geometry itself has its fairyland--a land in which the
+imagination, while adhering to the forms of the strictest
+demonstration, roams farther than it ever did in the dreams of
+Grimm or Andersen. One thing which gives this field its strictly
+mathematical character is that it was discovered and explored in
+the search after something to supply an actual want of
+mathematical science, and was incited by this want rather than by
+any desire to give play to fancy. Geometricians have always sought
+to found their science on the most logical basis possible, and
+thus have carefully and critically inquired into its foundations.
+The new geometry which has thus arisen is of two closely related
+yet distinct forms. One of these is called NON-EUCLIDIAN, because
+Euclid's axiom of parallels, which we shall presently explain, is
+ignored. In the other form space is assumed to have one or more
+dimensions in addition to the three to which the space we actually
+inhabit is confined. As we go beyond the limits set by Euclid in
+adding a fourth dimension to space, this last branch as well as
+the other is often designated non-Euclidian. But the more common
+term is hypergeometry, which, though belonging more especially to
+space of more than three dimensions, is also sometimes applied to
+any geometric system which transcends our ordinary ideas.
+
+In all geometric reasoning some propositions are necessarily taken
+for granted. These are called axioms, and are commonly regarded as
+self-evident. Yet their vital principle is not so much that of
+being self-evident as being, from the nature of the case,
+incapable of demonstration. Our edifice must have some support to
+rest upon, and we take these axioms as its foundation. One example
+of such a geometric axiom is that only one straight line can be
+drawn between two fixed points; in other words, two straight lines
+can never intersect in more than a single point. The axiom with
+which we are at present concerned is commonly known as the 11th of
+Euclid, and may be set forth in the following way: We have given a
+straight line, A B, and a point, P, with another line, C D,
+passing through it and capable of being turned around on P. Euclid
+assumes that this line C D will have one position in which it will
+be parallel to A B, that is, a position such that if the two lines
+are produced without end, they will never meet. His axiom is that
+only one such line can be drawn through P. That is to say, if we
+make the slightest possible change in the direction of the line C
+D, it will intersect the other line, either in one direction or
+the other.
+
+The new geometry grew out of the feeling that this proposition
+ought to be proved rather than taken as an axiom; in fact, that it
+could in some way be derived from the other axioms. Many
+demonstrations of it were attempted, but it was always found, on
+critical examination, that the proposition itself, or its
+equivalent, had slyly worked itself in as part of the base of the
+reasoning, so that the very thing to be proved was really taken
+for granted.
+
+[Illustration with caption: FIG. I]
+
+This suggested another course of inquiry. If this axiom of
+parallels does not follow from the other axioms, then from these
+latter we may construct a system of geometry in which the axiom of
+parallels shall not be true. This was done by Lobatchewsky and
+Bolyai, the one a Russian the other a Hungarian geometer, about
+1830.
+
+To show how a result which looks absurd, and is really
+inconceivable by us, can be treated as possible in geometry, we
+must have recourse to analogy. Suppose a world consisting of a
+boundless flat plane to be inhabited by reasoning beings who can
+move about at pleasure on the plane, but are not able to turn
+their heads up or down, or even to see or think of such terms as
+above them and below them, and things around them can be pushed or
+pulled about in any direction, but cannot be lifted up. People and
+things can pass around each other, but cannot step over anything.
+These dwellers in "flatland" could construct a plane geometry
+which would be exactly like ours in being based on the axioms of
+Euclid. Two parallel straight lines would never meet, though
+continued indefinitely.
+
+But suppose that the surface on which these beings live, instead
+of being an infinitely extended plane, is really the surface of an
+immense globe, like the earth on which we live. It needs no
+knowledge of geometry, but only an examination of any globular
+object--an apple, for example--to show that if we draw a line as
+straight as possible on a sphere, and parallel to it draw a small
+piece of a second line, and continue this in as straight a line as
+we can, the two lines will meet when we proceed in either
+direction one-quarter of the way around the sphere. For our "flat-
+land" people these lines would both be perfectly straight, because
+the only curvature would be in the direction downward, which they
+could never either perceive or discover. The lines would also
+correspond to the definition of straight lines, because any
+portion of either contained between two of its points would be the
+shortest distance between those points. And yet, if these people
+should extend their measures far enough, they would find any two
+parallel lines to meet in two points in opposite directions. For
+all small spaces the axioms of their geometry would apparently
+hold good, but when they came to spaces as immense as the semi-
+diameter of the earth, they would find the seemingly absurd result
+that two parallel lines would, in the course of thousands of
+miles, come together. Another result yet more astonishing would be
+that, going ahead far enough in a straight line, they would find
+that although they had been going forward all the time in what
+seemed to them the same direction, they would at the end of 25,000
+miles find themselves once more at their starting-point.
+
+One form of the modern non-Euclidian geometry assumes that a
+similar theorem is true for the space in which our universe is
+contained. Although two straight lines, when continued
+indefinitely, do not appear to converge even at the immense
+distances which separate us from the fixed stars, it is possible
+that there may be a point at which they would eventually meet
+without either line having deviated from its primitive direction
+as we understand the case. It would follow that, if we could start
+out from the earth and fly through space in a perfectly straight
+line with a velocity perhaps millions of times that of light, we
+might at length find ourselves approaching the earth from a
+direction the opposite of that in which we started. Our straight-
+line circle would be complete.
+
+Another result of the theory is that, if it be true, space, though
+still unbounded, is not infinite, just as the surface of a sphere,
+though without any edge or boundary, has only a limited extent of
+surface. Space would then have only a certain volume--a volume
+which, though perhaps greater than that of all the atoms in the
+material universe, would still be capable of being expressed in
+cubic miles. If we imagine our earth to grow larger and larger in
+every direction without limit, and with a speed similar to that we
+have described, so that to-morrow it was large enough to extend to
+the nearest fixed stars, the day after to yet farther stars, and
+so on, and we, living upon it, looked out for the result, we
+should, in time, see the other side of the earth above us, coming
+down upon us? as it were. The space intervening would grow
+smaller, at last being filled up. The earth would then be so
+expanded as to fill all existing space.
+
+This, although to us the most interesting form of the non-
+Euclidian geometry, is not the only one. The idea which
+Lobatchewsky worked out was that through a point more than one
+parallel to a given line could be drawn; that is to say, if
+through the point P we have already supposed another line were
+drawn making ever so small an angle with CD, this line also would
+never meet the line AB. It might approach the latter at first, but
+would eventually diverge. The two lines AB and CD, starting
+parallel, would eventually, perhaps at distances greater than that
+of the fixed stars, gradually diverge from each other. This system
+does not admit of being shown by analogy so easily as the other,
+but an idea of it may be had by supposing that the surface of
+"flat-land," instead of being spherical, is saddle-shaped.
+Apparently straight parallel lines drawn upon it would then
+diverge, as supposed by Bolyai. We cannot, however, imagine such a
+surface extended indefinitely without losing its properties. The
+analogy is not so clearly marked as in the other case.
+
+To explain hypergeometry proper we must first set forth what a
+fourth dimension of space means, and show how natural the way is
+by which it may be approached. We continue our analogy from "flat-
+land" In this supposed land let us make a cross--two straight
+lines intersecting at right angles. The inhabitants of this land
+understand the cross perfectly, and conceive of it just as we do.
+But let us ask them to draw a third line, intersecting in the same
+point, and perpendicular to both the other lines. They would at
+once pronounce this absurd and impossible. It is equally absurd
+and impossible to us if we require the third line to be drawn on
+the paper. But we should reply, "If you allow us to leave the
+paper or flat surface, then we can solve the problem by simply
+drawing the third line through the paper perpendicular to its
+surface."
+
+[Illustration with caption: FIG. 2]
+
+Now, to pursue the analogy, suppose that, after we have drawn
+three mutually perpendicular lines, some being from another sphere
+proposes to us the drawing of a fourth line through the same
+point, perpendicular to all three of the lines already there. We
+should answer him in the same way that the inhabitants of "flat-
+land" answered us: "The problem is impossible. You cannot draw any
+such line in space as we understand it." If our visitor conceived
+of the fourth dimension, he would reply to us as we replied to the
+"flat-land" people: "The problem is absurd and impossible if you
+confine your line to space as you understand it. But for me there
+is a fourth dimension in space. Draw your line through that
+dimension, and the problem will be solved. This is perfectly
+simple to me; it is impossible to you solely because your
+conceptions do not admit of more than three dimensions."
+
+Supposing the inhabitants of "flat-land" to be intellectual beings
+as we are, it would be interesting to them to be told what
+dwellers of space in three dimensions could do. Let us pursue the
+analogy by showing what dwellers in four dimensions might do.
+Place a dweller of "flat-land" inside a circle drawn on his plane,
+and ask him to step outside of it without breaking through it. He
+would go all around, and, finding every inch of it closed, he
+would say it was impossible from the very nature of the
+conditions. "But," we would reply, "that is because of your
+limited conceptions. We can step over it."
+
+"Step over it!" he would exclaim. "I do not know what that means.
+I can pass around anything if there is a way open, but I cannot
+imagine what you mean by stepping over it."
+
+But we should simply step over the line and reappear on the other
+side. So, if we confine a being able to move in a fourth dimension
+in the walls of a dungeon of which the sides, the floor, and the
+ceiling were all impenetrable, he would step outside of it without
+touching any part of the building, just as easily as we could step
+over a circle drawn on the plane without touching it. He would
+simply disappear from our view like a spirit, and perhaps reappear
+the next moment outside the prison. To do this he would only have
+to make a little excursion in the fourth dimension.
+
+[Illustration with caption: FIG. 3]
+
+Another curious application of the principle is more purely
+geometrical. We have here two triangles, of which the sides and
+angles of the one are all equal to corresponding sides and angles
+of the other. Euclid takes it for granted that the one triangle
+can be laid upon the other so that the two shall fit together. But
+this cannot be done unless we lift one up and turn it over. In the
+geometry of "flat-land" such a thing as lifting up is
+inconceivable; the two triangles could never be fitted together.
+
+[Illustration with caption: FIG 4]
+
+Now let us suppose two pyramids similarly related. All the faces
+and angles of the one correspond to the faces and angles of the
+other. Yet, lift them about as we please, we could never fit them
+together. If we fit the bases together the two will lie on
+opposite sides, one being below the other. But the dweller in four
+dimensions of space will fit them together without any trouble. By
+the mere turning over of one he will convert it into the other
+without any change whatever in the relative position of its parts.
+What he could do with the pyramids he could also do with one of us
+if we allowed him to take hold of us and turn a somersault with us
+in the fourth dimension. We should then come back into our natural
+space, but changed as if we were seen in a mirror. Everything on
+us would be changed from right to left, even the seams in our
+clothes, and every hair on our head. All this would be done
+without, during any of the motion, any change having occurred in
+the positions of the parts of the body.
+
+It is very curious that, in these transcendental speculations, the
+most rigorous mathematical methods correspond to the most
+mystical ideas of the Swedenborgian and other forms of religion.
+Right around us, but in a direction which we cannot conceive any
+more than the inhabitants of "flat-land" can conceive up and down,
+there may exist not merely another universe, but any number of
+universes. All that physical science can say against the
+supposition is that, even if a fourth dimension exists, there is
+some law of all the matter with which we are acquainted which
+prevents any of it from entering that dimension, so that, in our
+natural condition, it must forever remain unknown to us.
+
+Another possibility in space of four dimensions would be that of
+turning a hollow sphere, an india-rubber ball, for example, inside
+out by simple bending without tearing it. To show the motion in
+our space to which this is analogous, let us take a thin, round
+sheet of india-rubber, and cut out all the central part, leaving
+only a narrow ring round the border. Suppose the outer edge of
+this ring fastened down on a table, while we take hold of the
+inner edge and stretch it upward and outward over the outer edge
+until we flatten the whole ring on the table, upside down, with
+the inner edge now the outer one. This motion would be as
+inconceivable in "flat-land" as turning the ball inside out is to
+us.
+
+
+
+
+
+XI
+
+THE ORGANIZATION OF SCIENTIFIC RESEARCH
+
+
+The claims of scientific research on the public were never more
+forcibly urged than in Professor Ray Lankester's recent Romanes
+Lecture before the University of Oxford. Man is here eloquently
+pictured as Nature's rebel, who, under conditions where his great
+superior commands "Thou shalt die," replies "I will live." In
+pursuance of this determination, civilized man has proceeded so
+far in his interference with the regular course of Nature that he
+must either go on and acquire firmer control of the conditions, or
+perish miserably by the vengeance certain to be inflicted on the
+half-hearted meddler in great affairs. This rebel by every step
+forward renders himself liable to greater and greater penalties,
+and so cannot afford to pause or fail in one single step. One of
+Nature's most powerful agencies in thwarting his determination to
+live is found in disease-producing parasites. "Where there is one
+man of first-rate intelligence now employed in gaining knowledge
+of this agency, there should be a thousand. It should be as much
+the purpose of civilized nations to protect their citizens in this
+respect as it is to provide defence against human aggression."
+
+It was no part of the function of the lecturer to devise a plan
+for carrying on the great war he proposes to wage. The object of
+the present article is to contribute some suggestions in this
+direction; with especial reference to conditions in our own
+country; and no better text can be found for a discourse on the
+subject than the preceding quotation. In saying that there should
+be a thousand investigators of disease where there is now one, I
+believe that Professor Lankester would be the first to admit that
+this statement was that of an ideal to be aimed at, rather than of
+an end to be practically reached. Every careful thinker will agree
+that to gather a body of men, young or old, supply them with
+laboratories and microscopes, and tell them to investigate
+disease, would be much like sending out an army without trained
+leaders to invade an enemy's country.
+
+There is at least one condition of success in this line which is
+better fulfilled in our own country than in any other; and that is
+liberality of support on the part of munificent citizens desirous
+of so employing their wealth as to promote the public good.
+Combining this instrumentality with the general public spirit of
+our people, it must be admitted that, with all the disadvantages
+under which scientific research among us has hitherto labored,
+there is still no country to which we can look more hopefully than
+to our own as the field in which the ideal set forth by Professor
+Lankester is to be pursued. Some thoughts on the question how
+scientific research may be most effectively promoted in our own
+country through organized effort may therefore be of interest. Our
+first step will be to inquire what general lessons are to be
+learned from the experience of the past.
+
+The first and most important of these lessons is that research has
+never reached its highest development except at centres where
+bodies of men engaged in it have been brought together, and
+stimulated to action by mutual sympathy and support. We must call
+to mind that, although the beginnings of modern science were laid
+by such men as Copernicus, Galileo, Leonardo da Vinci, and
+Torricelli, before the middle of the seventeenth century, unbroken
+activity and progress date from the foundations of the Academy of
+Sciences of Paris and the Royal Society of London at that time.
+The historic fact that the bringing of men together, and their
+support by an intelligent and interested community, is the first
+requirement to be kept in view can easily be explained. Effective
+research involves so intricate a network of problems and
+considerations that no one engaged in it can fail to profit by the
+suggestions of kindred spirits, even if less acquainted with the
+subject than he is himself. Intelligent discussion suggests new
+ideas and continually carries the mind to a higher level of
+thought. We must not regard the typical scientific worker, even of
+the highest class, as one who, having chosen his special field and
+met with success in cultivating it, has only to be supplied with
+the facilities he may be supposed to need in order to continue his
+work in the most efficient way. What we have to deal with is not a
+fixed and permanent body of learned men, each knowing all about
+the field of work in which he is engaged, but a changing and
+growing class, constantly recruited by beginners at the bottom of
+the scale, and constantly depleted by the old dropping away at the
+top. No view of the subject is complete which does not embrace the
+entire activity of the investigator, from the tyro to the leader.
+The leader himself, unless engaged in the prosecution of some
+narrow specialty, can rarely be so completely acquainted with his
+field as not to need information from others. Without this, he is
+constantly liable to be repeating what has already been better
+done than he can do it himself, of following lines which are known
+to lead to no result, and of adopting methods shown by the
+experience of others not to be the best. Even the books and
+published researches to which he must have access may be so
+voluminous that he cannot find time to completely examine them for
+himself; or they may be inaccessible. All this will make it clear
+that, with an occasional exception, the best results of research
+are not to be expected except at centres where large bodies of men
+are brought into close personal contact.
+
+In addition to the power and facility acquired by frequent
+discussion with his fellows, the appreciation and support of an
+intelligent community, to whom the investigator may, from time to
+time, make known his thoughts and the results of his work, add a
+most effective stimulus. The greater the number of men of like
+minds that can be brought together and the larger the community
+which interests itself in what they are doing, the more rapid will
+be the advance and the more effective the work carried on. It is
+thus that London, with its munificently supported institutions,
+and Paris and Berlin, with their bodies of investigators supported
+either by the government or by various foundations, have been for
+more than three centuries the great centres where we find
+scientific activity most active and most effective. Looking at
+this undoubted fact, which has asserted itself through so long a
+period, and which asserts itself today more strongly than ever,
+the writer conceives that there can be no question as to one
+proposition. If we aim at the single object of promoting the
+advance of knowledge in the most effective way, and making our own
+country the leading one in research, our efforts should be
+directed towards bringing together as many scientific workers as
+possible at a single centre, where they can profit in the highest
+degree by mutual help, support, and sympathy.
+
+In thus strongly setting forth what must seem an indisputable
+conclusion, the writer does not deny that there are drawbacks to
+such a policy, as there are to every policy that can be devised
+aiming at a good result. Nature offers to society no good that she
+does not accompany by a greater or less measure of evil The only
+question is whether the good outweighs the evil. In the present
+case, the seeming evil, whether real or not, is that of
+centralization. A policy tending in this direction is held to be
+contrary to the best interests of science in quarters entitled to
+so much respect that we must inquire into the soundness of the
+objection.
+
+It would be idle to discuss so extreme a question as whether we
+shall take all the best scientific investigators of our country
+from their several seats of learning and attract them to some one
+point. We know that this cannot be done, even were it granted that
+success would be productive of great results. The most that can be
+done is to choose some existing centre of learning, population,
+wealth, and influence, and do what we can to foster the growth of
+science at that centre by attracting thither the greatest possible
+number of scientific investigators, especially of the younger
+class, and making it possible for them to pursue their researches
+in the most effective way. This policy would not result in the
+slightest harm to any institution or community situated elsewhere.
+It would not be even like building up a university to outrank all
+the others of our country; because the functions of the new
+institution, if such should be founded, would in its relations to
+the country be radically different from those of a university. Its
+primary object would not be the education of youth, but the
+increase of knowledge. So far as the interests of any community or
+of the world at large are concerned, it is quite indifferent where
+knowledge may be acquired, because, when once acquired and made
+public, it is free to the world. The drawbacks suffered by other
+centres would be no greater than those suffered by our Western
+cities, because all the great departments of the government are
+situated at a single distant point. Strong arguments could
+doubtless be made for locating some of these departments in the
+Far West, in the Mississippi Valley, or in various cities of the
+Atlantic coast; but every one knows that any local advantages thus
+gained would be of no importance compared with the loss of that
+administrative efficiency which is essential to the whole country.
+
+There is, therefore, no real danger from centralization. The
+actual danger is rather in the opposite direction; that the
+sentiment against concentrating research will prove to operate too
+strongly. There is a feeling that it is rather better to leave
+every investigator where he chances to be at the moment, a feeling
+which sometimes finds expression in the apothegm that we cannot
+transplant a genius. That such a proposition should find
+acceptance affords a striking example of the readiness of men to
+accept a euphonious phrase without inquiring whether the facts
+support the doctrine which it enunciates. The fact is that many,
+perhaps the majority, of the great scientific investigators of
+this and of former times have done their best work through being
+transplanted. As soon as the enlightened monarchs of Europe felt
+the importance of making their capitals great centres of learning,
+they began to invite eminent men of other countries to their own.
+Lagrange was an Italian transplanted to Paris, as a member of the
+Academy of Sciences, after he had shown his powers in his native
+country. His great contemporary, Euler, was a Swiss, transplanted
+first to St. Petersburg, then invited by Frederick the Great to
+become a member of the Berlin Academy, then again attracted to St.
+Petersburg. Huyghens was transplanted from his native country to
+Paris. Agassiz was an exotic, brought among us from Switzerland,
+whose activity during the generation he passed among us was as
+great and effective as at any time of his life. On the Continent,
+outside of France, the most eminent professors in the universities
+have been and still are brought from distant points. So numerous
+are the cases of which these are examples that it would be more in
+accord with the facts to claim that it is only by transplanting a
+genius that we stimulate him to his best work.
+
+Having shown that the best results can be expected only by
+bringing into contact as many scientific investigators as
+possible, the next question which arises is that of their
+relations to one another. It may be asked whether we shall aim at
+individualism or collectivism. Shall our ideal be an organized
+system of directors, professors, associates, assistants, fellows;
+or shall it be a collection of individual workers, each pursuing
+his own task in the way he deems best, untrammelled by authority?
+
+The reply to this question is that there is in this special case
+no antagonism between the two ideas. The most effective
+organization will aim both at the promotion of individual effort,
+and at subordination and co-operation. It would be a serious error
+to formulate any general rule by which all cases should be
+governed. The experience of the past should be our guide, so far
+as it applies to present and future conditions; but in availing
+ourselves of it we must remember that conditions are constantly
+changing, and must adapt our policy to the problems of the future.
+In doing this, we shall find that different fields of research
+require very different policies as regards co-operation and
+subordination. It will be profitable to point out those special
+differences, because we shall thereby gain a more luminous insight
+into the problems which now confront the scientific investigator,
+and better appreciate their variety, and the necessity of
+different methods of dealing with them.
+
+At one extreme, we have the field of normative science, work in
+which is of necessity that of the individual mind alone. This
+embraces pure mathematics and the methods of science in their
+widest range. The common interests of science require that these
+methods shall be worked out and formulated for the guidance of
+investigators generally, and this work is necessarily that of the
+individual brain.
+
+At the other extreme, we have the great and growing body of
+sciences of observation. Through the whole nineteenth century, to
+say nothing of previous centuries, organizations, and even
+individuals, have been engaged in recording the innumerable phases
+of the course of nature, hoping to accumulate material that
+posterity shall be able to utilize for its benefit. We have
+observations astronomical, meteorological, magnetic, and social,
+accumulating in constantly increasing volume, the mass of which is
+so unmanageable with our present organizations that the question
+might well arise whether almost the whole of it will not have to
+be consigned to oblivion. Such a conclusion should not be
+entertained until we have made a vigorous effort to find what pure
+metal of value can be extracted from the mass of ore. To do this
+requires the co-operation of minds of various orders, quite akin
+in their relations to those necessary in a mine or great
+manufacturing establishment. Laborers whose duties are in a large
+measure matters of routine must be guided by the skill of a class
+higher in quality and smaller in number than their own, and these
+again by the technical knowledge of leaders in research. Between
+these extremes we have a great variety of systems of co-operation.
+
+There is another feature of modern research the apprehension of
+which is necessary to the completeness of our view. A cursory
+survey of the field of science conveys the impression that it
+embraces only a constantly increasing number of disconnected
+specialties, in which each cultivator knows little or nothing of
+what is being done by others. Measured by its bulk, the published
+mass of scientific research is increasing in a more than
+geometrical ratio. Not only do the publications of nearly every
+scientific society increase in number and volume, but new and
+vigorous societies are constantly organized to add to the sum
+total. The stately quartos issued from the presses of the leading
+academies of Europe are, in most cases, to be counted by hundreds.
+The Philosophical Transactions of the Royal Society already number
+about two hundred volumes, and the time when the Memoirs of the
+French Academy of Sciences shall reach the thousand mark does not
+belong to the very remote future. Besides such large volumes,
+these and other societies publish smaller ones in a constantly
+growing number. In addition to the publications of learned
+societies, there are journals devoted to each scientific
+specialty, which seem to propagate their species by subdivision in
+much the same way as some of the lower orders of animal life.
+Every new publication of the kind is suggested by the wants of a
+body of specialists, who require a new medium for their researches
+and communications. The time has already come when we cannot
+assume that any specialist is acquainted with all that is being
+done even in his own line. To keep the run of this may well be
+beyond his own powers; more he can rarely attempt.
+
+What is the science of the future to do when this huge mass
+outgrows the space that can be found for it in the libraries, and
+what are we to say of the value of it all? Are all these
+scientific researches to be classed as really valuable
+contributions to knowledge, or have we only a pile in which
+nuggets of gold are here and there to be sought for? One
+encouraging answer to such a question is that, taking the
+interests of the world as a whole, scientific investigation has
+paid for itself in benefits to humanity a thousand times over, and
+that all that is known to-day is but an insignificant fraction of
+what Nature has to show us. Apart from this, another feature of
+the science of our time demands attention. While we cannot hope
+that the multiplication of specialties will cease, we find that
+upon the process of differentiation and subdivision is now being
+superposed a form of evolution, tending towards the general unity
+of all the sciences, of which some examples may be pointed out.
+
+Biological science, which a generation ago was supposed to be at
+the antipodes of exact science, is becoming more and more exact,
+and is cultivated by methods which are developed and taught by
+mathematicians. Psychophysics--the study of the operations of the
+mind by physical apparatus of the same general nature as that used
+by the chemist and physicist--is now an established branch of
+research. A natural science which, if any comparisons are
+possible, may outweigh all others in importance to the race, is
+the rising one of "eugenics,"--the improvement of the human race
+by controlling the production of its offspring. No better example
+of the drawbacks which our country suffers as a seat of science
+can be given than the fact that the beginning of such a science
+has been possible only at the seat of a larger body of cultivated
+men than our land has yet been able to bring together. Generations
+may elapse before the seed sown by Mr. Francis Galton, from which
+grew the Eugenic Society, shall bear full fruit in the adoption of
+those individual efforts and social regulations necessary to the
+propagation of sound and healthy offspring on the part of the
+human family. But when this comes about, then indeed will
+Professor Lankester's "rebel against Nature" find his independence
+acknowledged by the hitherto merciless despot that has decreed
+punishment for his treason.
+
+This new branch of science from which so much may be expected is
+the offshoot of another, the rapid growth of which illustrates the
+rapid invasion of the most important fields of thought by the
+methods of exact science. It is only a few years since it was
+remarked of Professor Karl Pearson's mathematical investigations
+into the laws of heredity, and the biological questions associated
+with these laws, that he was working almost alone, because the
+biologists did not understand his mathematics, while the
+mathematicians were not interested in his biology. Had he not
+lived at a great centre of active thought, within the sphere of
+influence of the two great universities of England, it is quite
+likely that this condition of isolation would have been his to the
+end. But, one by one, men were found possessing the skill and
+interest in the subject necessary to unite in his work, which now
+has not only a journal of its own, but is growing in a way which,
+though slow, has all the marks of healthy progress towards an end
+the importance of which has scarcely dawned upon the public mind.
+
+Admitting that an organized association of investigators is of the
+first necessity to secure the best results in the scientific work
+of the future, we meet the question of the conditions and auspices
+under which they are to be brought together. The first thought to
+strike us at this point may well be that we have, in our great
+universities, organizations which include most of the leading men
+now engaged in scientific research, whose personnel and facilities
+we should utilize. Admitting, as we all do, that there are already
+too many universities, and that better work would be done by a
+consolidation of the smaller ones, a natural conclusion is that
+the end in view will be best reached through existing
+organizations. But it would be a great mistake to jump at this
+conclusion without a careful study of the conditions. The brief
+argument--there are already too many institutions--instead of
+having more we should strengthen those we have--should not be
+accepted without examination. Had it been accepted thirty years
+ago, there are at least two great American universities of to-day
+which would not have come into being, the means devoted to their
+support having been divided among others. These are the Johns
+Hopkins and the University of Chicago. What would have been gained
+by applying the argument in these cases? The advantage would have
+been that, instead of 146 so-called universities which appear to-
+day in the Annual Report of the Bureau of Education, we should
+have had only 144. The work of these 144 would have been
+strengthened by an addition, to their resources, represented by
+the endowments of Baltimore and Chicago, and sufficient to add
+perhaps one professor to the staff of each. Would the result have
+been better than it actually has been? Have we not gained anything
+by allowing the argument to be forgotten in the cases of these two
+institutions? I do not believe that any who carefully look at the
+subject will hesitate in answering this question in the
+affirmative. The essential point is that the Johns Hopkins
+University did not merely add one to an already overcrowded list,
+but that it undertook a mission which none of the others was then
+adequately carrying out. If it did not plant the university idea
+in American soil, it at least gave it an impetus which has now
+made it the dominant one in the higher education of almost every
+state.
+
+The question whether the country at large would have reaped a
+greater benefit, had the professors of the University of Chicago,
+with the appliances they now command, been distributed among fifty
+or a hundred institutions in every quarter of the land, than it
+has actually reaped from that university, is one which answers
+itself. Our two youngest universities have attained success, not
+because two have thus been added to the number of American
+institutions of learning, but because they had a special mission,
+required by the advance of the age, for which existing
+institutions were inadequate.
+
+The conclusion to which these considerations lead is simple. No
+new institution is needed to pursue work on traditional lines,
+guided by traditional ideas. But, if a new idea is to be
+vigorously prosecuted, then a young and vigorous institution,
+specially organized to put the idea into effect, is necessary. The
+project of building up in our midst, at the most appropriate
+point, an organization of leading scientific investigators, for
+the single purpose of giving a new impetus to American science
+and, if possible, elevating the thought of the country and of the
+world to a higher plane, involves a new idea, which can best be
+realized by an institution organized for the special purpose.
+While this purpose is quite in line with that of the leading
+universities, it goes too far beyond them to admit of its complete
+attainment through their instrumentality. The first object of a
+university is the training of the growing individual for the
+highest duties of life. Additions to the mass of knowledge have
+not been its principal function, nor even an important function in
+our own country, until a recent time. The primary object of the
+proposed institution is the advance of knowledge and the opening
+up of new lines of thought, which, it may be hoped, are to prove
+of great import to humanity. It does not follow that the function
+of teaching shall be wholly foreign to its activities. It must
+take up the best young men at the point where universities leave
+them, and train them in the arts of thinking and investigating.
+But this training will be beyond that which any regular university
+is carrying out.
+
+In pursuing our theme the question next arises as to the special
+features of the proposed association. The leading requirement is
+one that cannot be too highly emphasized. How clearly soever the
+organizers may have in their minds' eye the end in view, they must
+recognize the fact that it cannot be attained in a day. In every
+branch of work which is undertaken, there must be a single leader,
+and he must be the best that the country, perhaps even the world,
+can produce. The required man is not to be found without careful
+inquiry; in many branches he may be unattainable for years. When
+such is the case, wait patiently till he appears. Prudence
+requires that the fewest possible risks would be taken, and that
+no leader should be chosen except one of tried experience and
+world-wide reputation. Yet we should not leave wholly out of sight
+the success of the Johns Hopkins University in selecting, at its
+very foundation, young men who were to prove themselves the
+leaders of the future. This experience may admit of being
+repeated, if it be carefully borne in mind that young men of
+promise are to be avoided and young men of performance only to be
+considered. The performance need not be striking: ex pede Herculem
+may be possible; but we must be sure of the soundness of our
+judgment before accepting our Hercules. This requires a master.
+Clerk-Maxwell, who never left his native island to visit our
+shores, is entitled to honor as a promoter of American science for
+seeing the lion's paw in the early efforts of Rowland, for which
+the latter was unable to find a medium of publication in his own
+country. It must also be admitted that the task is more serious
+now than it was then, because, from the constantly increasing
+specialization of science, it has become difficult for a
+specialist in one line to ascertain the soundness of work in
+another. With all the risks that may be involved in the
+proceeding, it will be quite possible to select an effective body
+of leaders, young and old, with whom an institution can begin. The
+wants of these men will be of the most varied kind. One needs
+scarcely more than a study and library; another must have small
+pieces of apparatus which he can perhaps design and make for
+himself. Another may need apparatus and appliances so expensive
+that only an institution at least as wealthy as an ordinary
+university would be able to supply them. The apparatus required by
+others will be very largely human--assistants of every grade, from
+university graduates of the highest standing down to routine
+drudges and day-laborers. Workrooms there must be; but it is
+hardly probable that buildings and laboratories of a highly
+specialized character will be required at the outset. The best
+counsel will be necessary at every step, and in this respect the
+institution must start from simple beginnings and grow slowly.
+Leaders must be added one by one, each being judged by those who
+have preceded him before becoming in his turn a member of the
+body. As the body grows its members must be kept in personal
+touch, talk together, pull together, and act together.
+
+The writer submits these views to the great body of his fellow-
+citizens interested in the promotion of American science with the
+feeling that, though his conclusions may need amendment in
+details, they rest upon facts of the past and present which have
+not received the consideration which they merit. What he most
+strongly urges is that the whole subject of the most efficient
+method of promoting research upon a higher plane shall be
+considered with special reference to conditions in our own
+country; and that the lessons taught by the history and progress
+of scientific research in all countries shall be fully weighed and
+discussed by those most interested in making this form of effort a
+more important feature of our national life. When this is done, he
+will feel that his purpose in inviting special consideration to
+his individual views has been in great measure reached.
+
+
+
+
+
+XII
+
+CAN WE MAKE IT RAIN?
+
+
+To the uncritical observer the possible achievements of invention
+and discovery seem boundless. Half a century ago no idea could
+have appeared more visionary than that of holding communication in
+a few seconds of time with our fellows in Australia, or having a
+talk going on viva voce between a man in Washington and another in
+Boston. The actual attainment of these results has naturally given
+rise to the belief that the word "impossible" has disappeared from
+our vocabulary. To every demonstration that a result cannot be
+reached the answer is, Did not one Lardner, some sixty years ago,
+demonstrate that a steamship could not cross the Atlantic? If we
+say that for every actual discovery there are a thousand visionary
+projects, we are told that, after all, any given project may be
+the one out of the thousand.
+
+In a certain way these hopeful anticipations are justified. We
+cannot set any limit either to the discovery of new laws of nature
+or to the ingenious combination of devices to attain results which
+now look impossible. The science of to-day suggests a boundless
+field of possibilities. It demonstrates that the heat which the
+sun radiates upon the earth in a single day would suffice to drive
+all the steamships now on the ocean and run all the machinery on
+the land for a thousand years. The only difficulty is how to
+concentrate and utilize this wasted energy. From the stand-point
+of exact science aerial navigation is a very simple matter. We
+have only to find the proper combination of such elements as
+weight, power, and mechanical force. Whenever Mr. Maxim can make
+an engine strong and light enough, and sails large, strong, and
+light enough, and devise the machinery required to connect the
+sails and engine, he will fly. Science has nothing but encouraging
+words for his project, so far as general principles are concerned.
+Such being the case, I am not going to maintain that we can never
+make it rain.
+
+But I do maintain two propositions. If we are ever going to make
+it rain, or produce any other result hitherto unattainable, we
+must employ adequate means. And if any proposed means or agency is
+already familiar to science, we may be able to decide beforehand
+whether it is adequate. Let us grant that out of a thousand
+seemingly visionary projects one is really sound. Must we try the
+entire thousand to find the one? By no means. The chances are that
+nine hundred of them will involve no agency that is not already
+fully understood, and may, therefore, be set aside without even
+being tried. To this class belongs the project of producing rain
+by sound. As I write, the daily journals are announcing the
+brilliant success of experiments in this direction; yet I
+unhesitatingly maintain that sound cannot make rain, and propose
+to adduce all necessary proof of my thesis. The nature of sound is
+fully understood, and so are the conditions under which the
+aqueous vapor in the atmosphere may be condensed. Let us see how
+the case stands.
+
+A room of average size, at ordinary temperature and under usual
+conditions, contains about a quart of water in the form of
+invisible vapor. The whole atmosphere is impregnated with vapor in
+about the same proportion. We must, however, distinguish between
+this invisible vapor and the clouds or other visible masses to
+which the same term is often applied. The distinction may be very
+clearly seen by watching the steam coming from the spout of a
+boiling kettle. Immediately at the spout the escaping steam is
+transparent and invisible; an inch or two away a white cloud is
+formed, which we commonly call steam, and which is seen belching
+out to a distance of one or more feet, and perhaps filling a
+considerable space around the kettle; at a still greater distance
+this cloud gradually disappears. Properly speaking, the visible
+cloud is not vapor or steam at all, but minute particles or drops
+of water in a liquid state. The transparent vapor at the mouth of
+the kettle is the true vapor of water, which is condensed into
+liquid drops by cooling; but after being diffused through the air
+these drops evaporate and again become true vapor. Clouds, then,
+are not formed of true vapor, but consist of impalpable particles
+of liquid water floating or suspended in the air.
+
+But we all know that clouds do not always fall as rain. In order
+that rain may fall the impalpable particles of water which form
+the cloud must collect into sensible drops large enough to fall to
+the earth. Two steps are therefore necessary to the formation of
+rain: the transparent aqueous vapor in the air must be condensed
+into clouds, and the material of the clouds must agglomerate into
+raindrops.
+
+No physical fact is better established than that, under the
+conditions which prevail in the atmosphere, the aqueous vapor of
+the air cannot be condensed into clouds except by cooling. It is
+true that in our laboratories it can be condensed by compression.
+But, for reasons which I need not explain, condensation by
+compression cannot take place in the air. The cooling which
+results in the formation of clouds and rain may come in two ways.
+Rains which last for several hours or days are generally produced
+by the intermixture of currents of air of different temperatures.
+A current of cold air meeting a current of warm, moist air in its
+course may condense a considerable portion of the moisture into
+clouds and rain, and this condensation will go on as long as the
+currents continue to meet. In a hot spring day a mass of air which
+has been warmed by the sun, and moistened by evaporation near the
+surface of the earth, may rise up and cool by expansion to near
+the freezing-point. The resulting condensation of the moisture may
+then produce a shower or thunder-squall. But the formation of
+clouds in a clear sky without motion of the air or change in the
+temperature of the vapor is simply impossible. We know by abundant
+experiments that a mass of true aqueous vapor will never condense
+into clouds or drops so long as its temperature and the pressure
+of the air upon it remain unchanged.
+
+Now let us consider sound as an agent for changing the state of
+things in the air. It is one of the commonest and simplest
+agencies in the world, which we can experiment upon without
+difficulty. It is purely mechanical in its action. When a bomb
+explodes, a certain quantity of gas, say five or six cubic yards,
+is suddenly produced. It pushes aside and compresses the
+surrounding air in all directions, and this motion and compression
+are transmitted from one portion of the air to another. The amount
+of motion diminishes as the square of the distance; a simple
+calculation shows that at a quarter of a mile from the point of
+explosion it would not be one ten-thousandth of an inch. The
+condensation is only momentary; it may last the hundredth or the
+thousandth of a second, according to the suddenness and violence
+of the explosion; then elasticity restores the air to its original
+condition and everything is just as it was before the explosion. A
+thousand detonations can produce no more effect upon the air, or
+upon the watery vapor in it, than a thousand rebounds of a small
+boy's rubber ball would produce upon a stonewall. So far as the
+compression of the air could produce even a momentary effect, it
+would be to prevent rather than to cause condensation of its
+vapor, because it is productive of heat, which produces
+evaporation, not condensation.
+
+The popular notion that sound may produce rain is founded
+principally upon the supposed fact that great battles have been
+followed by heavy rains. This notion, I believe, is not confirmed
+by statistics; but, whether it is or not, we can say with
+confidence that it was not the sound of the cannon that produced
+the rain. That sound as a physical factor is quite insignificant
+would be evident were it not for our fallacious way of measuring
+it. The human ear is an instrument of wonderful delicacy, and when
+its tympanum is agitated by a sound we call it a "concussion"
+when, in fact, all that takes place is a sudden motion back and
+forth of a tenth, a hundredth, or a thousandth of an inch,
+accompanied by a slight momentary condensation. After these
+motions are completed the air is exactly in the same condition as
+it was before; it is neither hotter nor colder; no current has
+been produced, no moisture added.
+
+If the reader is not satisfied with this explanation, he can try a
+very simple experiment which ought to be conclusive. If he will
+explode a grain of dynamite, the concussion within a foot of the
+point of explosion will be greater than that which can be produced
+by the most powerful bomb at a distance of a quarter of a mile. In
+fact, if the latter can condense vapor a quarter of a mile away,
+then anybody can condense vapor in a room by slapping his hands.
+Let us, therefore, go to work slapping our hands, and see how long
+we must continue before a cloud begins to form.
+
+What we have just said applies principally to the condensation of
+invisible vapor. It may be asked whether, if clouds are already
+formed, something may not be done to accelerate their condensation
+into raindrops large enough to fall to the ground. This also may
+be the subject of experiment. Let us stand in the steam escaping
+from a kettle and slap our hands. We shall see whether the steam
+condenses into drops. I am sure the experiment will be a failure;
+and no other conclusion is possible than that the production of
+rain by sound or explosions is out of the question.
+
+It must, however, be added that the laws under which the
+impalpable particles of water in clouds agglomerate into drops of
+rain are not yet understood, and that opinions differ on this
+subject. Experiments to decide the question are needed, and it is
+to be hoped that the Weather Bureau will undertake them. For
+anything we know to the contrary, the agglomeration may be
+facilitated by smoke in the air. If it be really true that rains
+have been produced by great battles, we may say with confidence
+that they were produced by the smoke from the burning powder
+rising into the clouds and forming nuclei for the agglomeration
+into drops, and not by the mere explosion. If this be the case, if
+it was the smoke and not the sound that brought the rain, then by
+burning gunpowder and dynamite we are acting much like Charles
+Lamb's Chinamen who practised the burning of their houses for
+several centuries before finding out that there was any cheaper
+way of securing the coveted delicacy of roast pig.
+
+But how, it may be asked, shall we deal with the fact that Mr.
+Dyrenforth's recent explosions of bombs under a clear sky in Texas
+were followed in a few hours, or a day or two, by rains in a
+region where rain was almost unknown? I know too little about the
+fact, if such it be, to do more than ask questions about it
+suggested by well-known scientific truths. If there is any
+scientific result which we can accept with confidence, it is that
+ten seconds after the sound of the last bomb died away, silence
+resumed her sway. From that moment everything in the air--
+humidity, temperature, pressure, and motion--was exactly the same
+as if no bomb had been fired. Now, what went on during the hours
+that elapsed between the sound of the last bomb and the falling of
+the first drop of rain? Did the aqueous vapor already in the
+surrounding air slowly condense into clouds and raindrops in
+defiance of physical laws? If not, the hours must have been
+occupied by the passage of a mass of thousands of cubic miles of
+warm, moist air coming from some other region to which the sound
+could not have extended. Or was Jupiter Pluvius awakened by the
+sound after two thousand years of slumber, and did the laws of
+nature become silent at his command? When we transcend what is
+scientifically possible, all suppositions are admissible; and we
+leave the reader to take his choice between these and any others
+he may choose to invent.
+
+One word in justification of the confidence with which I have
+cited established physical laws. It is very generally supposed
+that most great advances in applied science are made by rejecting
+or disproving the results reached by one's predecessors. Nothing
+could be farther from the truth. As Huxley has truly said, the
+army of science has never retreated from a position once gained.
+Men like Ohm and Maxwell have reduced electricity to a
+mathematical science, and it is by accepting, mastering, and
+applying the laws of electric currents which they discovered and
+expounded that the electric light, electric railway, and all other
+applications of electricity have been developed. It is by applying
+and utilizing the laws of heat, force, and vapor laid down by such
+men as Carnot and Regnault that we now cross the Atlantic in six
+days. These same laws govern the condensation of vapor in the
+atmosphere; and I say with confidence that if we ever do learn to
+make it rain, it will be by accepting and applying them, and not
+by ignoring or trying to repeal them.
+
+How much the indisposition of our government to secure expert
+scientific evidence may cost it is strikingly shown by a recent
+example. It expended several million dollars on a tunnel and
+water-works for the city of Washington, and then abandoned the
+whole work. Had the project been submitted to a commission of
+geologists, the fact that the rock-bed under the District of
+Columbia would not stand the continued action of water would have
+been immediately reported, and all the money expended would have
+been saved. The fact is that there is very little to excite
+popular interest in the advance of exact science. Investigators
+are generally quiet, unimpressive men, rather diffident, and
+wholly wanting in the art of interesting the public in their work.
+It is safe to say that neither Lavoisier, Galvani, Ohm, Regnault,
+nor Maxwell could have gotten the smallest appropriation through
+Congress to help make discoveries which are now the pride of our
+century. They all dealt in facts and conclusions quite devoid of
+that grandeur which renders so captivating the project of
+attacking the rains in their aerial stronghold with dynamite
+bombs.
+
+
+
+
+
+XIII
+
+THE ASTRONOMICAL EPHEMERIS AND THE NAUTICAL ALMANAC
+
+[Footnote: Read before the U S Naval Institute, January 10, 1879.]
+
+
+Although the Nautical Almanacs of the world, at the present time,
+are of comparatively recent origin, they have grown from small
+beginnings, the tracing of which is not unlike that of the origin
+of species by the naturalist of the present day. Notwithstanding
+its familiar name, it has always been designed rather for
+astronomical than for nautical purposes. Such a publication would
+have been of no use to the navigator before he had instruments
+with which to measure the altitudes of the heavenly bodies. The
+earlier navigators seldom ventured out of sight of land, and
+during the night they are said to have steered by the "Cynosure"
+or constellation of the Great Bear, a practice which has brought
+the name of the constellation into our language of the present day
+to designate an object on which all eyes are intently fixed. This
+constellation was a little nearer the pole in former ages than at
+the present time; still its distance was always so great that its
+use as a mark of the northern point of the horizon does not
+inspire us with great respect for the accuracy with which the
+ancient navigators sought to shape their course.
+
+The Nautical Almanac of the present day had its origin in the
+Astronomical Ephemerides called forth by the needs of predictions
+of celestial motions both on the part of the astronomer and the
+citizen. So long as astrology had a firm hold on the minds of men,
+the positions of the planets were looked to with great interest.
+The theories of Ptolemy, although founded on a radically false
+system, nevertheless sufficed to predict the position of the sun,
+moon, and planets, with all the accuracy necessary for the
+purposes of the daily life of the ancients or the sentences of
+their astrologers. Indeed, if his tables were carried down to the
+present time, the positions of the heavenly bodies would be so few
+degrees in error that their recognition would be very easy. The
+times of most of the eclipses would be predicted within a few
+hours, and the conjunctions of the planets within a few days. Thus
+it was possible for the astronomers of the Middle Ages to prepare
+for their own use, and that of the people, certain rude
+predictions respecting the courses of the sun and moon and the
+aspect of the heavens, which served the purpose of daily life and
+perhaps lessened the confusion arising from their complicated
+calendars. In the signs of the zodiac and the different effects
+which follow from the sun and moon passing from sign to sign,
+still found in our farmers' almanacs, we have the dying traces of
+these ancient ephemerides.
+
+The great Kepler was obliged to print an astrological almanac in
+virtue of his position as astronomer of the court of the King of
+Austria. But, notwithstanding the popular belief that astronomy
+had its origin in astrology, the astronomical writings of all ages
+seem to show that the astronomers proper never had any belief in
+astrology. To Kepler himself the necessity for preparing this
+almanac was a humiliation to which he submitted only through the
+pressure of poverty. Subsequent ephemerides were prepared with
+more practical objects. They gave the longitudes of the planets,
+the position of the sun, the time of rising and setting, the
+prediction of eclipses, etc.
+
+They have, of course, gradually increased in accuracy as the
+tables of the celestial motions were improved from time to time.
+At first they were not regular, annual publications, issued by
+governments, as at the present time, but the works of individual
+astronomers who issued their ephemerides for several years in
+advance, at irregular intervals. One man might issue one, two, or
+half a dozen such volumes, as a private work, for the benefit of
+his fellows, and each might cover as many years as he thought
+proper.
+
+The first publication of this sort, which I have in my possession,
+is the Ephemerides of Manfredi, of Bonn, computed for the years
+1715 to 1725, in two volumes.
+
+Of the regular annual ephemerides the earliest, so far as I am
+aware, is the Connaissance des Temps or French Nautical Almanac.
+The first issue was in the year 1679, by Picard, and it has been
+continued without interruption to the present time. Its early
+numbers were, of course, very small, and meagre in their details.
+They were issued by the astronomers of the French Academy of
+Sciences, under the combined auspices of the academy and the
+government. They included not merely predictions from the tables,
+but also astronomical observations made at the Paris Observatory
+or elsewhere. When the Bureau of Longitudes was created in 1795,
+the preparation of the work was intrusted to it, and has remained
+in its charge until the present time. As it is the oldest, so, in
+respect at least to number of pages, it is the largest ephemeris
+of the present time. The astronomical portion of the volume for
+1879 fills more than seven hundred pages, while the table of
+geographical positions, which has always been a feature of the
+work, contains nearly one hundred pages more.
+
+The first issue of the British Nautical Almanac was that for the
+year 1767 and appeared in 1766. It differs from the French Almanac
+in owing its origin entirely to the needs of navigation. The
+British nation, as the leading maritime power of the world, was
+naturally interested in the discovery of a method by which the
+longitude could be found at sea. As most of my hearers are
+probably aware, there was, for many years, a standing offer by the
+British government, of ten thousand pounds for the discovery of a
+practical and sufficiently accurate method of attaining this
+object. If I am rightly informed, the requirement was that a ship
+should be able to determine the Greenwich time within two minutes,
+after being six months at sea. When the office of Astronomer Royal
+was established in 1765, the duty of the incumbent was declared to
+be "to apply himself with the most exact care and diligence to the
+rectifying the Tables of the Motions of the Heavens, and the
+places of the Fixed Stars in order to find out the so much desired
+Longitude at Sea for the perfecting the Art of Navigation."
+
+About the middle of the last century the lunar tables were so far
+improved that Dr. Maskelyne considered them available for
+attaining this long-wished-for object. The method which I think
+was then, for the first time, proposed was the now familiar one of
+lunar distances. Several trials of the method were made by
+accomplished gentlemen who considered that nothing was wanting to
+make it practical at sea but a Nautical Ephemeris. The tables of
+the moon, necessary for the purpose, were prepared by Tobias
+Mayer, of Gottingen, and the regular annual issue of the work was
+commenced in 1766, as already stated. Of the reward which had been
+offered, three thousand pounds were paid to the widow of Mayer,
+and three thousand pounds to the celebrated mathematician Euler
+for having invented the methods used by Mayer in the construction
+of his tables. The issue of the Nautical Ephemeris was intrusted
+to Dr. Maskelyne. Like other publications of this sort this
+ephemeris has gradually increased in volume. During the first
+sixty or seventy years the data were extremely meagre, including
+only such as were considered necessary for the determination of
+positions.
+
+In 1830 the subject of improving the Nautical Almanac was referred
+by the Lord Commissioners of the Admiralty to a committee of the
+Astronomical Society of London. A subcommittee, including eleven
+of the most distinguished astronomers and one scientific
+navigator, made an, exhaustive report, recommending a radical
+rearrangement and improvement of the work. The recommendations of
+this committee were first carried into effect in the Nautical
+Almanac for the year 1834. The arrangement of the Navigator's
+Ephemeris then devised has been continued in the British Almanac
+to the present time.
+
+A good deal of matter has been added to the British Almanac during
+the forty years and upwards which have elapsed, but it has been
+worked in rather by using smaller type and closer printing than by
+increasing the number of pages. The almanac for 1834 contains five
+hundred and seventeen pages and that for 1880 five hundred and
+nineteen pages. The general aspect of the page is now somewhat
+crowded, yet, considering the quantity of figures on each page the
+arrangement is marvellously clear and legible.
+
+The Spanish "Almanaque Nautico" has been issued since the
+beginning of the century. Like its fellows it has been gradually
+enlarged and improved, in recent times, and is now of about the
+same number of pages with the British and American almanacs. As a
+rule there is less matter on a page, so that the data actually
+given are not so complete as in some other publications.
+
+In Germany two distinct publications of this class are issued, the
+one purely astronomical, the other purely nautical.
+
+The astronomical publication has been issued for more than a
+century under the title of "Berliner Astronomisches Jahrbuch." It
+is intended principally for the theoretical astronomer, and in
+respect to matter necessary to the determinations of positions on
+the earth it is rather meagre. It is issued by the Berlin
+Observatory, at the expense of the government.
+
+The companion of this work, intended for the use of the German
+marine, is the "Nautisches Jahrbuch," prepared and issued under
+the direction of the minister of commerce and public works. It is
+copied largely from the British Nautical Almanac, and in respect
+to arrangement and data is similar to our American Nautical
+Almanac, prepared for the use of navigators, giving, however, more
+matter, but in a less convenient form. The right ascension and
+declination of the moon are given for every three hours instead of
+for every hour; one page of each month is devoted to eclipses of
+Jupiter's satellites, phenomena which we never consider necessary
+in the nautical portion of our own almanac. At the end of the work
+the apparent positions of seventy or eighty of the brightest stars
+are given for every ten days, while it is considered that our own
+navigators will be satisfied with the mean places for the
+beginning of the year. At the end is a collection of tables which
+I doubt whether any other than a German navigator would ever use.
+Whether they use them or not I am not prepared to say.
+
+The preceding are the principal astronomical and nautical
+ephemerides of the world, but there are a number of minor
+publications, of the same class, of which I cannot pretend to give
+a complete list. Among them is the Portuguese Astronomical
+Ephemeris for the meridian of the University of Coimbra, prepared
+for Portuguese navigators. I do not know whether the Portuguese
+navigators really reckon their longitudes from this point: if they
+do the practice must be attended with more or less confusion. All
+the matter is given by months, as in the solar and lunar ephemeris
+of our own and the British Almanac. For the sun we have its
+longitude, right ascension, and declination, all expressed in arc
+and not in time. The equation of time and the sidereal time of
+mean noon complete the ephemeris proper. The positions of the
+principal planets are given in no case oftener than for every
+third day. The longitude and latitude of the moon are given for
+noon and midnight. One feature not found in any other almanac is
+the time at which the moon enters each of the signs of the zodiac.
+It may be supposed that this information is designed rather for
+the benefit of the Portuguese landsman than of the navigator. The
+right ascensions and declinations of the moon and the lunar
+distances are also given for intervals of twelve hours. Only the
+last page gives the eclipses of the satellites of Jupiter. The
+Fixed Stars are wholly omitted.
+
+An old ephemeris, and one well known in astronomy is that
+published by the Observatory of Milan, Italy, which has lately
+entered upon the second century of its existence. Its data are
+extremely meagre and of no interest whatever to the navigator. The
+greater part of the volume is taken up with observations at the
+Milan Observatory.
+
+Since taking charge of the American Ephemeris I have endeavored to
+ascertain what nautical almanacs are actually used by the
+principal maritime nations of Europe. I have been able to obtain
+none except those above mentioned. As a general rule I think the
+British Nautical Almanac is used by all the northern nations, as
+already indicated. The German Nautical Jahrbuch is principally a
+reprint from the British. The Swedish navigators, being all well
+acquainted with the English language, use the British Almanac
+without change. The Russian government, however, prints an
+explanation of the various terms in the language of their own
+people and binds it in at the end of the British Almanac. This
+explanation includes translations of the principal terms used in
+the heading of pages, such as the names of the months and days,
+the different planets, constellations, and fixed stars, and the
+phenomena of angle and time. They have even an index of their own
+in which the titles of the different articles are given in
+Russian. This explanation occupies, in all, seventy-five pages--
+more than double that taken up by the original explanation.
+
+One of the first considerations which strikes us in comparing
+these multitudinous publications is the confusion which must arise
+from the use of so many meridians. If each of these southern
+nations, the Spanish and Portuguese for instance, actually use a
+meridian of their own, the practice must lead to great confusion.
+If their navigators do not do so but refer their longitudes to the
+meridian of Greenwich, then their almanacs must be as good as
+useless. They would find it far better to buy an ephemeris
+referred to the meridian of Greenwich than to attempt to use their
+own The northern nations, I think, have all begun to refer to the
+meridian of Greenwich, and the same thing is happily true of our
+own marine. We may, therefore, hope that all commercial nations
+will, before long, refer their longitudes to one and the same
+meridian, and the resulting confusion be thus avoided.
+
+The preparation of the American Ephemeris and Nautical Almanac was
+commenced in 1849, under the superintendence of the late Rear-
+Admiral, then Lieutenant, Charles Henry Davis. The first volume to
+be issued was that for the year 1855. Both in the preparation of
+that work and in the connected work of mapping the country, the
+question of the meridian to be adopted was one of the first
+importance, and received great attention from Admiral Davis, who
+made an able report on the subject. Our situation was in some
+respects peculiar, owing to the great distance which separated us
+from Europe and the uncertainty of the exact difference of
+longitude between the two continents. It was hardly practicable to
+refer longitudes in our own country to any European meridian. The
+attempt to do so would involve continual changes as the
+transatlantic longitude was from time to time corrected. On the
+other hand, in order to avoid confusion in navigation, it was
+essential that our navigators should continue to reckon from the
+meridian of Greenwich. The trouble arising from uncertainty of the
+exact longitude does not affect the navigator, because, for his
+purpose, astronomical precision is not necessary.
+
+The wisest solution was probably that embodied in the act of
+Congress, approved September 28, 1850, on the recommendation of
+Lieutenant Davis, if I mistake not. "The meridian of the
+Observatory at Washington shall be adopted and used as the
+American meridian for all astronomical purposes, and the meridian
+of Greenwich shall be adopted for all nautical purposes." The
+execution of this law necessarily involves the question, "What
+shall be considered astronomical and what nautical purposes?"
+Whether it was from the difficulty of deciding this question, or
+from nobody's remembering the law, the latter has been practically
+a dead letter. Surely, if there is any region of the globe which
+the law intended should be referred to the meridian of Washington,
+it is the interior of our own country. Yet, notwithstanding the
+law, all acts of Congress relating to the territories have, so far
+as I know, referred everything to the meridian of Greenwich and
+not to that of Washington. Even the maps issued by our various
+surveys are referred to the same transatlantic meridian. The
+absurdity culminated in a local map of the city of Washington and
+the District of Columbia, issued by private parties, in 1861, in
+which we find even the meridians passing through the city of
+Washington referred to a supposed Greenwich.
+
+This practice has led to a confusion which may not be evident at
+first sight, but which is so great and permanent that it may be
+worth explaining. If, indeed, we could actually refer all our
+longitudes to an accurate meridian of Greenwich in the first
+place; if, for instance, any western region could be at once
+connected by telegraph with the Greenwich Observatory, and thus
+exchange longitude signals night after night, no trouble or
+confusion would arise from referring to the meridian of Greenwich.
+But this, practically, cannot be done. All our interior longitudes
+have been and are determined differentially by comparison with
+some point in this country. One of the most frequent points of
+reference used this way has been the Cambridge Observatory.
+Suppose, then, a surveyor at Omaha makes a telegraphic longitude
+determination between that point and the Cambridge Observatory.
+Since he wants his longitude reduced to Greenwich, he finds some
+supposed longitude of the Cambridge Observatory from Greenwich and
+adds that to his own longitude. Thus, what he gives is a longitude
+actually determined, plus an assumed longitude of Cambridge, and,
+unless the assumed longitude of Cambridge is distinctly marked on
+his maps, we may not know what it is,
+
+After a while a second party determines the longitude of Ogden
+from Cambridge. In the mean time, the longitude of Cambridge from
+Greenwich has been corrected, and we have a longitude of Ogden
+which will be discordant with that of Omaha, owing to the change
+in the longitude of Cambridge. A third party determines the
+longitudes of, let us suppose, St. Louis from Washington, he adds
+the assumed longitudes of Washington from Greenwich which may not
+agree with either of the longitudes of Cambridge and gets his
+longitude. Thus we have a series of results for our western
+longitude all nominally referred to the meridian of Greenwich, but
+actually referred to a confused collection of meridians, nobody
+knows what. If the law had only provided that the longitude of
+Washington from Greenwich should be invariably fixed at a certain
+quantity, say 77 degrees 3', this confusion would not have arisen.
+It is true that the longitude thus established by law might not
+have been perfectly correct, but this would not cause any trouble
+nor confusion. Our longitude would have been simply referred to a
+certain assumed Greenwich, the small error of which would have
+been of no importance to the navigator or astronomer. It would
+have differed from the present system only in that the assumed
+Greenwich would have been invariable instead of dancing about from
+time to time as it has done under the present system. You
+understand that when the astronomer, in computing an interior
+longitude, supposes that of Cambridge from Greenwich to be a
+certain definite amount, say 4h 44m 30s, what he actually does is
+to count from a meridian just that far east of Cambridge. When he
+changes the assumed longitude of Cambridge he counts from a
+meridian farther east or farther west of his former one: in other
+words, he always counts from an assumed Greenwich, which changes
+its position from time to time, relative to our own country.
+
+Having two meridians to look after, the form of the American
+Ephemeris, to be best adapted to the wants both of navigators and
+astronomers was necessarily peculiar. Had our navigators referred
+their longitudes to any meridian of our own country the
+arrangement of the work need not have differed materially from
+that of foreign ones. But being referred to a meridian far outside
+our limits and at the same time designed for use within those
+limits, it was necessary to make a division of the matter.
+Accordingly, the American Ephemeris has always been divided into
+two parts: the first for the use of navigators, referred to the
+meridian of Greenwich, the second for that of astronomers,
+referred to the meridian of Washington. The division of the matter
+without serious duplication is more easy than might at first be
+imagined. In explaining it, I will take the ephemeris as it now
+is, with the small changes which have been made from time to time.
+
+One of the purposes of any ephemeris, and especially of that of
+the navigators, is to give the position of the heavenly bodies at
+equidistant intervals of time, usually one day. Since it is noon
+at some point of the earth all the time, it follows that such an
+ephemeris will always be referred to noon at some meridian. What
+meridian this shall be is purely a practical question, to be
+determined by convenience and custom. Greenwich noon, being that
+necessarily used by the navigator, is adopted as the standard, but
+we must not conclude that the ephemeris for Greenwich noon is
+referred to the meridian of Greenwich in the sense that we refer a
+longitude to that meridian. Greenwich noon is 18h 51m 48s,
+Washington mean time; so the ephemeris which gives data for every
+Greenwich noon may be considered as referred to the meridian of
+Washington giving the data for 17h 51m 48s, Washington time, every
+day. The rule adopted, therefore, is to have all the ephemerides
+which refer to absolute time, without any reference to a meridian,
+given for Greenwich noon, unless there may be some special reason
+to the contrary. For the needs of the navigator and the
+theoretical astronomer these are the most convenient epochs.
+
+Another part of the ephemeris gives the position of the heavenly
+bodies, not at equidistant intervals, but at transit over some
+meridian. For this purpose the meridian of Washington is chosen
+for obvious reasons. The astronomical part of our ephemeris,
+therefore, gives the positions of the principal fixed stars, the
+sun, moon, and all the larger planets at the moment of transit
+over our own meridian.
+
+The third class of data in the ephemeris comprises phenomena to be
+predicted and observed. Such are eclipses of the sun and moon,
+occultations of fixed stars by the moon, and eclipses of Jupiter's
+satellites. These phenomena are all given in Washington mean time
+as being most convenient for observers in our own country. There
+is a partial exception, however, in the case of eclipses of the
+sun and moon. The former are rather for the world in general than
+for our own country, and it was found difficult to arrange them to
+be referred to the meridian of Washington without having the maps
+referred to the same meridian. Since, however, the meridian of
+Greenwich is most convenient outside of our own territory, and
+since but a small portion of the eclipses are visible within it,
+it is much the best to have the eclipses referred entirely to the
+meridian of Greenwich. I am the more ready to adopt this change
+because when the eclipses are to be computed for our own country
+the change of meridians will be very readily understood by those
+who make the computation.
+
+It may be interesting to say something of the tables and theories
+from which the astronomical ephemerides are computed. To
+understand them completely it is necessary to trace them to their
+origin. The problem of calculating the motions of the heavenly
+bodies and the changes in the aspect of the celestial sphere was
+one of the first with which the students of astronomy were
+occupied. Indeed, in ancient times, the only astronomical problems
+which could be attacked were of this class, for the simple reason
+that without the telescope and other instruments of research it
+was impossible to form any idea of the physical constitution of
+the heavenly bodies. To the ancients the stars and planets were
+simply points or surfaces in motion. They might have guessed that
+they were globes like that on which we live, but they were unable
+to form any theory of the nature of these globes. Thus, in The
+Almagest of Ptolemy, the most complete treatise on the ancient
+astronomy which we possess, we find the motions of all the
+heavenly bodies carefully investigated and tables given for the
+convenient computation of their positions. Crude and imperfect
+though these tables may be, they were the beginnings from which
+those now in use have arisen.
+
+No radical change was made in the general principles on which
+these theories and tables were constructed until the true system
+of the world was propounded by Copernicus. On this system the
+apparent motion of each planet in the epicycle was represented by
+a motion of the earth around the sun, and the problem of
+correcting the position of the planet on account of the epicycle
+was reduced to finding its geocentric from its heliocentric
+position. This was the greatest step ever taken in theoretical
+astronomy, yet it was but a single step. So far as the materials
+were concerned and the mode of representing the planetary motions,
+no other radical advance was made by Copernicus. Indeed, it is
+remarkable that he introduced an epicycle which was not considered
+necessary by Ptolemy in order to represent the inequalities in the
+motions of the planets around the sun.
+
+The next great advance made in the theory of the planetary motion
+was the discovery by Kepler of the celebrated laws which bear his
+name. When it was established that each planet moved in an ellipse
+having the sun in one focus it became possible to form tables of
+the motions of the heavenly bodies much more accurate than had
+before been known. Such tables were published by Kepler in 1632,
+under the name of Rudolphine Tables, in memory of his patron, the
+Emperor Rudolph. But the laws of Kepler took no account of the
+action of the planets on one another. It is well known that if
+each planet moved only under the influence of the gravitating
+force of the sun its motion would accord rigorously with the laws
+of Kepler, and the problems of theoretical astronomy would be
+greatly simplified. When, therefore, the results of Kepler's laws
+were compared with ancient and modern observations it was found
+that they were not exactly represented by the theory. It was
+evident that the elliptic orbits of the planets were subject to
+change, but it was entirely beyond the power of investigation, at
+that time, to assign any cause for such changes. Notwithstanding
+the simplicity of the causes which we now know to produce them,
+they are in form extremely complex. Without the knowledge of the
+theory of gravitation it would be entirely out of the question to
+form any tables of the planetary motions which would at all satisfy
+our modern astronomers.
+
+When the theory of universal gravitation was propounded by Newton
+he showed that a planet subjected only to the gravitation of a
+central body, like the sun, would move in exact accordance with
+Kepler's laws. But by his theory the planets must attract one
+another and these attractions must cause the motions of each to
+deviate slightly from the laws in question. Since such deviations
+were actually observed it was very natural to conclude that they
+were due to this cause, but how shall we prove it? To do this with
+all the rigor required in a mathematical investigation it is
+necessary to calculate the effect of the mutual action of the
+planets in changing their orbits. This calculation must be made
+with such precision that there shall be no doubt respecting the
+results of the theory. Then its results must be compared with the
+best observations. If the slightest outstanding difference is
+established there is something wrong and the requirements of
+astronomical science are not satisfied. The complete solution of
+this problem was entirely beyond the power of Newton. When his
+methods of research were used he was indeed able to show that the
+mutual action of the planets would produce deviations in their
+motions of the same general nature with those observed, but he was
+not able to calculate these deviations with numerical exactness.
+His most successful attempt in this direction was perhaps made in
+the case of the moon. He showed that the sun's disturbing force on
+this body would produce several inequalities the existence of
+which had been established by observation, and he was also able to
+give a rough estimate of their amount, but this was as far as his
+method could go. A great improvement had to be made, and this was
+effected not by English, but by continental mathematicians.
+
+The latter saw, clearly, that it was impossible to effect the
+required solution by the geometrical mode of reasoning employed by
+Newton. The problem, as it presented itself to their minds, was to
+find algebraic expressions for the positions of the planets at any
+time. The latitude, longitude, and radius-vector of each planet
+are constantly varying, but they each have a determined value at
+each moment of time. They may therefore be regarded as functions
+of the time, and the problem was to express these functions by
+algebraic formulae. These algebraic expressions would contain,
+besides the time, the elements of the planetary orbits to be
+derived from observation. The time which we may suppose to be
+represented algebraically by the symbol t, would remain as an
+unknown quantity to the end. What the mathematician sought to do
+was to present the astronomer with a series of algebraic
+expressions containing t as an indeterminate quantity, and so, by
+simply substituting for t any year and fraction of a year
+whatever--1600, 1700, 1800, for example, the result would give the
+latitude, longitude, or radius-vector of a planet.
+
+The problem as thus presented was one of the most difficult we can
+perceive of, but the difficulty was only an incentive to attacking
+it with all the greater energy. So long as the motion was supposed
+purely elliptical, so long as the action of the planets was
+neglected, the problem was a simple one, requiring for its
+solution only the analytic geometry of the ellipse. The real
+difficulties commenced when the mutual action of the planets was
+taken into account. It is, of course, out of the question to give
+any technical description or analysis of the processes which have
+been invented for solving the problem; but a brief historical
+sketch may not be out of place. A complete and rigorous solution
+of the problem is out of the question--that is, it is impossible
+by any known method to form an algebraic expression for the co-
+ordinates of a planet which shall be absolutely exact in a
+mathematical sense. In whatever way we go to work the expression
+comes out in the form of an infinite series of terms, each term
+being, on the whole, a little smaller as we increase the number.
+So, by increasing the number of these various terms, we can
+approach nearer and nearer to a mathematical exactness, but can
+never reach it. The mathematician and astronomer have to be
+satisfied when they have carried the solution so far that the
+neglected quantities are entirely beyond the powers of
+observation.
+
+Mathematicians have worked upon the problem in its various phases
+for nearly two centuries, and many improvements in detail have,
+from time to time, been made, but no general method, applicable to
+all cases, has been devised. One plan is to be used in treating
+the motion of the moon, another for the interior planets, another
+for Jupiter and Saturn, another for the minor planets, and so on.
+Under these circumstances it will not surprise you to learn that
+our tables of the celestial motions do not, in general, correspond
+in accuracy to the present state of practical astronomy. There is
+no authority and no office in the world whose duty it is to look
+after the preparations of the formulae I have described. The work
+of computing them has been almost entirely left to individual
+mathematicians whose taste lay in that direction, and who have
+sometimes devoted the greater part of their lives to calculations
+on a single part of the work. As a striking instance of this, the
+last great work on the Motion of the Moon, that of Delaunay, of
+Paris, involved some fifteen years of continuous hard labor.
+
+Hansen, of Germany, who died five years ago, devoted almost his
+whole life to investigations of this class and to the development
+of new methods of computation. His tables of the moon are those
+now used for predicting the places of the moon in all the
+ephemerides of the world.
+
+The only successful attempt to prepare systematic tables for all
+the large planets is that completed by Le Verrier just before his
+death; but he used only a small fraction of the material at his
+disposal, and did not employ the modern methods, confining himself
+wholly to those invented by his countrymen about the beginning of
+the present century. For him Jacobi and Hansen had lived in vain.
+
+The great difficulty which besets the subject arises from the fact
+that mathematical processes alone will not give us the position of
+a planet, there being seven unknown quantities for each planet
+which must be determined by observations. A planet, for instance,
+may move in any ellipse whatever, having the sun in one focus, and
+it is impossible to tell what ellipse it is, except from
+observation. The mean motion of a planet, or its period of
+revolution, can only be determined by a long series of
+observations, greater accuracy being obtained the longer the
+observations are continued. Before the time of Bradley, who
+commenced work at the Greenwich Observatory about 1750, the
+observations were so far from accurate that they are now of no use
+whatever, unless in exceptional cases. Even Bradley's observations
+are in many cases far less accurate than those made now. In
+consequence, we have not heretofore had a sufficiently extended
+series of observations to form an entirely satisfactory theory of
+the celestial motions.
+
+As a consequence of the several difficulties and drawbacks, when
+the computation of our ephemeris was started, in the year 1849,
+there were no tables which could be regarded as really
+satisfactory in use. In the British Nautical Almanac the places of
+the moon were derived from the tables of Burckhardt published in
+the year 1812. You will understand, in a case like this, no
+observations subsequent to the issue of the tables are made use
+of; the place of the moon of any day, hour, and minute of
+Greenwich time, mean time, was precisely what Burckhardt would
+have computed nearly a half a century before. Of the tables of the
+larger planets the latest were those of Bouvard, published in
+1812, while the places of Venus were from tables published by
+Lindenau in 1810. Of course such tables did not possess
+astronomical accuracy. At that time, in the case of the moon,
+completely new tables were constructed from the results reached by
+Professor Airy in his reduction of the Greenwich observations of
+the moon from 1750 to 1830. These were constructed under the
+direction of Professor Pierce and represented the places of the
+moon with far greater accuracy than the older tables of
+Burckhardt. For the larger planets corrections were applied to the
+older tables to make them more nearly represent observations
+before new ones were constructed. These corrections, however, have
+not proved satisfactory, not being founded on sufficiently
+thorough investigations. Indeed, the operation of correcting
+tables by observation, as we would correct the dead-reckoning of a
+ship, is a makeshift, the result of which must always be somewhat
+uncertain, and it tends to destroy that unity which is an
+essential element of the astronomical ephemeris designed for
+permanent future use. The result of introducing them, while no
+doubt an improvement on the old tables, has not been all that
+should be desired. The general lack of unity in the tables
+hitherto employed is such that I can only state what has been done
+by mentioning each planet in detail.
+
+For Mercury, new tables were constructed by Professor Winlock,
+from formulae published by Le Verrier in 1846. These tables have,
+however, been deviating from the true motion of the planet, owing
+to the motion of the perihelion of Mercury, subsequently
+discovered by Le Verrier himself. They are now much less accurate
+than the newer tables published by Le Verrier ten years later.
+
+Of Venus new tables were constructed by Mr. Hill in 1872. They are
+more accurate than any others, being founded on later data than
+those of Le Verrier, and are therefore satisfactory so far as
+accuracy of prediction is concerned.
+
+The place of Mars, Jupiter, and Saturn are still computed from the
+old tables, with certain necessary corrections to make them better
+represent observations.
+
+The places of Uranus and Neptune are derived from new tables which
+will probably be sufficiently accurate for some time to come.
+
+For the moon, Pierce's tables have been employed up to the year
+1882 inclusive. Commencing with the ephemeris for the year 1883,
+Hansen's tables are introduced with corrections to the mean
+longitude founded on two centuries of observation.
+
+With so great a lack of uniformity, and in the absence of any
+existing tables which have any other element of unity than that of
+being the work of the same authors, it is extremely desirable that
+we should be able to compute astronomical ephemerides from a
+single uniform and consistent set of astronomical data. I hope, in
+the course of years, to render this possible.
+
+When our ephemeris was first commenced, the corrections applied to
+existing tables rendered it more accurate than any other. Since
+that time, the introduction into foreign ephemerides of the
+improved tables of Le Verrier have rendered them, on the whole,
+rather more accurate than our own. In one direction, however, our
+ephemeris will hereafter be far ahead of all others. I mean in its
+positions of the fixed stars. This portion of it is of particular
+importance to us, owing to the extent to which our government is
+engaged in the determination of positions on this continent, and
+especially in our western territories. Although the places of the
+stars are determined far more easily than those of the planets,
+the discussion of star positions has been in almost as backward a
+state as planetary positions. The errors of old observers have
+crept in and been continued through two generations of
+astronomers. A systematic attempt has been made to correct the
+places of the stars for all systematic errors of this kind, and
+the work of preparing a catalogue of stars which shall be
+completely adapted to the determination of time and longitude,
+both in the fixed observatory and in the field, is now approaching
+completion. The catalogue cannot be sufficiently complete to give
+places of the stars for determining the latitude by the zenith
+telescope, because for such a purpose a much greater number of
+stars is necessary than can be incorporated in the ephemeris.
+
+From what I have said, it will be seen that the astronomical
+tables, in general, do not satisfy the scientific condition of
+completely representing observations to the last degree of
+accuracy. Few, I think, have an idea how unsystematically work of
+this kind has hitherto been performed. Until very lately the
+tables we have possessed have been the work of one man here,
+another there, and another one somewhere else, each using
+different methods and different data. The result of this is that
+there is nothing uniform and systematic among them, and that they
+have every range of precision. This is no doubt due in part to the
+fact that the construction of such tables, founded on the mass of
+observation hitherto made, is entirely beyond the power of any one
+man. What is wanted is a number of men of different degrees of
+capacity, all co-operating on a uniform system, so as to obtain a
+uniform result, like the astronomers in a large observatory. The
+Greenwich Observatory presents an example of co-operative work of
+this class extending over more than a century. But it has never
+extended its operations far outside the field of observation,
+reduction, and comparison with existing tables. It shows clearly,
+from time to time, the errors of the tables used in the British
+Nautical Almanac, but does nothing further, occasional
+investigations excepted, in the way of supplying new tables. An
+exception to this is a great work on the theory of the moon's
+motion, in which Professor Airy is now engaged.
+
+It will be understood that several distinct conditions not yet
+fulfilled are desirable in astronomical tables; one is that each
+set of tables shall be founded on absolutely consistent data, for
+instance, that the masses of the planets shall be the same
+throughout. Another requirement is that this data shall be as near
+the truth as astronomical data will suffice to determine them. The
+third is that the results shall be correct in theory. That is,
+whether they agree or disagree with observations, they shall be
+such as result mathematically from the adopted data.
+
+Tables completely fulfilling these conditions are still a work of
+the future. It is yet to be seen whether such co-operation as is
+necessary to their production can be secured under any arrangement
+whatever.
+
+
+
+
+
+
+XIV
+
+THE WORLD'S DEBT TO ASTRONOMY
+
+
+Astronomy is more intimately connected than any other science with
+the history of mankind. While chemistry, physics, and we might say
+all sciences which pertain to things on the earth, are
+comparatively modern, we find that contemplative men engaged in
+the study of the celestial motions even before the commencement of
+authentic history. The earliest navigators of whom we know must
+have been aware that the earth was round. This fact was certainly
+understood by the ancient Greeks and Egyptians, as well as it is
+at the present day. True, they did not know that the earth
+revolved on its axis, but thought that the heavens and all that in
+them is performed a daily revolution around our globe, which was,
+therefore, the centre of the universe. It was the cynosure, or
+constellation of the Little Bear, by which the sailors used to
+guide their ships before the discovery of the mariner's compass.
+Thus we see both a practical and contemplative side to astronomy
+through all history. The world owes two debts to that science: one
+for its practical uses, and the other for the ideas it has
+afforded us of the immensity of creation.
+
+The practical uses of astronomy are of two kinds: One relates to
+geography; the other to times, seasons, and chronology. Every
+navigator who sails long out of sight of land must be something of
+an astronomer. His compass tells him where are east, west, north,
+and south, but it gives him no information as to where on the wide
+ocean he may be, or whither the currents may be carrying him. Even
+with the swiftest modern steamers it is not safe to trust to the
+compass in crossing the Atlantic. A number of years ago the
+steamer City of Washington set out on her usual voyage from
+Liverpool to New York. By rare bad luck the weather was stormy or
+cloudy during her whole passage, so that the captain could not get
+a sight on the sun, and therefore had to trust to his compass and
+his log-line, the former telling him in what direction he had
+steamed, and the latter how fast he was going each hour. The
+result was that the ship ran ashore on the coast of Nova Scotia,
+when the captain thought he was approaching Nantucket.
+
+Not only the navigator but the surveyor in the western wilds must
+depend on astronomical observations to learn his exact position on
+the earth's surface, or the latitude and longitude of the camp
+which he occupies. He is able to do this because the earth is
+round, and the direction of the plumb-line not exactly the same at
+any two places. Let us suppose that the earth stood still, so as
+not to revolve on its axis at all. Then we should always see the
+stars at rest and the star which was in the zenith of any place,
+say a farm-house in New York, at any time, would be there every
+night and every hour of the year. Now the zenith is simply the
+point from which the plumb-line seems to drop. Lie on the ground;
+hang a plummet above your head, sight on the line with one eye,
+and the direction of the sight will be the zenith of your place.
+Suppose the earth was still, and a certain star was at your
+zenith. Then if you went to another place a mile away, the
+direction of the plumb-line would be slightly different. The
+change would, indeed, be very small, so small that you could not
+detect it by sighting with the plumb-line. But astronomers and
+surveyors have vastly more accurate instruments than the plumb-
+line and the eye, instruments by which a deviation that the
+unaided eye could not detect can be seen and measured. Instead of
+the plumb-line they use a spirit-level or a basin of quicksilver.
+The surface of quicksilver is exactly level and so at right angles
+to the true direction of the plumb-line or the force of gravity.
+Its direction is therefore a little different at two different
+places on the surface, and the change can be measured by its
+effect on the apparent direction of a star seen by reflection from
+the surface.
+
+It is true that a considerable distance on the earth's surface
+will seem very small in its effect on the position of a star.
+Suppose there were two stars in the heavens, the one in the zenith
+of the place where you now stand, and the other in the zenith of a
+place a mile away. To the best eye unaided by a telescope those
+two stars would look like a single one. But let the two places be
+five miles apart, and the eye could see that there were two of
+them. A good telescope could distinguish between two stars
+corresponding to places not more than a hundred feet apart. The
+most exact measurements can determine distances ranging from
+thirty to sixty feet. If a skilful astronomical observer should
+mount a telescope on your premises, and determine his latitude by
+observations on two or three evenings, and then you should try to
+trick him by taking up the instrument and putting it at another
+point one hundred feet north or south, he would find out that
+something was wrong by a single night's work.
+
+Within the past three years a wobbling of the earth's axis has
+been discovered, which takes place within a circle thirty feet in
+radius and sixty feet in diameter. Its effect was noticed in
+astronomical observations many years ago, but the change it
+produced was so small that men could not find out what the matter
+was. The exact nature and amount of the wobbling is a work of the
+exact astronomy of the present time.
+
+We cannot measure across oceans from island to island. Until a
+recent time we have not even measured across the continent, from
+New York to San Francisco, in the most precise way. Without
+astronomy we should know nothing of the distance between New York
+and Liverpool, except by the time which it took steamers to run
+it, a measure which would be very uncertain indeed. But by the aid
+of astronomical observations and the Atlantic cables the distance
+is found within a few hundred yards. Without astronomy we could
+scarcely make an accurate map of the United States, except at
+enormous labor and expense, and even then we could not be sure of
+its correctness. But the practical astronomer being able to
+determine his latitude and longitude within fifty yards, the
+positions of the principal points in all great cities of the
+country are known, and can be laid down on maps.
+
+The world has always had to depend on astronomy for all its
+knowledge concerning times and seasons. The changes of the moon
+gave us the first month, and the year completes its round as the
+earth travels in its orbit. The results of astronomical
+observation are for us condensed into almanacs, which are now in
+such universal use that we never think of their astronomical
+origin. But in ancient times people had no almanacs, and they
+learned the time of year, or the number of days in the year, by
+observing the time when Sirius or some other bright star rose or
+set with the sun, or disappeared from view in the sun's rays. At
+Alexandria, in Egypt, the length of the year was determined yet
+more exactly by observing when the sun rose exactly in the east
+and set exactly in the west, a date which fixed the equinox for
+them as for us. More than seventeen hundred years ago, Ptolemy,
+the great author of The Almagest, had fixed the length of the year
+to within a very few minutes. He knew it was a little less than
+365 1/2 days. The dates of events in ancient history depend very
+largely on the chronological cycles of astronomy. Eclipses of the
+sun and moon sometimes fixed the date of great events, and we
+learn the relation of ancient calendars to our own through the
+motions of the earth and moon, and can thus measure out the years
+for the events in ancient history on the same scale that we
+measure out our own.
+
+At the present day, the work of the practical astronomer is made
+use of in our daily life throughout the whole country in yet
+another way. Our fore-fathers had to regulate their clocks by a
+sundial, or perhaps by a mark at the corner of the house, which
+showed where the shadow of the house fell at noon. Very rude
+indeed was this method; and it was uncertain for another reason.
+It is not always exactly twenty-four hours between two noons by
+the sun, Sometimes for two or three months the sun will make it
+noon earlier and earlier every day; and during several other
+months later and later every day. The result is that, if a clock
+is perfectly regulated, the sun will be sometimes a quarter of an
+hour behind it, and sometimes nearly the same amount before it.
+Any effort to keep the clock in accord with this changing sun was
+in vain, and so the time of day was always uncertain.
+
+Now, however, at some of the principal observatories of the
+country astronomical observations are made on every clear night
+for the express purpose of regulating an astronomical clock with
+the greatest exactness. Every day at noon a signal is sent to
+various parts of the country by telegraph, so that all operators
+and railway men who hear that signal can set their clock at noon
+within two or three seconds. People who live near railway stations
+can thus get their time from it, and so exact time is diffused
+into every household of the land which is at all near a railway
+station, without the trouble of watching the sun. Thus increased
+exactness is given to the time on all our railroads, increased
+safety is obtained, and great loss of time saved to every one. If
+we estimated the money value of this saving alone we should no
+doubt find it to be greater than all that our study of astronomy
+costs.
+
+It must therefore be conceded that, on the whole, astronomy is a
+science of more practical use than one would at first suppose. To
+the thoughtless man, the stars seem to have very little relation
+to his daily life; they might be forever hid from view without his
+being the worse for it. He wonders what object men can have in
+devoting themselves to the study of the motions or phenomena of
+the heavens. But the more he looks into the subject, and the wider
+the range which his studies include, the more he will be impressed
+with the great practical usefulness of the science of the heavens.
+And yet I think it would be a serious error to say that the
+world's greatest debt to astronomy was owing to its usefulness in
+surveying, navigation, and chronology. The more enlightened a man
+is, the more he will feel that what makes his mind what it is, and
+gives him the ideas of himself and creation which he possesses, is
+more important than that which gains him wealth. I therefore hold
+that the world's greatest debt to astronomy is that it has taught
+us what a great thing creation is, and what an insignificant part
+of the Creator's work is this earth on which we dwell, and
+everything that is upon it. That space is infinite, that wherever
+we go there is a farther still beyond it, must have been accepted
+as a fact by all men who have thought of the subject since men
+began to think at all. But it is very curious how hard even the
+astronomers found it to believe that creation is as large as we
+now know it to be. The Greeks had their gods on or not very far
+above Olympus, which was a sort of footstool to the heavens.
+Sometimes they tried to guess how far it probably was from the
+vault of heaven to the earth, and they had a myth as to the time
+it took Vulcan to fall. Ptolemy knew that the moon was about
+thirty diameters of the earth distant from us, and he knew that
+the sun was many times farther than the moon; he thought it about
+twenty times as far, but could not be sure. We know that it is
+nearly four hundred times as far.
+
+When Copernicus propounded the theory that the earth moved around
+the sun, and not the sun around the earth, he was able to fix the
+relative distances of the several planets, and thus make a map of
+the solar system. But he knew nothing about the scale of this map.
+He knew, for example, that Venus was a little more than two-thirds
+the distance of the earth from the sun, and that Mars was about
+half as far again as the earth, Jupiter about five times, and
+Saturn about ten times; but he knew nothing about the distance of
+any one of them from the sun. He had his map all right, but he
+could not give any scale of miles or any other measurements upon
+it. The astronomers who first succeeded him found that the
+distance was very much greater than had formerly been supposed;
+that it was, in fact, for them immeasurably great, and that was
+all they could say about it.
+
+The proofs which Copernicus gave that the earth revolved around
+the sun were so strong that none could well doubt them. And yet
+there was a difficulty in accepting the theory which seemed
+insuperable. If the earth really moved in so immense an orbit as
+it must, then the stars would seem to move in the opposite
+direction, just as, if you were in a train that is shunting off
+cars one after another, as the train moves back and forth you see
+its motion in the opposite motion of every object around you. If
+then the earth at one side of its orbit was exactly between two
+stars, when it moved to the other side of its orbit it would not
+be in a line between them, but each star would have seemed to move
+in the opposite direction.
+
+For centuries astronomers made the most exact observations that
+they were able without having succeeded in detecting any such
+apparent motion among the stars. Here was a mystery which they
+could not solve. Either the Copernican system was not true, after
+all, and the earth did not move in an orbit, or the stars were at
+such immense distances that the whole immeasurable orbit of the
+earth is a mere point in comparison. Philosophers could not
+believe that the Creator would waste room by allowing the
+inconceivable spaces which appeared to lie between our system and
+the fixed stars to remain unused, and so thought there must be
+something wrong in the theory of the earth's motion.
+
+Not until the nineteenth century was well in progress did the most
+skilful observers of their time, Bessel and Struve, having at
+command the most refined instruments which science was then able
+to devise, discover the reality of the parallax of the stars, and
+show that the nearest of these bodies which they could find was
+more than 400,000 times as far as the 93,000,000 of miles which
+separate the earth from the sun. During the half-century and more
+which has elapsed since this discovery, astronomers have been
+busily engaged in fathoming the heavenly depths. The nearest star
+they have been able to find is about 280,000 times the sun's
+distance. A dozen or a score more are within 1,000,000 times that
+distance. Beyond this all is unfathomable by any sounding-line yet
+known to man.
+
+The results of these astronomical measures are stupendous beyond
+conception. No mere statement in numbers conveys any idea of it.
+Nearly all the brighter stars are known to be flying through space
+at speeds which generally range between ten and forty or fifty
+miles per second, some slower and some swifter, even up to one or
+two hundred miles a second. Such a speed would carry us across the
+Atlantic while we were reading two or three of these sentences.
+These motions take place some in one direction and some in
+another. Some of the stars are coming almost straight towards us.
+Should they reach us, and pass through our solar system, the
+result would be destructive to our earth, and perhaps to our sun.
+
+Are we in any danger? No, because, however madly they may come,
+whether ten, twenty, or one hundred miles per second, so many
+millions of years must elapse before they reach us that we need
+give ourselves no concern in the matter. Probably none of them are
+coming straight to us; their course deviates just a hair's-breadth
+from our system, but that hair's-breadth is so large a quantity
+that when the millions of years elapse their course will lie on
+one side or the other of our system and they will do no harm to
+our planet; just as a bullet fired at an insect a mile away would
+be nearly sure to miss it in one direction or the other.
+
+Our instrument makers have constructed telescopes more and more
+powerful, and with these the whole number of stars visible is
+carried up into the millions, say perhaps to fifty or one hundred
+millions. For aught we know every one of those stars may have
+planets like our own circling round it, and these planets may be
+inhabited by beings equal to ourselves. To suppose that our globe
+is the only one thus inhabited is something so unlikely that no
+one could expect it. It would be very nice to know something about
+the people who may inhabit these bodies, but we must await our
+translation to another sphere before we can know anything on the
+subject. Meanwhile, we have gained what is of more value than gold
+or silver; we have learned that creation transcends all our
+conceptions, and our ideas of its Author are enlarged accordingly.
+
+
+
+
+
+XV
+
+AN ASTRONOMICAL FRIENDSHIP
+
+
+There are few men with whom I would like so well to have a quiet
+talk as with Father Hell. I have known more important and more
+interesting men, but none whose acquaintance has afforded me a
+serener satisfaction, or imbued me with an ampler measure of a
+feeling that I am candid enough to call self-complacency. The ties
+that bind us are peculiar. When I call him my friend, I do not
+mean that we ever hobnobbed together. But if we are in sympathy,
+what matters it that he was dead long before I was born, that he
+lived in one century and I in another? Such differences of
+generation count for little in the brotherhood of astronomy, the
+work of whose members so extends through all time that one might
+well forget that he belongs to one century or to another.
+
+Father Hell was an astronomer. Ask not whether he was a very great
+one, for in our science we have no infallible gauge by which we
+try men and measure their stature. He was a lover of science and
+an indefatigable worker, and he did what in him lay to advance our
+knowledge of the stars. Let that suffice. I love to fancy that in
+some other sphere, either within this universe of ours or outside
+of it, all who have successfully done this may some time gather
+and exchange greetings. Should this come about there will be a
+few--Hipparchus and Ptolemy, Copernicus and Newton, Galileo and
+Herschel--to be surrounded by admiring crowds. But these men will
+have as warm a grasp and as kind a word for the humblest of their
+followers, who has merely discovered a comet or catalogued a
+nebula, as for the more brilliant of their brethren.
+
+My friend wrote the letters S. J. after his name. This would
+indicate that he had views and tastes which, in some points, were
+very different from my own. But such differences mark no dividing
+line in the brotherhood of astronomy. My testimony would count for
+nothing were I called as witness for the prosecution in a case
+against the order to which my friend belonged. The record would be
+very short: Deponent saith that he has at various times known
+sundry members of the said order; and that they were lovers of
+sound learning, devoted to the discovery and propagation of
+knowledge; and further deponent saith not.
+
+If it be true that an undevout astronomer is mad, then was Father
+Hell the sanest of men. In his diary we find entries like these:
+"Benedicente Deo, I observed the Sun on the meridian to-day....
+Deo quoque benedicente, I to-day got corresponding altitudes of
+the Sun's upper limb." How he maintained the simplicity of his
+faith in the true spirit of the modern investigator is shown by
+his proceedings during a momentous voyage along the coast of
+Norway, of which I shall presently speak. He and his party were
+passengers on a Norwegian vessel. For twelve consecutive days they
+had been driven about by adverse storms, threatened with shipwreck
+on stony cliffs, and finally compelled to take refuge in a little
+bay, with another ship bound in the same direction, there to wait
+for better weather.
+
+Father Hell was philosopher enough to know that unusual events do
+not happen without cause. Perhaps he would have undergone a week
+of storm without its occurring to him to investigate the cause of
+such a bad spell of weather. But when he found the second week
+approaching its end and yet no sign of the sun appearing or the
+wind abating, he was satisfied that something must be wrong. So he
+went to work in the spirit of the modern physician who, when there
+is a sudden outbreak of typhoid fever, looks at the wells and
+examines their water with the microscope to find the microbes
+that must be lurking somewhere. He looked about, and made careful
+inquiries to find what wickedness captain and crew had been guilty
+of to bring such a punishment. Success soon rewarded his efforts.
+The King of Denmark had issued a regulation that no fish or oil
+should be sold along the coast except by the regular dealers in
+those articles. And the vessel had on board contraband fish and
+blubber, to be disposed of in violation of this law.
+
+The astronomer took immediate and energetic measures to insure the
+public safety. He called the crew together, admonished them of
+their sin, the suffering they were bringing on themselves, and the
+necessity of getting back to their families. He exhorted them to
+throw the fish overboard, as the only measure to secure their
+safety. In the goodness of his heart, he even offered to pay the
+value of the jettison as soon as the vessel reached Drontheim.
+
+But the descendants of the Vikings were stupid and unenlightened
+men--"educatione sua et professione homines crassissimi"--and
+would not swallow the medicine so generously offered. They claimed
+that, as they had bought the fish from the Russians, their
+proceedings were quite lawful. As for being paid to throw the fish
+overboard, they must have spot cash in advance or they would not
+do it.
+
+After further fruitless conferences, Father Hell determined to
+escape the danger by transferring his party to the other vessel.
+They had not more than got away from the wicked crew than Heaven
+began to smile on their act--"factum comprobare Deus ipse
+videtur"--the clouds cleared away, the storm ceased to rage, and
+they made their voyage to Copenhagen under sunny skies. I regret
+to say that the narrative is silent as to the measure of storm
+subsequently awarded to the homines crassissimi of the forsaken
+vessel.
+
+For more than a century Father Hell had been a well-known figure
+in astronomical history. His celebrity was not, however, of such a
+kind as the Royal Astronomer of Austria that he was ought to
+enjoy. A not unimportant element in his fame was a suspicion of
+his being a black sheep in the astronomical flock. He got under
+this cloud through engaging in a trying and worthy enterprise. On
+June 3, 1769, an event occurred which had for generations been
+anticipated with the greatest interest by the whole astronomical
+world. This was a transit of Venus over the disk of the sun. Our
+readers doubtless know that at that time such a transit afforded
+the most accurate method known of determining the distance of the
+earth from the sun. To attain this object, parties were sent to
+the most widely separated parts of the globe, not only over wide
+stretches of longitude, but as near as possible to the two poles
+of the earth. One of the most favorable and important regions of
+observation was Lapland, and the King of Denmark, to whom that
+country then belonged, interested himself in getting a party sent
+thither. After a careful survey of the field he selected Father
+Hell, Chief of the Observatory at Vienna, and well known as editor
+and publisher of an annual ephemeris, in which the movements and
+aspects of the heavenly bodies were predicted. The astronomer
+accepted the mission and undertook what was at that time a rather
+hazardous voyage. His station was at Vardo in the region of the
+North Cape. What made it most advantageous for the purpose was its
+being situated several degrees within the Arctic Circle, so that
+on the date of the transit the sun did not set. The transit began
+when the sun was still two or three hours from his midnight goal,
+and it ended nearly an equal time afterwards. The party consisted
+of Hell himself, his friend and associate, Father Sajnovics, one
+Dominus Borgrewing, of whom history, so far as I know, says
+nothing more, and an humble individual who in the record receives
+no other designation than "Familias." This implies, we may
+suppose, that he pitched the tent and made the coffee. If he did
+nothing but this we might pass him over in silence. But we learn
+that on the day of the transit he stood at the clock and counted
+the all-important seconds while the observations were going on.
+
+The party was favored by cloudless weather, and made the required
+observations with entire success. They returned to Copenhagen, and
+there Father Hell remained to edit and publish his work.
+Astronomers were naturally anxious to get the results, and showed
+some impatience when it became known that Hell refused to announce
+them until they were all reduced and printed in proper form under
+the auspices of his royal patron. While waiting, the story got
+abroad that he was delaying the work until he got the results of
+observations made elsewhere, in order to "doctor" his own and make
+them fit in with the others. One went so far as to express a
+suspicion that Hell had not seen the transit at all, owing to
+clouds, and that what he pretended to publish were pure
+fabrications. But his book came out in a few months in such good
+form that this suspicion was evidently groundless. Still, the
+fears that the observations were not genuine were not wholly
+allayed, and the results derived from them were, in consequence,
+subject to some doubt. Hell himself considered the reflections
+upon his integrity too contemptible to merit a serious reply. It
+is said that he wrote to some one offering to exhibit his journal
+free from interlineations or erasures, but it does not appear that
+there is any sound authority for this statement. What is of some
+interest is that he published a determination of the parallax of
+the sun based on the comparison of his own observations with those
+made at other stations. The result was 8".70. It was then, and
+long after, supposed that the actual value of the parallax was
+about 8".50, and the deviation of Hell's result from this was
+considered to strengthen the doubt as to the correctness of his
+work. It is of interest to learn that, by the most recent
+researches, the number in question must be between 8".75 and
+8".80, so that in reality Hell's computations came nearer the
+truth than those generally current during the century following
+his work.
+
+Thus the matter stood for sixty years after the transit, and for a
+generation after Father Hell had gone to his rest. About 1830 it
+was found that the original journal of his voyage, containing the
+record of his work as first written down at the station, was still
+preserved at the Vienna Observatory. Littrow, then an astronomer
+at Vienna, made a critical examination of this record in order to
+determine whether it had been tampered with. His conclusions were
+published in a little book giving a transcript of the journal, a
+facsimile of the most important entries, and a very critical
+description of the supposed alterations made in them. He reported
+in substance that the original record had been so tampered with
+that it was impossible to decide whether the observations as
+published were genuine or not. The vital figures, those which told
+the times when Venus entered upon the sun, had been erased, and
+rewritten with blacker ink. This might well have been done after
+the party returned to Copenhagen. The case against the observer
+seemed so well made out that professors of astronomy gave their
+hearers a lesson in the value of truthfulness, by telling them how
+Father Hell had destroyed what might have been very good
+observations by trying to make them appear better than they really
+were.
+
+In 1883 I paid a visit to Vienna for the purpose of examining the
+great telescope which had just been mounted in the observatory
+there by Grubb, of Dublin. The weather was so unfavorable that it
+was necessary to remain two weeks, waiting for an opportunity to
+see the stars. One evening I visited the theatre to see Edwin
+Booth, in his celebrated tour over the Continent, play King Lear
+to the applauding Viennese. But evening amusements cannot be
+utilized to kill time during the day. Among the works I had
+projected was that of rediscussing all the observations made on
+the transits of Venus which had occurred in 1761 and 1769, by the
+light of modern discovery. As I have already remarked, Hell's
+observations were among the most important made, if they were only
+genuine. So, during my almost daily visits to the observatory, I
+asked permission of the director to study Hell's manuscript, which
+was deposited in the library of the institution. Permission was
+freely given, and for some days I pored over the manuscript. It is
+a very common experience in scientific research that a subject
+which seems very unpromising when first examined may be found more
+and more interesting as one looks further into it. Such was the
+case here. For some time there did not seem any possibility of
+deciding the question whether the record was genuine. But every
+time I looked at it some new point came to light. I compared the
+pages with Littrow's published description and was struck by a
+seeming want of precision, especially when he spoke of the ink
+with which the record had been made. Erasers were doubtless
+unknown in those days--at least our astronomer had none on his
+expedition--so when he found he had written the wrong word he
+simply wiped the place off with, perhaps, his finger and wrote
+what he wanted to say. In such a case Littrow described the matter
+as erased and new matter written. When the ink flowed freely from
+the quill pen it was a little dark. Then Littrow said a different
+kind of ink had been used, probably after he had got back from his
+journey. On the other hand, there was a very singular case in
+which there had been a subsequent interlineation in ink of quite a
+different tint, which Littrow said nothing about. This seemed so
+curious that I wrote in my notes as follows:
+
+"That Littrow, in arraying his proofs of Hell's forgery, should
+have failed to dwell upon the obvious difference between this ink
+and that with which the alterations were made leads me to suspect
+a defect in his sense of color."
+
+The more I studied the description and the manuscript the stronger
+this impression became. Then it occurred to me to inquire whether
+perhaps such could have been the case. So I asked Director Weiss
+whether anything was known as to the normal character of Littrow's
+power of distinguishing colors. His answer was prompt and
+decisive. "Oh yes, Littrow was color-blind to red. He could not
+distinguish between the color of Aldebaran and the whitest star."
+No further research was necessary. For half a century the
+astronomical world had based an impression on the innocent but
+mistaken evidence of a color-blind man--respecting the tints of
+ink in a manuscript.
+
+It has doubtless happened more than once that when an intimate
+friend has suddenly and unexpectedly passed away, the reader has
+ardently wished that it were possible to whisper just one word of
+appreciation across the dark abyss. And so it is that I have ever
+since felt that I would like greatly to tell Father Hell the story
+of my work at Vienna in 1883.
+
+
+
+
+
+XVI
+
+THE EVOLUTION OF THE SCIENTIFIC INVESTIGATOR
+
+[Footnote: Presidential address at the opening of the
+International Congress of Arts and Science, St. Louis Exposition,
+September 21: 1904.]
+
+
+As we look at the assemblage gathered in this hall, comprising so
+many names of widest renown in every branch of learning--we might
+almost say in every field of human endeavor--the first inquiry
+suggested must be after the object of our meeting. The answer is
+that our purpose corresponds to the eminence of the assemblage. We
+aim at nothing less than a survey of the realm of knowledge, as
+comprehensive as is permitted by the limitations of time and
+space. The organizers of our congress have honored me with the
+charge of presenting such preliminary view of its field as may
+make clear the spirit of our undertaking.
+
+Certain tendencies characteristic of the science of our day
+clearly suggest the direction of our thoughts most appropriate to
+the occasion. Among the strongest of these is one towards laying
+greater stress on questions of the beginnings of things, and
+regarding a knowledge of the laws of development of any object of
+study as necessary to the understanding of its present form. It
+may be conceded that the principle here involved is as applicable
+in the broad field before us as in a special research into the
+properties of the minutest organism. It therefore seems meet that
+we should begin by inquiring what agency has brought about the
+remarkable development of science to which the world of to-day
+bears witness. This view is recognized in the plan of our
+proceedings by providing for each great department of knowledge a
+review of its progress during the century that has elapsed since
+the great event commemorated by the scenes outside this hall. But
+such reviews do not make up that general survey of science at
+large which is necessary to the development of our theme, and
+which must include the action of causes that had their origin long
+before our time. The movement which culminated in making the
+nineteenth century ever memorable in history is the outcome of a
+long series of causes, acting through many centuries, which are
+worthy of especial attention on such an occasion as this. In
+setting them forth we should avoid laying stress on those visible
+manifestations which, striking the eye of every beholder, are in
+no danger of being overlooked, and search rather for those
+agencies whose activities underlie the whole visible scene, but
+which are liable to be blotted out of sight by the very brilliancy
+of the results to which they have given rise. It is easy to draw
+attention to the wonderful qualities of the oak; but, from that
+very fact, it may be needful to point out that the real wonder
+lies concealed in the acorn from which it grew.
+
+Our inquiry into the logical order of the causes which have made
+our civilization what it is to-day will be facilitated by bringing
+to mind certain elementary considerations--ideas so familiar that
+setting them forth may seem like citing a body of truisms--and yet
+so frequently overlooked, not only individually, but in their
+relation to each other, that the conclusion to which they lead may
+be lost to sight. One of these propositions is that psychical
+rather than material causes are those which we should regard as
+fundamental in directing the development of the social organism.
+The human intellect is the really active agent in every branch of
+endeavor--the primum mobile of civilization--and all those
+material manifestations to which our attention is so often
+directed are to be regarded as secondary to this first agency. If
+it be true that "in the world is nothing great but man; in man is
+nothing great but mind," then should the key-note of our discourse
+be the recognition of this first and greatest of powers.
+
+Another well-known fact is that those applications of the forces
+of nature to the promotion of human welfare which have made our
+age what it is are of such comparatively recent origin that we
+need go back only a single century to antedate their most
+important features, and scarcely more than four centuries to find
+their beginning. It follows that the subject of our inquiry should
+be the commencement, not many centuries ago, of a certain new form
+of intellectual activity.
+
+Having gained this point of view, our next inquiry will be into
+the nature of that activity and its relation to the stages of
+progress which preceded and followed its beginning. The
+superficial observer, who sees the oak but forgets the acorn,
+might tell us that the special qualities which have brought out
+such great results are expert scientific knowledge and rare
+ingenuity, directed to the application of the powers of steam and
+electricity. From this point of view the great inventors and the
+great captains of industry were the first agents in bringing about
+the modern era. But the more careful inquirer will see that the
+work of these men was possible only through a knowledge of the
+laws of nature, which had been gained by men whose work took
+precedence of theirs in logical order, and that success in
+invention has been measured by completeness in such knowledge.
+While giving all due honor to the great inventors, let us remember
+that the first place is that of the great investigators, whose
+forceful intellects opened the way to secrets previously hidden
+from men. Let it be an honor and not a reproach to these men that
+they were not actuated by the love of gain, and did not keep
+utilitarian ends in view in the pursuit of their researches. If it
+seems that in neglecting such ends they were leaving undone the
+most important part of their work, let us remember that Nature
+turns a forbidding face to those who pay her court with the hope
+of gain, and is responsive only to those suitors whose love for
+her is pure and undefiled. Not only is the special genius required
+in the investigator not that generally best adapted to applying
+the discoveries which he makes, but the result of his having
+sordid ends in view would be to narrow the field of his efforts,
+and exercise a depressing effect upon his activities. The true man
+of science has no such expression in his vocabulary as "useful
+knowledge." His domain is as wide as nature itself, and he best
+fulfils his mission when he leaves to others the task of applying
+the knowledge he gives to the world.
+
+We have here the explanation of the well-known fact that the
+functions of the investigator of the laws of nature, and of the
+inventor who applies these laws to utilitarian purposes, are
+rarely united in the same person. If the one conspicuous exception
+which the past century presents to this rule is not unique, we
+should probably have to go back to Watt to find another.
+
+From this view-point it is clear that the primary agent in the
+movement which has elevated man to the masterful position he now
+occupies is the scientific investigator. He it is whose work has
+deprived plague and pestilence of their terrors, alleviated human
+suffering, girdled the earth with the electric wire, bound the
+continent with the iron way, and made neighbors of the most
+distant nations. As the first agent which has made possible this
+meeting of his representatives, let his evolution be this day our
+worthy theme. As we follow the evolution of an organism by
+studying the stages of its growth, so we have to show how the work
+of the scientific investigator is related to the ineffectual
+efforts of his predecessors.
+
+In our time we think of the process of development in nature as
+one going continuously forward through the combination of the
+opposite processes of evolution and dissolution. The tendency of
+our thought has been in the direction of banishing cataclysms to
+the theological limbo, and viewing Nature as a sleepless plodder,
+endowed with infinite patience, waiting through long ages for
+results. I do not contest the truth of the principle of continuity
+on which this view is based. But it fails to make known to us the
+whole truth. The building of a ship from the time that her keel is
+laid until she is making her way across the ocean is a slow and
+gradual process; yet there is a cataclysmic epoch opening up a new
+era in her history. It is the moment when, after lying for months
+or years a dead, inert, immovable mass, she is suddenly endowed
+with the power of motion, and, as if imbued with life, glides into
+the stream, eager to begin the career for which she was designed.
+
+I think it is thus in the development of humanity. Long ages may
+pass during which a race, to all external observation, appears to
+be making no real progress. Additions may be made to learning, and
+the records of history may constantly grow, but there is nothing
+in its sphere of thought, or in the features of its life, that can
+be called essentially new. Yet, Nature may have been all along
+slowly working in a way which evades our scrutiny, until the
+result of her operations suddenly appears in a new and
+revolutionary movement, carrying the race to a higher plane of
+civilization.
+
+It is not difficult to point out such epochs in human progress.
+The greatest of all, because it was the first, is one of which we
+find no record either in written or geological history. It was the
+epoch when our progenitors first took conscious thought of the
+morrow, first used the crude weapons which Nature had placed
+within their reach to kill their prey, first built a fire to warm
+their bodies and cook their food. I love to fancy that there was
+some one first man, the Adam of evolution, who did all this, and
+who used the power thus acquired to show his fellows how they
+might profit by his example. When the members of the tribe or
+community which he gathered around him began to conceive of life
+as a whole--to include yesterday, to-day, and to-morrow in the
+same mental grasp--to think how they might apply the gifts of
+Nature to their own uses--a movement was begun which should
+ultimately lead to civilization.
+
+Long indeed must have been the ages required for the development
+of this rudest primitive community into the civilization revealed
+to us by the most ancient tablets of Egypt and Assyria. After
+spoken language was developed, and after the rude representation
+of ideas by visible marks drawn to resemble them had long been
+practised, some Cadmus must have invented an alphabet. When the
+use of written language was thus introduced, the word of command
+ceased to be confined to the range of the human voice, and it
+became possible for master minds to extend their influence as far
+as a written message could be carried. Then were communities
+gathered into provinces; provinces into kingdoms, kingdoms into
+great empires of antiquity. Then arose a stage of civilization
+which we find pictured in the most ancient records--a stage in
+which men were governed by laws that were perhaps as wisely
+adapted to their conditions as our laws are to ours--in which the
+phenomena of nature were rudely observed, and striking occurrences
+in the earth or in the heavens recorded in the annals of the
+nation.
+
+Vast was the progress of knowledge during the interval between
+these empires and the century in which modern science began. Yet,
+if I am right in making a distinction between the slow and regular
+steps of progress, each growing naturally out of that which
+preceded it, and the entrance of the mind at some fairly definite
+epoch into an entirely new sphere of activity, it would appear
+that there was only one such epoch during the entire interval.
+This was when abstract geometrical reasoning commenced, and
+astronomical observations aiming at precision were recorded,
+compared, and discussed. Closely associated with it must have been
+the construction of the forms of logic. The radical difference
+between the demonstration of a theorem of geometry and the
+reasoning of every-day life which the masses of men must have
+practised from the beginning, and which few even to-day ever get
+beyond, is so evident at a glance that I need not dwell upon it.
+The principal feature of this advance is that, by one of those
+antinomies of human intellect of which examples are not wanting
+even in our own time, the development of abstract ideas preceded
+the concrete knowledge of natural phenomena. When we reflect that
+in the geometry of Euclid the science of space was brought to such
+logical perfection that even to-day its teachers are not agreed as
+to the practicability of any great improvement upon it, we cannot
+avoid the feeling that a very slight change in the direction of
+the intellectual activity of the Greeks would have led to the
+beginning of natural science. But it would seem that the very
+purity and perfection which was aimed at in their system of
+geometry stood in the way of any extension or application of its
+methods and spirit to the field of nature. One example of this is
+worthy of attention. In modern teaching the idea of magnitude as
+generated by motion is freely introduced. A line is described by a
+moving point; a plane by a moving line; a solid by a moving plane.
+It may, at first sight, seem singular that this conception finds
+no place in the Euclidian system. But we may regard the omission
+as a mark of logical purity and rigor. Had the real or supposed
+advantages of introducing motion into geometrical conceptions been
+suggested to Euclid, we may suppose him to have replied that the
+theorems of space are independent of time; that the idea of motion
+necessarily implies time, and that, in consequence, to avail
+ourselves of it would be to introduce an extraneous element into
+geometry.
+
+It is quite possible that the contempt of the ancient philosophers
+for the practical application of their science, which has
+continued in some form to our own time, and which is not
+altogether unwholesome, was a powerful factor in the same
+direction. The result was that, in keeping geometry pure from
+ideas which did not belong to it, it failed to form what might
+otherwise have been the basis of physical science. Its founders
+missed the discovery that methods similar to those of geometric
+demonstration could be extended into other and wider fields than
+that of space. Thus not only the development of applied geometry
+but the reduction of other conceptions to a rigorous mathematical
+form was indefinitely postponed.
+
+There is, however, one science which admitted of the immediate
+application of the theorems of geometry, and which did not require
+the application of the experimental method. Astronomy is
+necessarily a science of observation pure and simple, in which
+experiment can have no place except as an auxiliary. The vague
+accounts of striking celestial phenomena handed down by the
+priests and astrologers of antiquity were followed in the time of
+the Greeks by observations having, in form at least, a rude
+approach to precision, though nothing like the degree of precision
+that the astronomer of to-day would reach with the naked eye,
+aided by such instruments as he could fashion from the tools at
+the command of the ancients.
+
+The rude observations commenced by the Babylonians were continued
+with gradually improving instruments--first by the Greeks and
+afterwards by the Arabs--but the results failed to afford any
+insight into the true relation of the earth to the heavens. What
+was most remarkable in this failure is that, to take a first step
+forward which would have led on to success, no more was necessary
+than a course of abstract thinking vastly easier than that
+required for working out the problems of geometry. That space is
+infinite is an unexpressed axiom, tacitly assumed by Euclid and
+his successors. Combining this with the most elementary
+consideration of the properties of the triangle, it would be seen
+that a body of any given size could be placed at such a distance
+in space as to appear to us like a point. Hence a body as large as
+our earth, which was known to be a globe from the time that the
+ancient Phoenicians navigated the Mediterranean, if placed in the
+heavens at a sufficient distance, would look like a star. The
+obvious conclusion that the stars might be bodies like our globe,
+shining either by their own light or by that of the sun, would
+have been a first step to the understanding of the true system of
+the world.
+
+There is historic evidence that this deduction did not wholly
+escape the Greek thinkers. It is true that the critical student
+will assign little weight to the current belief that the vague
+theory of Pythagoras--that fire was at the centre of all things--
+implies a conception of the heliocentric theory of the solar
+system. But the testimony of Archimedes, confused though it is in
+form, leaves no serious doubt that Aristarchus of Samos not only
+propounded the view that the earth revolves both on its own axis
+and around the sun, but that he correctly removed the great
+stumbling-block in the way of this theory by adding that the
+distance of the fixed stars was infinitely greater than the
+dimensions of the earth's orbit. Even the world of philosophy was
+not yet ready for this conception, and, so far from seeing the
+reasonableness of the explanation, we find Ptolemy arguing against
+the rotation of the earth on grounds which careful observations of
+the phenomena around him would have shown to be ill-founded.
+
+Physical science, if we can apply that term to an uncoordinated
+body of facts, was successfully cultivated from the earliest
+times. Something must have been known of the properties of metals,
+and the art of extracting them from their ores must have been
+practised, from the time that coins and medals were first stamped.
+The properties of the most common compounds were discovered by
+alchemists in their vain search for the philosopher's stone, but
+no actual progress worthy of the name rewarded the practitioners
+of the black art.
+
+Perhaps the first approach to a correct method was that of
+Archimedes, who by much thinking worked out the law of the lever,
+reached the conception of the centre of gravity, and demonstrated
+the first principles of hydrostatics. It is remarkable that he did
+not extend his researches into the phenomena of motion, whether
+spontaneous or produced by force. The stationary condition of the
+human intellect is most strikingly illustrated by the fact that
+not until the time of Leonardo was any substantial advance made on
+his discovery. To sum up in one sentence the most characteristic
+feature of ancient and medieval science, we see a notable contrast
+between the precision of thought implied in the construction and
+demonstration of geometrical theorems and the vague indefinite
+character of the ideas of natural phenomena generally, a contrast
+which did not disappear until the foundations of modern science
+began to be laid.
+
+We should miss the most essential point of the difference between
+medieval and modern learning if we looked upon it as mainly a
+difference either in the precision or the amount of knowledge. The
+development of both of these qualities would, under any
+circumstances, have been slow and gradual, but sure. We can hardly
+suppose that any one generation, or even any one century, would
+have seen the complete substitution of exact for inexact ideas.
+Slowness of growth is as inevitable in the case of knowledge as in
+that of a growing organism. The most essential point of difference
+is one of those seemingly slight ones, the importance of which we
+are too apt to overlook. It was like the drop of blood in the
+wrong place, which some one has told us makes all the difference
+between a philosopher and a maniac. It was all the difference
+between a living tree and a dead one, between an inert mass and a
+growing organism. The transition of knowledge from the dead to the
+living form must, in any complete review of the subject, be looked
+upon as the really great event of modern times. Before this event
+the intellect was bound down by a scholasticism which regarded
+knowledge as a rounded whole, the parts of which were written in
+books and carried in the minds of learned men. The student was
+taught from the beginning of his work to look upon authority as
+the foundation of his beliefs. The older the authority the greater
+the weight it carried. So effective was this teaching that it
+seems never to have occurred to individual men that they had all
+the opportunities ever enjoyed by Aristotle of discovering truth,
+with the added advantage of all his knowledge to begin with.
+Advanced as was the development of formal logic, that practical
+logic was wanting which could see that the last of a series of
+authorities, every one of which rested on those which preceded it,
+could never form a surer foundation for any doctrine than that
+supplied by its original propounder.
+
+The result of this view of knowledge was that, although during the
+fifteen centuries following the death of the geometer of Syracuse
+great universities were founded at which generations of professors
+expounded all the learning of their time, neither professor nor
+student ever suspected what latent possibilities of good were
+concealed in the most familiar operations of Nature. Every one
+felt the wind blow, saw water boil, and heard the thunder crash,
+but never thought of investigating the forces here at play. Up to
+the middle of the fifteenth century the most acute observer could
+scarcely have seen the dawn of a new era.
+
+In view of this state of things it must be regarded as one of the
+most remarkable facts in evolutionary history that four or five
+men, whose mental constitution was either typical of the new order
+of things, or who were powerful agents in bringing it about, were
+all born during the fifteenth century, four of them at least, at
+so nearly the same time as to be contemporaries.
+
+Leonardo da Vinci, whose artistic genius has charmed succeeding
+generations, was also the first practical engineer of his time,
+and the first man after Archimedes to make a substantial advance
+in developing the laws of motion. That the world was not prepared
+to make use of his scientific discoveries does not detract from
+the significance which must attach to the period of his birth.
+
+Shortly after him was born the great navigator whose bold spirit
+was to make known a new world, thus giving to commercial
+enterprise that impetus which was so powerful an agent in bringing
+about a revolution in the thoughts of men.
+
+The birth of Columbus was soon followed by that of Copernicus, the
+first after Aristarchus to demonstrate the true system of the
+world. In him more than in any of his contemporaries do we see the
+struggle between the old forms of thought and the new. It seems
+almost pathetic and is certainly most suggestive of the general
+view of knowledge taken at that time that, instead of claiming
+credit for bringing to light great truths before unknown, he made
+a labored attempt to show that, after all, there was nothing
+really new in his system, which he claimed to date from Pythagoras
+and Philolaus. In this connection it is curious that he makes no
+mention of Aristarchus, who I think will be regarded by
+conservative historians as his only demonstrated predecessor. To
+the hold of the older ideas upon his mind we must attribute the
+fact that in constructing his system he took great pains to make
+as little change as possible in ancient conceptions.
+
+Luther, the greatest thought-stirrer of them all, practically of
+the same generation with Copernicus, Leonardo and Columbus, does
+not come in as a scientific investigator, but as the great
+loosener of chains which had so fettered the intellect of men that
+they dared not think otherwise than as the authorities thought.
+
+Almost coeval with the advent of these intellects was the
+invention of printing with movable type. Gutenberg was born during
+the first decade of the century, and his associates and others
+credited with the invention not many years afterwards. If we
+accept the principle on which I am basing my argument, that in
+bringing out the springs of our progress we should assign the
+first place to the birth of those psychic agencies which started
+men on new lines of thought, then surely was the fifteenth the
+wonderful century.
+
+Let us not forget that, in assigning the actors then born to their
+places, we are not narrating history, but studying a special phase
+of evolution. It matters not for us that no university invited
+Leonardo to its halls, and that his science was valued by his
+contemporaries only as an adjunct to the art of engineering. The
+great fact still is that he was the first of mankind to propound
+laws of motion. It is not for anything in Luther's doctrines that
+he finds a place in our scheme. No matter for us whether they were
+sound or not. What he did towards the evolution of the scientific
+investigator was to show by his example that a man might question
+the best-established and most venerable authority and still live--
+still preserve his intellectual integrity--still command a hearing
+from nations and their rulers. It matters not for us whether
+Columbus ever knew that he had discovered a new continent. His
+work was to teach that neither hydra, chimera nor abyss--neither
+divine injunction nor infernal machination--was in the way of men
+visiting every part of the globe, and that the problem of
+conquering the world reduced itself to one of sails and rigging,
+hull and compass. The better part of Copernicus was to direct man
+to a view-point whence he should see that the heavens were of like
+matter with the earth. All this done, the acorn was planted from
+which the oak of our civilization should spring. The mad quest for
+gold which followed the discovery of Columbus, the questionings
+which absorbed the attention of the learned, the indignation
+excited by the seeming vagaries of a Paracelsus, the fear and
+trembling lest the strange doctrine of Copernicus should undermine
+the faith of centuries, were all helps to the germination of the
+seed--stimuli to thought which urged it on to explore the new
+fields opened up to its occupation. This given, all that has since
+followed came out in regular order of development, and need be
+here considered only in those phases having a special relation to
+the purpose of our present meeting.
+
+So slow was the growth at first that the sixteenth century may
+scarcely have recognized the inauguration of a new era. Torricelli
+and Benedetti were of the third generation after Leonardo, and
+Galileo, the first to make a substantial advance upon his theory,
+was born more than a century after him. Only two or three men
+appeared in a generation who, working alone, could make real
+progress in discovery, and even these could do little in leavening
+the minds of their fellowmen with the new ideas.
+
+Up to the middle of the seventeenth century an agent which all
+experience since that time shows to be necessary to the most
+productive intellectual activity was wanting. This was the
+attrition of like minds, making suggestions to one another,
+criticising, comparing, and reasoning. This element was introduced
+by the organization of the Royal Society of London and the Academy
+of Sciences of Paris.
+
+The members of these two bodies seem like ingenious youth suddenly
+thrown into a new world of interesting objects, the purposes and
+relations of which they had to discover. The novelty of the
+situation is strikingly shown in the questions which occupied the
+minds of the incipient investigators. One natural result of
+British maritime enterprise was that the aspirations of the
+Fellows of the Royal Society were not confined to any continent or
+hemisphere. Inquiries were sent all the way to Batavia to know
+"whether there be a hill in Sumatra which burneth continually, and
+a fountain which runneth pure balsam." The astronomical precision
+with which it seemed possible that physiological operations might
+go on was evinced by the inquiry whether the Indians can so
+prepare that stupefying herb Datura that "they make it lie several
+days, months, years, according as they will, in a man's body without
+doing him any harm, and at the end kill him without missing an
+hour's time." Of this continent one of the inquiries was whether
+there be a tree in Mexico that yields water, wine, vinegar, milk,
+honey, wax, thread and needles.
+
+Among the problems before the Paris Academy of Sciences those of
+physiology and biology took a prominent place. The distillation of
+compounds had long been practised, and the fact that the more
+spirituous elements of certain substances were thus separated
+naturally led to the question whether the essential essences of
+life might not be discoverable in the same way. In order that all
+might participate in the experiments, they were conducted in open
+session of the academy, thus guarding against the danger of any
+one member obtaining for his exclusive personal use a possible
+elixir of life. A wide range of the animal and vegetable kingdom,
+including cats, dogs and birds of various species, were thus
+analyzed. The practice of dissection was introduced on a large
+scale. That of the cadaver of an elephant occupied several
+sessions, and was of such interest that the monarch himself was a
+spectator.
+
+To the same epoch with the formation and first work of these two
+bodies belongs the invention of a mathematical method which in its
+importance to the advance of exact science may be classed with the
+invention of the alphabet in its relation to the progress of
+society at large. The use of algebraic symbols to represent
+quantities had its origin before the commencement of the new era,
+and gradually grew into a highly developed form during the first
+two centuries of that era. But this method could represent
+quantities only as fixed. It is true that the elasticity inherent
+in the use of such symbols permitted of their being applied to any
+and every quantity; yet, in any one application, the quantity was
+considered as fixed and definite. But most of the magnitudes of
+nature are in a state of continual variation; indeed, since all
+motion is variation, the latter is a universal characteristic of
+all phenomena. No serious advance could be made in the application
+of algebraic language to the expression of physical phenomena
+until it could be so extended as to express variation in
+quantities, as well as the quantities themselves. This extension,
+worked out independently by Newton and Leibnitz, may be classed as
+the most fruitful of conceptions in exact science. With it the way
+was opened for the unimpeded and continually accelerated progress
+of the last two centuries.
+
+The feature of this period which has the closest relation to the
+purpose of our coming together is the seemingly unending
+subdivision of knowledge into specialties, many of which are
+becoming so minute and so isolated that they seem to have no
+interest for any but their few pursuers. Happily science itself
+has afforded a corrective for its own tendency in this direction.
+The careful thinker will see that in these seemingly diverging
+branches common elements and common principles are coming more and
+more to light. There is an increasing recognition of methods of
+research, and of deduction, which are common to large branches, or
+to the whole of science. We are more and more recognizing the
+principle that progress in knowledge implies its reduction to more
+exact forms, and the expression of its ideas in language more or
+less mathematical. The problem before the organizers of this
+Congress was, therefore, to bring the sciences together, and seek
+for the unity which we believe underlies their infinite diversity.
+
+The assembling of such a body as now fills this hall was scarcely
+possible in any preceding generation, and is made possible now
+only through the agency of science itself. It differs from all
+preceding international meetings by the universality of its scope,
+which aims to include the whole of knowledge. It is also unique in
+that none but leaders have been sought out as members. It is
+unique in that so many lands have delegated their choicest
+intellects to carry on its work. They come from the country to
+which our republic is indebted for a third of its territory,
+including the ground on which we stand; from the land which has
+taught us that the most scholarly devotion to the languages and
+learning of the cloistered past is compatible with leadership in
+the practical application of modern science to the arts of life;
+from the island whose language and literature have found a new
+field and a vigorous growth in this region; from the last seat of
+the holy Roman Empire; from the country which, remembering a
+monarch who made an astronomical observation at the Greenwich
+Observatory, has enthroned science in one of the highest places in
+its government; from the peninsula so learned that we have invited
+one of its scholars to come and tells us of our own language; from
+the land which gave birth to Leonardo, Galileo, Torricelli,
+Columbus, Volta--what an array of immortal names!--from the little
+republic of glorious history which, breeding men rugged as its
+eternal snow-peaks, has yet been the seat of scientific
+investigation since the day of the Bernoullis; from the land whose
+heroic dwellers did not hesitate to use the ocean itself to
+protect it against invaders, and which now makes us marvel at the
+amount of erudition compressed within its little area; from the
+nation across the Pacific, which, by half a century of unequalled
+progress in the arts of life, has made an important contribution
+to evolutionary science through demonstrating the falsity of the
+theory that the most ancient races are doomed to be left in the
+rear of the advancing age--in a word, from every great centre of
+intellectual activity on the globe I see before me eminent
+representatives of that world--advance in knowledge which we have
+met to celebrate. May we not confidently hope that the discussions
+of such an assemblage will prove pregnant of a future for science
+which shall outshine even its brilliant past.
+
+Gentlemen and scholars all! You do not visit our shores to find
+great collections in which centuries of humanity have given
+expression on canvas and in marble to their hopes, fears, and
+aspirations. Nor do you expect institutions and buildings hoary
+with age. But as you feel the vigor latent in the fresh air of
+these expansive prairies, which has collected the products of
+human genius by which we are here surrounded, and, I may add,
+brought us together; as you study the institutions which we have
+founded for the benefit, not only of our own people, but of
+humanity at large; as you meet the men who, in the short space of
+one century, have transformed this valley from a savage wilderness
+into what it is today--then may you find compensation for the
+want of a past like yours by seeing with prophetic eye a future
+world-power of which this region shall be the seat. If such is to
+be the outcome of the institutions Which we are now building up,
+then may your present visit be a blessing both to your posterity
+and ours by making that power one for good to all man-kind. Your
+deliberations will help to demonstrate to us and to the world at
+large that the reign of law must supplant that of brute force in
+the relations of the nations, just as it has supplanted it in the
+relations of individuals. You will help to show that the war which
+science is now waging against the sources of diseases, pain, and
+misery offers an even nobler field for the exercise of heroic
+qualities than can that of battle. We hope that when, after your
+all too-fleeting sojourn in our midst, you return to your own
+shores, you will long feel the influence of the new air you have
+breathed in an infusion of increased vigor in pursuing your varied
+labors. And if a new impetus is thus given to the great
+intellectual movement of the past century, resulting not only in
+promoting the unification of knowledge, but in widening its field
+through new combinations of effort on the part of its votaries,
+the projectors, organizers and supporters of this Congress of Arts
+and Science will be justified of their labors.
+
+
+
+
+
+
+XVII
+
+THE EVOLUTION OF ASTRONOMICAL KNOWLEDGE
+
+[Footnote: Address at the dedication of the Flower Observatory,
+University of Pennsylvania, May 12, 1897--Science, May 21, 1897]
+
+
+Assembled, as we are, to dedicate a new institution to the
+promotion of our knowledge of the heavens, it appeared to me that
+an appropriate and interesting subject might be the present and
+future problems of astronomy. Yet it seemed, on further
+reflection, that, apart from the difficulty of making an adequate
+statement of these problems on such an occasion as the present,
+such a wording of the theme would not fully express the idea which
+I wish to convey. The so-called problems of astronomy are not
+separate and independent, but are rather the parts of one great
+problem, that of increasing our knowledge of the universe in its
+widest extent. Nor is it easy to contemplate the edifice of
+astronomical science as it now stands, without thinking of the
+past as well as of the present and future. The fact is that our
+knowledge of the universe has been in the nature of a slow and
+gradual evolution, commencing at a very early period in human
+history, and destined to go forward without stop, as we hope, so
+long as civilization shall endure. The astronomer of every age has
+built on the foundations laid by his predecessors, and his work
+has always formed, and must ever form, the base on which his
+successors shall build. The astronomer of to-day may look back
+upon Hipparchus and Ptolemy as the earliest ancestors of whom he
+has positive knowledge. He can trace his scientific descent from
+generation to generation, through the periods of Arabian and
+medieval science, through Copernicus, Kepler, Newton, Laplace, and
+Herschel, down to the present time. The evolution of astronomical
+knowledge, generally slow and gradual, offering little to excite
+the attention of the public, has yet been marked by two
+cataclysms. One of these is seen in the grand conception of
+Copernicus that this earth on which we dwell is not a globe fixed
+in the centre of the universe, but is simply one of a number of
+bodies, turning on their own axes and at the same time moving
+around the sun as a centre. It has always seemed to me that the
+real significance of the heliocentric system lies in the greatness
+of this conception rather than in the fact of the discovery
+itself. There is no figure in astronomical history which may more
+appropriately claim the admiration of mankind through all time
+than that of Copernicus. Scarcely any great work was ever so
+exclusively the work of one man as was the heliocentric system the
+work of the retiring sage of Frauenburg. No more striking contrast
+between the views of scientific research entertained in his time
+and in ours can be found than that afforded by the fact that,
+instead of claiming credit for his great work, he deemed it rather
+necessary to apologize for it and, so far as possible, to
+attribute his ideas to the ancients.
+
+A century and a half after Copernicus followed the second great
+step, that taken by Newton. This was nothing less than showing
+that the seemingly complicated and inexplicable motions of the
+heavenly bodies were only special cases of the same kind of
+motion, governed by the same forces, that we see around us
+whenever a stone is thrown by the hand or an apple falls to the
+ground. The actual motions of the heavens and the laws which
+govern them being known, man had the key with which he might
+commence to unlock the mysteries of the universe.
+
+When Huyghens, in 1656, published his Systema Saturnium, where he
+first set forth the mystery of the rings of Saturn, which, for
+nearly half a century, had perplexed telescopic observers, he
+prefaced it with a remark that many, even among the learned, might
+condemn his course in devoting so much time and attention to
+matters far outside the earth, when he might better be studying
+subjects of more concern to humanity. Notwithstanding that the
+inventor of the pendulum clock was, perhaps, the last astronomer
+against whom a neglect of things terrestrial could be charged, he
+thought it necessary to enter into an elaborate defence of his
+course in studying the heavens. Now, however, the more distant
+objects are in space--I might almost add the more distant events
+are in time--the more they excite the attention of the astronomer,
+if only he can hope to acquire positive knowledge about them. Not,
+however, because he is more interested in things distant than in
+things near, but because thus he may more completely embrace in
+the scope of his work the beginning and the end, the boundaries of
+all things, and thus, indirectly, more fully comprehend all that
+they include. From his stand-point,
+
+    "All are but parts of one stupendous whole,
+     Whose body Nature is and God the soul."
+
+Others study Nature and her plans as we see them developed on the
+surface of this little planet which we inhabit, the astronomer
+would fain learn the plan on which the whole universe is
+constructed. The magnificent conception of Copernicus is, for him,
+only an introduction to the yet more magnificent conception of
+infinite space containing a collection of bodies which we call the
+visible universe. How far does this universe extend? What are the
+distances and arrangements of the stars? Does the universe
+constitute a system? If so, can we comprehend the plan on which
+this system is formed, of its beginning and of its end? Has it
+bounds outside of which nothing exists but the black and starless
+depths of infinity itself? Or are the stars we see simply such
+members of an infinite collection as happen to be the nearest our
+system? A few such questions as these we are perhaps beginning to
+answer; but hundreds, thousands, perhaps even millions, of years
+may elapse without our reaching a complete solution. Yet the
+astronomer does not view them as Kantian antinomies, in the nature
+of things insoluble, but as questions to which he may hopefully
+look for at least a partial answer.
+
+The problem of the distances of the stars is of peculiar interest
+in connection with the Copernican system. The greatest objection
+to this system, which must have been more clearly seen by
+astronomers themselves than by any others, was found in the
+absence of any apparent parallax of the stars. If the earth
+performed such an immeasurable circle around the sun as Copernicus
+maintained, then, as it passed from side to side of its orbit, the
+stars outside the solar system must appear to have a corresponding
+motion in the other direction, and thus to swing back and forth as
+the earth moved in one and the other direction. The fact that not
+the slightest swing of that sort could be seen was, from the time
+of Ptolemy, the basis on which the doctrine of the earth's
+immobility rested. The difficulty was not grappled with by
+Copernicus or his immediate successors. The idea that Nature would
+not squander space by allowing immeasurable stretches of it to go
+unused seems to have been one from which medieval thinkers could
+not entirely break away. The consideration that there could be no
+need of any such economy, because the supply was infinite, might
+have been theoretically acknowledged, but was not practically
+felt. The fact is that magnificent as was the conception of
+Copernicus, it was dwarfed by the conception of stretches from
+star to star so vast that the whole orbit of the earth was only a
+point in comparison.
+
+An indication of the extent to which the difficulty thus arising
+was felt is seen in the title of a book published by Horrebow, the
+Danish astronomer, some two centuries ago. This industrious
+observer, one of the first who used an instrument resembling our
+meridian transit of the present day, determined to see if he could
+find the parallax of the stars by observing the intervals at which
+a pair of stars in opposite quarters of the heavens crossed his
+meridian at opposite seasons of the year. When, as he thought, he
+had won success, he published his observations and conclusions
+under the title of Copernicus Triumphans. But alas! the keen
+criticism of his successors showed that what he supposed to be a
+swing of the stars from season to season arose from a minute
+variation in the rate of his clock, due to the different
+temperatures to which it was exposed during the day and the night.
+The measurement of the distance even of the nearest stars evaded
+astronomical research until Bessel and Struve arose in the early
+part of the present century.
+
+On some aspects of the problem of the extent of the universe light
+is being thrown even now. Evidence is gradually accumulating which
+points to the probability that the successive orders of smaller
+and smaller stars, which our continually increasing telescopic
+power brings into view, are not situated at greater and greater
+distances, but that we actually see the boundary of our universe.
+This indication lends a peculiar interest to various questions
+growing out of the motions of the stars. Quite possibly the
+problem of these motions will be the great one of the future
+astronomer. Even now it suggests thoughts and questions of the
+most far-reaching character.
+
+I have seldom felt a more delicious sense of repose than when
+crossing the ocean during the summer months I sought a place where
+I could lie alone on the deck, look up at the constellations, with
+Lyra near the zenith, and, while listening to the clank of the
+engine, try to calculate the hundreds of millions of years which
+would be required by our ship to reach the star a Lyrae, if she
+could continue her course in that direction without ever stopping.
+It is a striking example of how easily we may fail to realize our
+knowledge when I say that I have thought many a time how
+deliciously one might pass those hundred millions of years in a
+journey to the star a Lyrae, without its occurring to me that we
+are actually making that very journey at a speed compared with
+which the motion of a steamship is slow indeed. Through every
+year, every hour, every minute, of human history from the first
+appearance of man on the earth, from the era of the builders of
+the Pyramids, through the times of Caesar and Hannibal, through
+the period of every event that history records, not merely our
+earth, but the sun and the whole solar system with it, have been
+speeding their way towards the star of which I speak on a journey
+of which we know neither the beginning nor the end. We are at this
+moment thousands of miles nearer to a Lyrae than we were a few
+minutes ago when I began this discourse, and through every future
+moment, for untold thousands of years to come, the earth and all
+there is on it will be nearer to a Lyrae, or nearer to the place
+where that star now is, by hundreds of miles for every minute of
+time come and gone. When shall we get there? Probably in less than
+a million years, perhaps in half a million. We cannot tell
+exactly, but get there we must if the laws of nature and the laws
+of motion continue as they are. To attain to the stars was the
+seemingly vain wish of an ancient philosopher, but the whole human
+race is, in a certain sense, realizing this wish as rapidly as a
+speed of ten miles a second can bring it about.
+
+I have called attention to this motion because it may, in the not
+distant future, afford the means of approximating to a solution of
+the problem already mentioned--that of the extent of the universe.
+Notwithstanding the success of astronomers during the present
+century in measuring the parallax of a number of stars, the most
+recent investigations show that there are very few, perhaps hardly
+more than a score, of stars of which the parallax, and therefore
+the distance, has been determined with any approach to certainty.
+Many parallaxes determined about the middle of the nineteenth
+century have had to disappear before the powerful tests applied by
+measures with the heliometer; others have been greatly reduced and
+the distances of the stars increased in proportion. So far as
+measurement goes, we can only say of the distances of all the
+stars, except the few whose parallaxes have been determined, that
+they are immeasurable. The radius of the earth's orbit, a line
+more than ninety millions of miles in length, not only vanishes
+from sight before we reach the distance of the great mass of
+stars, but becomes such a mere point that when magnified by the
+powerful instruments of modern times the most delicate appliances
+fail to make it measurable. Here the solar motion comes to our
+help. This motion, by which, as I have said, we are carried
+unceasingly through space, is made evident by a motion of most of
+the stars in the opposite direction, just as passing through a
+country on a railway we see the houses on the right and on the
+left being left behind us. It is clear enough that the apparent
+motion will be more rapid the nearer the object. We may therefore
+form some idea of the distance of the stars when we know the
+amount of the motion. It is found that in the great mass of stars
+of the sixth magnitude, the smallest visible to the naked eye, the
+motion is about three seconds per century. As a measure thus
+stated does not convey an accurate conception of magnitude to one
+not practised in the subject, I would say that in the heavens, to
+the ordinary eye, a pair of stars will appear single unless they
+are separated by a distance of 150 or 200 seconds. Let us, then,
+imagine ourselves looking at a star of the sixth magnitude, which
+is at rest while we are carried past it with the motion of six to
+eight miles per second which I have described. Mark its position
+in the heavens as we see it to-day; then let its position again be
+marked five thousand years hence. A good eye will just be able to
+perceive that there are two stars marked instead of one. The two
+would be so close together that no distinct space between them
+could be perceived by unaided vision. It is due to the magnifying
+power of the telescope, enlarging such small apparent distances,
+that the motion has been determined in so small a period as the
+one hundred and fifty years during which accurate observations of
+the stars have been made.
+
+The motion just described has been fairly well determined for
+what, astronomically speaking, are the brighter stars; that is to
+say, those visible to the naked eye. But how is it with the
+millions of faint telescopic stars, especially those which form
+the cloud masses of the Milky Way? The distance of these stars is
+undoubtedly greater, and the apparent motion is therefore smaller.
+Accurate observations upon such stars have been commenced only
+recently, so that we have not yet had time to determine the amount
+of the motion. But the indication seems to be that it will prove
+quite a measurable quantity and that before the twentieth century
+has elapsed, it will be determined for very much smaller stars
+than those which have heretofore been studied. A photographic
+chart of the whole heavens is now being constructed by an
+association of observatories in some of the leading countries of
+the world. I cannot say all the leading countries, because then we
+should have to exclude our own, which, unhappily, has taken no
+part in this work. At the end of the twentieth century we may
+expect that the work will be repeated. Then, by comparing the
+charts, we shall see the effect of the solar motion and perhaps
+get new light upon the problem in question.
+
+Closely connected with the problem of the extent of the universe
+is another which appears, for us, to be insoluble because it
+brings us face to face with infinity itself. We are familiar
+enough with eternity, or, let us say, the millions or hundreds of
+millions of years which geologists tell us must have passed while
+the crust of the earth was assuming its present form, our
+mountains being built, our rocks consolidated, and successive
+orders of animals coming and going. Hundreds of millions of years
+is indeed a long time, and yet, when we contemplate the changes
+supposed to have taken place during that time, we do not look out
+on eternity itself, which is veiled from our sight, as it were, by
+the unending succession of changes that mark the progress of time.
+But in the motions of the stars we are brought face to face with
+eternity and infinity, covered by no veil whatever. It would be
+bold to speak dogmatically on a subject where the springs of being
+are so far hidden from mortal eyes as in the depths of the
+universe. But, without declaring its positive certainty, it must
+be said that the conclusion seems unavoidable that a number of
+stars are moving with a speed such that the attraction of all the
+bodies of the universe could never stop them. One such case is
+that of Arcturus, the bright reddish star familiar to mankind
+since the days of Job, and visible near the zenith on the clear
+evenings of May and June. Yet another case is that of a star known
+in astronomical nomenclature as 1830 Groombridge, which exceeds
+all others in its angular proper motion as seen from the earth. We
+should naturally suppose that it seems to move so fast because it
+is near us. But the best measurements of its parallax seem to show
+that it can scarcely be less than two million times the distance
+of the earth from the sun, while it may be much greater. Accepting
+this result, its velocity cannot be much less than two hundred
+miles per second, and may be much more. With this speed it would
+make the circuit of our globe in two minutes, and had it gone
+round and round in our latitudes we should have seen it fly past
+us a number of times since I commenced this discourse. It would
+make the journey from the earth to the sun in five days. If it is
+now near the centre of our universe it would probably reach its
+confines in a million of years. So far as our knowledge goes,
+there is no force in nature which would ever have set it in motion
+and no force which can ever stop it. What, then, was the history
+of this star, and, if there are planets circulating around, what
+the experience of beings who may have lived on those planets
+during the ages which geologists and naturalists assure us our
+earth has existed? Was there a period when they saw at night only
+a black and starless heaven? Was there a time when in that heaven
+a small faint patch of light began gradually to appear? Did that
+patch of light grow larger and larger as million after million of
+years elapsed? Did it at last fill the heavens and break up into
+constellations as we now see them? As millions more of years
+elapse will the constellations gather together in the opposite
+quarter and gradually diminish to a patch of light as the star
+pursues its irresistible course of two hundred miles per second
+through the wilderness of space, leaving our universe farther and
+farther behind it, until it is lost in the distance? If the
+conceptions of modern science are to be considered as good for all
+time--a point on which I confess to a large measure of scepticism--
+then these questions must be answered in the affirmative.
+
+The problems of which I have so far spoken are those of what may
+be called the older astronomy. If I apply this title it is because
+that branch of the science to which the spectroscope has given
+birth is often called the new astronomy. It is commonly to be
+expected that a new and vigorous form of scientific research will
+supersede that which is hoary with antiquity. But I am not willing
+to admit that such is the case with the old astronomy, if old we
+may call it. It is more pregnant with future discoveries today
+than it ever has been, and it is more disposed to welcome the
+spectroscope as a useful handmaid, which may help it on to new
+fields, than it is to give way to it. How useful it may thus
+become has been recently shown by a Dutch astronomer, who finds
+that the stars having one type of spectrum belong mostly to the
+Milky Way, and are farther from us than the others.
+
+In the field of the newer astronomy perhaps the most interesting
+work is that associated with comets. It must be confessed,
+however, that the spectroscope has rather increased than
+diminished the mystery which, in some respects, surrounds the
+constitution of these bodies. The older astronomy has
+satisfactorily accounted for their appearance, and we might also
+say for their origin and their end, so far as questions of origin
+can come into the domain of science. It is now known that comets
+are not wanderers through the celestial spaces from star to star,
+but must always have belonged to our system. But their orbits are
+so very elongated that thousands, or even hundreds of thousands,
+of years are required for a revolution. Sometimes, however, a
+comet passing near to Jupiter is so fascinated by that planet
+that, in its vain attempts to follow it, it loses so much of its
+primitive velocity as to circulate around the sun in a period of a
+few years, and thus to become, apparently, a new member of our
+system. If the orbit of such a comet, or in fact of any comet,
+chances to intersect that of the earth, the latter in passing the
+point of intersection encounters minute particles which cause a
+meteoric shower.
+
+But all this does not tell us much about the nature and make-up of
+a comet. Does it consist of nothing but isolated particles, or is
+there a solid nucleus, the attraction of which tends to keep the
+mass together? No one yet knows. The spectroscope, if we interpret
+its indications in the usual way, tells us that a comet is simply
+a mass of hydrocarbon vapor, shining by its own light. But there
+must be something wrong in this interpretation. That the light is
+reflected sunlight seems to follow necessarily from the increased
+brilliancy of the comet as it approaches the sun and its
+disappearance as it passes away.
+
+Great attention has recently been bestowed upon the physical
+constitution of the planets and the changes which the surfaces of
+those bodies may undergo. In this department of research we must
+feel gratified by the energy of our countrymen who have entered
+upon it. Should I seek to even mention all the results thus made
+known I might be stepping on dangerous ground, as many questions
+are still unsettled. While every astronomer has entertained the
+highest admiration for the energy and enthusiasm shown by Mr.
+Percival Lowell in founding an observatory in regions where the
+planets can be studied under the most favorable conditions, they
+cannot lose sight of the fact that the ablest and most experienced
+observers are liable to error when they attempt to delineate the
+features of a body 50,000,000 or 100,000,000 miles away through
+such a disturbing medium as our atmosphere. Even on such a subject
+as the canals of Mars doubts may still be felt. That certain
+markings to which Schiaparelli gave the name of canals exist, few
+will question. But it may be questioned whether these markings are
+the fine, sharp, uniform lines found on Schiaparelli's map and
+delineated in Lowell's beautiful book. It is certainly curious
+that Barnard at Mount Hamilton, with the most powerful instrument
+and under the most favorable circumstances, does not see these
+markings as canals.
+
+I can only mention among the problems of the spectroscope the
+elegant and remarkable solution of the mystery surrounding the
+rings of Saturn, which has been effected by Keeler at Allegheny.
+That these rings could not be solid has long been a conclusion of
+the laws of mechanics, but Keeler was the first to show that they
+really consist of separate particles, because the inner portions
+revolve more rapidly than the outer.
+
+The question of the atmosphere of Mars has also received an
+important advance by the work of Campbell at Mount Hamilton.
+Although it is not proved that Mars has no atmosphere, for the
+existence of some atmosphere can scarcely be doubted, yet the
+Mount Hamilton astronomer seems to have shown, with great
+conclusiveness, that it is so rare as not to produce any sensible
+absorption of the solar rays.
+
+I have left an important subject for the close. It belongs
+entirely to the older astronomy, and it is one with which I am
+glad to say this observatory is expected to especially concern
+itself. I refer to the question of the variation of latitudes,
+that singular phenomenon scarcely suspected ten years ago, but
+brought out by observations in Germany during the past eight
+years, and reduced to law with such brilliant success by our own
+Chandler. The north pole is not a fixed point on the earth's
+surface, but moves around in rather an irregular way. True, the
+motion is small; a circle of sixty feet in diameter will include
+the pole in its widest range. This is a very small matter so far
+as the interests of daily life are concerned; but it is very
+important to the astronomer. It is not simply a motion of the pole
+of the earth, but a wobbling of the solid earth itself. No one
+knows what conclusions of importance to our race may yet follow
+from a study of the stupendous forces necessary to produce even
+this slight motion.
+
+The director of this new observatory has already distinguished
+himself in the delicate and difficult work of investigating this
+motion, and I am glad to know that he is continuing the work here
+with one of the finest instruments ever used for the purpose, a
+splendid product of American mechanical genius. I can assure you
+that astronomers the world over will look with the greatest
+interest for Professor Doolittle's success in the arduous task he
+has undertaken.
+
+There is one question connected with these studies of the universe
+on which I have not touched, and which is, nevertheless, of
+transcendent interest. What sort of life, spiritual and
+intellectual, exists in distant worlds? We cannot for a moment
+suppose that our little planet is the only one throughout the
+whole universe on which may be found the fruits of civilization,
+family affection, friendship, the desire to penetrate the
+mysteries of creation. And yet this question is not to-day a
+problem of astronomy, nor can we see any prospect that it ever
+will be, for the simple reason that science affords us no hope of
+an answer to any question that we may send through the fathomless
+abyss. When the spectroscope was in its infancy it was suggested
+that possibly some difference might be found in the rays reflected
+from living matter, especially from vegetation, that might enable
+us to distinguish them from rays reflected by matter not endowed
+with life. But this hope has not been realized, nor does it seem
+possible to realize it. The astronomer cannot afford to waste his
+energies on hopeless speculation about matters of which he cannot
+learn anything, and he therefore leaves this question of the
+plurality of worlds to others who are as competent to discuss it
+as he is. All he can tell the world is:
+
+     He who through vast immensity can pierce,
+     See worlds on worlds compose one universe;
+     Observe how system into system runs,
+     What other planets circle other suns,
+     What varied being peoples every star,
+     May tell why Heaven has made us as we are.
+
+
+
+
+
+XVIII
+
+ASPECTS OF AMERICAN ASTRONOMY
+
+[Footnote: Address delivered at the University of Chicago, October
+22, 1897, in connection with the dedication of the Yerkes
+Observatory. Printed m the Astro physical Journal. November, 1897.]
+
+
+The University of Chicago yesterday accepted one of the most
+munificent gifts ever made for the promotion of any single
+science, and with appropriate ceremonies dedicated it to the
+increase of our knowledge of the heavenly bodies.
+
+The president of your university has done me the honor of inviting
+me to supplement what was said on that occasion by some remarks of
+a more general nature suggested by the celebration. One is
+naturally disposed to say first what is uppermost in his mind. At
+the present moment this will naturally be the general impression
+made by what has been seen and heard. The ceremonies were
+attended, not only by a remarkable delegation of citizens, but by
+a number of visiting astronomers which seems large when we
+consider that the profession itself is not at all numerous in any
+country. As one of these, your guests, I am sure that I give
+expression only to their unanimous sentiment in saying that we
+have been extremely gratified in many ways by all that we have
+seen and heard. The mere fact of so munificent a gift to science
+cannot but excite universal admiration. We knew well enough that
+it was nothing more than might have been expected from the public
+spirit of this great West; but the first view of a towering
+snowpeak is none the less impressive because you have learned in
+your geography how many feet high it is, and great acts are none
+the less admirable because they correspond to what you have heard
+and read, and might therefore be led to expect.
+
+The next gratifying feature is the great public interest excited
+by the occasion. That the opening of a purely scientific
+institution should have led so large an assemblage of citizens to
+devote an entire day, including a long journey by rail, to the
+celebration of yesterday is something most suggestive from its
+unfamiliarity. A great many scientific establishments have been
+inaugurated during the last half-century, but if on any such
+occasion so large a body of citizens has gone so great a distance
+to take part in the inauguration, the fact has at the moment
+escaped my mind.
+
+That the interest thus shown is not confined to the hundreds of
+attendants, but must be shared by your great public, is shown by
+the unfailing barometer of journalism. Here we have a field in
+which the non-survival of the unfit is the rule in its most
+ruthless form. The journals that we see and read are merely the
+fortunate few of a countless number, dead and forgotten, that did
+not know what the public wanted to read about. The eagerness shown
+by the representatives of your press in recording everything your
+guests would say was accomplished by an enterprise in making known
+everything that occurred, and, in case of an emergency requiring a
+heroic measure, what did NOT occur, showing that smart journalists
+of the East must have learned their trade, or at least breathed
+their inspiration, in these regions. I think it was some twenty
+years since I told a European friend that the eighth wonder of the
+world was a Chicago daily newspaper. Since that time the course of
+journalistic enterprise has been in the reverse direction to that
+of the course of empire, eastward instead of westward.
+
+It has been sometimes said--wrongfully, I think--that scientific
+men form a mutual admiration society. One feature of the occasion
+made me feel that we, your guests, ought then and there to have
+organized such a society and forthwith proceeded to business. This
+feature consisted in the conferences on almost every branch of
+astronomy by which the celebration of yesterday was preceded. The
+fact that beyond the acceptance of a graceful compliment I
+contributed nothing to these conferences relieves me from the
+charge of bias or self-assertion in saying that they gave me a new
+and most inspiring view of the energy now being expended in
+research by the younger generation of astronomers. All the
+experience of the past leads us to believe that this energy will
+reap the reward which nature always bestows upon those who seek
+her acquaintance from unselfish motives. In one way it might
+appear that little was to be learned from a meeting like that of
+the present week. Each astronomer may know by publications
+pertaining to the science what all the others are doing. But
+knowledge obtained in this way has a sort of abstractness about it
+a little like our knowledge of the progress of civilization in
+Japan, or of the great extent of the Australian continent. It was,
+therefore, a most happy thought on the part of your authorities to
+bring together the largest possible number of visiting astronomers
+from Europe, as well as America, in order that each might see,
+through the attrition of personal contact, what progress the
+others were making in their researches. To the visitors at least I
+am sure that the result of this meeting has been extremely
+gratifying. They earnestly hope, one and all, that the callers of
+the conference will not themselves be more disappointed in its
+results; that, however little they may have actually to learn of
+methods and results, they will feel stimulated to well-directed
+efforts and find themselves inspired by thoughts which, however
+familiar, will now be more easily worked out.
+
+We may pass from the aspects of the case as seen by the strictly
+professional class to those general aspects fitted to excite the
+attention of the great public. From the point of view of the
+latter it may well appear that the most striking feature of the
+celebration is the great amount of effort which is shown to be
+devoted to the cultivation of a field quite outside the ordinary
+range of human interests. The workers whom we see around us are
+only a detachment from an army of investigators who, in many parts
+of the world, are seeking to explore the mysteries of creation.
+Why so great an expenditure of energy? Certainly not to gain
+wealth, for astronomy is perhaps the one field of scientific work
+which, in our expressive modern phrase, "has no money in it." It
+is true that the great practical use of astronomical science to
+the country and the world in affording us the means of determining
+positions on land and at sea is frequently pointed out. It is said
+that an Astronomer Royal of England once calculated that every
+meridian observation of the moon made at Greenwich was worth a
+pound sterling, on account of the help it would afford to the
+navigation of the ocean. An accurate map of the United States
+cannot be constructed without astronomical observations at
+numerous points scattered over the whole country, aided by data
+which great observatories have been accumulating for more than a
+century, and must continue to accumulate in the future.
+
+But neither the measurement of the earth, the making of maps, nor
+the aid of the navigator is the main object which the astronomers
+of to-day have in view. If they do not quite share the sentiment
+of that eminent mathematician, who is said to have thanked God
+that his science was one which could not be prostituted to any
+useful purpose, they still know well that to keep utilitarian
+objects in view would only prove & handicap on their efforts.
+Consequently they never ask in what way their science is going to
+benefit mankind. As the great captain of industry is moved by the
+love of wealth, and the political leader by the love of power over
+men, so the astronomer is moved by the love of knowledge for its
+own sake, and not for the sake of its useful applications. Yet he
+is proud to know that his science has been worth more to mankind
+than it has cost. He does not value its results merely as a means
+of crossing the ocean or mapping the country, for he feels that
+man does not live by bread alone. If it is not more than bread to
+know the place we occupy in the universe, it is certainly
+something which we should place not far behind the means of
+subsistence. That we now look upon a comet as something very
+interesting, of which the sight affords us a pleasure unmixed with
+fear of war, pestilence, or other calamity, and of which we
+therefore wish the return, is a gain we cannot measure by money.
+In all ages astronomy has been an index to the civilization of the
+people who cultivated it. It has been crude or exact, enlightened
+or mingled with superstition, according to the current mode of
+thought. When once men understand the relation of the planet on
+which they dwell to the universe at large, superstition is doomed
+to speedy extinction. This alone is an object worth more than
+money.
+
+Astronomy may fairly claim to be that science which transcends all
+others in its demands upon the practical application of our
+reasoning powers. Look at the stars that stud the heavens on a
+clear evening. What more hopeless problem to one confined to earth
+than that of determining their varying distances, their motions,
+and their physical constitution? Everything on earth we can handle
+and investigate. But how investigate that which is ever beyond our
+reach, on which we can never make an experiment? On certain
+occasions we see the moon pass in front of the sun and hide it
+from our eyes. To an observer a few miles away the sun was not
+entirely hidden, for the shadow of the moon in a total eclipse is
+rarely one hundred miles wide. On another continent no eclipse at
+all may have been visible. Who shall take a map of the world and
+mark upon it the line on which the moon's shadow will travel
+during some eclipse a hundred years hence? Who shall map out the
+orbits of the heavenly bodies as they are going to appear in a
+hundred thousand years? How shall we ever know of what chemical
+elements the sun and the stars are made? All this has been done,
+but not by the intellect of any one man. The road to the stars has
+been opened only by the efforts of many generations of
+mathematicians and observers, each of whom began where his
+predecessor had left off.
+
+We have reached a stage where we know much of the heavenly
+bodies. We have mapped out our solar system with great precision.
+But how with that great universe of millions of stars in which our
+solar system is only a speck of star-dust, a speck which a
+traveller through the wilds of space might pass a hundred times
+without notice? We have learned much about this universe, though
+our knowledge of it is still dim. We see it as a traveller on a
+mountain-top sees a distant city in a cloud of mist, by a few
+specks of glimmering light from steeples or roofs. We want to know
+more about it, its origin and its destiny; its limits in time and
+space, if it has any; what function it serves in the universal
+economy. The journey is long, yet we want, in knowledge at least,
+to make it. Hence we build observatories and train observers and
+investigators. Slow, indeed, is progress in the solution of the
+greatest of problems, when measured by what we want to know. Some
+questions may require centuries, others thousands of years for
+their answer. And yet never was progress more rapid than during
+our time. In some directions our astronomers of to-day are out of
+sight of those of fifty years ago; we are even gaining heights
+which twenty years ago looked hopeless. Never before had the
+astronomer so much work--good, hard, yet hopeful work--before him
+as to-day. He who is leaving the stage feels that he has only
+begun and must leave his successors with more to do than his
+predecessors left him.
+
+To us an interesting feature of this progress is the part taken in
+it by our own country. The science of our day, it is true, is of
+no country. Yet we very appropriately speak of American science
+from the fact that our traditional reputation has not been that of
+a people deeply interested in the higher branches of intellectual
+work. Men yet living can remember when in the eyes of the
+universal church of learning, all cisatlantic countries, our own
+included, were partes infidelium.
+
+Yet American astronomy is not entirely of our generation. In the
+middle of the last century Professor Winthrop, of Harvard, was an
+industrious observer of eclipses and kindred phenomena, whose work
+was recorded in the transactions of learned societies. But the
+greatest astronomical activity during our colonial period was that
+called out by the transit of Venus in 1769, which was visible in
+this country. A committee of the American Philosophical Society,
+at Philadelphia, organized an excellent system of observations,
+which we now know to have been fully as successful, perhaps more
+so, than the majority of those made on other continents, owing
+mainly to the advantages of air and climate. Among the observers
+was the celebrated Rittenhouse, to whom is due the distinction of
+having been the first American astronomer whose work has an
+important place in the history of the science. In addition to the
+observations which he has left us, he was the first inventor or
+proposer of the collimating telescope, an instrument which has
+become almost a necessity wherever accurate observations are made.
+The fact that the subsequent invention by Bessel may have been
+independent does not detract from the merits of either.
+
+Shortly after the transit of Venus, which I have mentioned, the
+war of the Revolution commenced. The generation which carried on
+that war and the following one, which framed our Constitution and
+laid the bases of our political institutions, were naturally too
+much occupied with these great problems to pay much attention to
+pure science. While the great mathematical astronomers of Europe
+were laying the foundation of celestial mechanics their writings
+were a sealed book to every one on this side of the Atlantic, and
+so remained until Bowditch appeared, early in the present century.
+His translation of the Mecanique Celeste made an epoch in American
+science by bringing the great work of Laplace down to the reach of
+the best American students of his time.
+
+American astronomers must always honor the names of Rittenhouse
+and Bowditch. And yet in one respect their work was disappointing
+of results. Neither of them was the founder of a school. Rittenhouse
+left no successor to carry on his work. The help which
+Bowditch afforded his generation was invaluable to isolated
+students who, here and there, dived alone and unaided into the
+mysteries of the celestial motions. His work was not mainly in the
+field of observational astronomy, and therefore did not materially
+influence that branch of science. In 1832 Professor Airy,
+afterwards Astronomer Royal of England, made a report to the
+British Association on the condition of practical astronomy in
+various countries. In this report he remarked that he was unable
+to say anything about American astronomy because, so far as he
+knew, no public observatory existed in the United States.
+
+William C. Bond, afterwards famous as the first director of the
+Harvard Observatory, was at that time making observations with a
+small telescope, first near Boston and afterwards at Cambridge.
+But with so meagre an outfit his establishment could scarcely lay
+claim to being an astronomical observatory, and it was not
+surprising if Airy did not know anything of his modest efforts.
+
+If at this time Professor Airy had extended his investigations
+into yet another field, with a view of determining the prospects
+for a great city at the site of Fort Dearborn, on the southern
+shore of Lake Michigan, he would have seen as little prospect of
+civic growth in that region as of a great development of astronomy
+in the United States at large. A plat of the proposed town of
+Chicago had been prepared two years before, when the place
+contained perhaps half a dozen families. In the same month in
+which Professor Airy made his report, August, 1832, the people of
+the place, then numbering twenty-eight voters, decided to become
+incorporated, and selected five trustees to carry on their
+government.
+
+In 1837 a city charter was obtained from the legislature of
+Illinois. The growth of this infant city, then small even for an
+infant, into the great commercial metropolis of the West has been
+the just pride of its people and the wonder of the world. I
+mention it now because of a remarkable coincidence. With this
+civic growth has quietly gone on another, little noted by the
+great world, and yet in its way equally wonderful and equally
+gratifying to the pride of those who measure greatness by
+intellectual progress. Taking knowledge of the universe as a
+measure of progress, I wish to invite attention to the fact that
+American astronomy began with your city, and has slowly but surely
+kept pace with it, until to-day our country stands second only to
+Germany in the number of researches being prosecuted, and second
+to none in the number of men who have gained the highest
+recognition by their labors.
+
+In 1836 Professor Albert Hopkins, of Williams College, and
+Professor Elias Loomis, of Western Reserve College, Ohio, both
+commenced little observatories. Professor Loomis went to Europe
+for all his instruments, but Hopkins was able even then to get
+some of his in this country. Shortly afterwards a little wooden
+structure was erected by Captain Gilliss on Capitol Hill, at
+Washington, and supplied with a transit instrument for observing
+moon culminations, in conjunction with Captain Wilkes, who was
+then setting out on his exploring expedition to the southern
+hemisphere. The date of these observatories was practically the
+same as that on which a charter for the city of Chicago was
+obtained from the legislature. With their establishment the
+population of your city had increased to 703.
+
+The next decade, 1840 to 1850, was that in which our practical
+astronomy seriously commenced. The little observatory of Captain
+Gilliss was replaced by the Naval, then called the National
+Observatory, erected at Washington during the years 1843-44, and
+fitted out with what were then the most approved instruments.
+About the same time the appearance of the great comet of 1843 led
+the citizens of Boston to erect the observatory of Harvard
+College. Thus it is little more than a half-century since the two
+principal observatories in the United States were established. But
+we must not for a moment suppose that the mere erection of an
+observatory can mark an epoch in scientific history. What must
+make the decade of which I speak ever memorable in American
+astronomy was not merely the erection of buildings, but the
+character of the work done by astronomers away from them as well
+as in them.
+
+The National Observatory soon became famous by two remarkable
+steps which raised our country to an important position among
+those applying modern science to practical uses. One of these
+consisted of the researches of Sears Cook Walker on the motion of
+the newly discovered planet Neptune. He was the first astronomer
+to determine fairly good elements of the orbit of that planet,
+and, what is yet more remarkable, he was able to trace back the
+movement of the planet in the heavens for half a century and to
+show that it had been observed as a fixed star by Lalande in 1795,
+without the observer having any suspicion of the true character of
+the object.
+
+The other work to which I refer was the application to astronomy
+and to the determination of longitudes of the chronographic method
+of registering transits of stars or other phenomena requiring an
+exact record of the instant of their occurrence. It is to be
+regretted that the history of this application has not been fully
+written. In some points there seems to be as much obscurity as
+with the discovery of ether as an anaesthetic, which took place
+about the same time. Happily, no such contest has been fought over
+the astronomical as over the surgical discovery, the fact being
+that all who were engaged in the application of the new method
+were more anxious to perfect it than they were to get credit for
+themselves. We know that Saxton, of the Coast Survey; Mitchell and
+Locke, of Cincinnati; Bond, at Cambridge, as well as Walker, and
+other astronomers at the Naval Observatory, all worked at the
+apparatus; that Maury seconded their efforts with untiring zeal;
+that it was used to determine the longitude of Baltimore as early
+as 1844 by Captain Wilkes, and that it was put into practical use
+in recording observations at the Naval Observatory as early as
+1846.
+
+At the Cambridge Observatory the two Bonds, father and son,
+speedily began to show the stuff of which the astronomer is made.
+A well-devised system of observations was put in operation. The
+discovery of the dark ring of Saturn and of a new satellite to
+that planet gave additional fame to the establishment.
+
+Nor was activity confined to the observational side of the
+science. The same decade of which I speak was marked by the
+beginning of Professor Pierce's mathematical work, especially his
+determination of the perturbations of Uranus and Neptune. At this
+time commenced the work of Dr. B. A. Gould, who soon became the
+leading figure in American astronomy. Immediately on graduating at
+Harvard in 1845, he determined to devote all the energies of his
+life to the prosecution of his favorite science. He studied in
+Europe for three years, took the doctor's degree at Gottingen,
+came home, founded the Astronomical Journal, and took an active
+part in that branch of the work of the Coast Survey which included
+the determination of longitudes by astronomical methods.
+
+An episode which may not belong to the history of astronomy must
+be acknowledged to have had a powerful influence in exciting
+public interest in that science. Professor O. M. Mitchell, the
+founder and first director of the Cincinnati Observatory, made the
+masses of our intelligent people acquainted with the leading facts
+of astronomy by courses of lectures which, in lucidity and
+eloquence, have never been excelled. The immediate object of the
+lectures was to raise funds for establishing his observatory and
+fitting it out with a fine telescope. The popular interest thus
+excited in the science had an important effect in leading the
+public to support astronomical research. If public support, based
+on public interest, is what has made the present fabric of
+American astronomy possible, then should we honor the name of a
+man whose enthusiasm leavened the masses of his countrymen with
+interest in our science.
+
+The Civil War naturally exerted a depressing influence upon our
+scientific activity. The cultivator of knowledge is no less
+patriotic than his fellow-citizens, and vies with them in devotion
+to the public welfare. The active interest which such cultivators
+took, first in the prosecution of the war and then in the
+restoration of the Union, naturally distracted their attention
+from their favorite pursuits. But no sooner was political
+stability reached than a wave of intellectual activity set in,
+which has gone on increasing up to the present time. If it be true
+that never before in our history has so much attention been given
+to education as now; that never before did so many men devote
+themselves to the diffusion of knowledge, it is no less true that
+never was astronomical work so energetically pursued among us as
+at the present time.
+
+One deplorable result of the Civil War was that Gould's
+Astronomical Journal had to be suspended. Shortly after the
+restoration of peace, instead of re-establishing the journal, its
+founder conceived the project of exploring the southern heavens.
+The northern hemisphere being the seat of civilization, that
+portion of the sky which could not be seen from our latitudes was
+comparatively neglected. What had been done in the southern
+hemisphere was mostly the occasional work of individuals and of
+one or two permanent observatories. The latter were so few in
+number and so meagre in their outfit that a splendid field was
+open to the inquirer. Gould found the patron which he desired in
+the government of the Argentine Republic, on whose territory he
+erected what must rank in the future as one of the memorable
+astronomical establishments of the world. His work affords a most
+striking example of the principle that the astronomer is more
+important than his instruments. Not only were the means at the
+command of the Argentine Observatory slender in the extreme when
+compared with those of the favored institutions of the North, but,
+from the very nature of the case, the Argentine Republic could not
+supply trained astronomers. The difficulties thus growing out of
+the administration cannot be overestimated. And yet the sixteen
+great volumes in which the work of the institution has been
+published will rank in the future among the classics of astronomy.
+
+Another wonderful focus of activity, in which one hardly knows
+whether he ought most to admire the exhaustless energy or the
+admirable ingenuity which he finds displayed, is the Harvard
+Observatory. Its work has been aided by gifts which have no
+parallel in the liberality that prompted them. Yet without energy
+and skill such gifts would have been useless. The activity of the
+establishment includes both hemispheres. Time would fail to tell
+how it has not only mapped out important regions of the heavens
+from the north to the south pole, but analyzed the rays of light
+which come from hundreds of thousands of stars by recording their
+spectra in permanence on photographic plates.
+
+The work of the establishment is so organized that a new star
+cannot appear in any part of the heavens nor a known star undergo
+any noteworthy change without immediate detection by the
+photographic eye of one or more little telescopes, all-seeing and
+never-sleeping policemen that scan the heavens unceasingly while
+the astronomer may sleep, and report in the morning every case of
+irregularity in the proceedings of the heavenly bodies.
+
+Yet another example, showing what great results may be obtained
+with limited means, is afforded by the Lick Observatory, on Mount
+Hamilton, California. During the ten years of its activity its
+astronomers have made it known the world over by works and
+discoveries too varied and numerous to be even mentioned at the
+present time.
+
+The astronomical work of which I have thus far spoken has been
+almost entirely that done at observatories. I fear that I may in
+this way have strengthened an erroneous impression that the seat
+of important astronomical work is necessarily connected with an
+observatory. It must be admitted that an institution which has a
+local habitation and a magnificent building commands public
+attention so strongly that valuable work done elsewhere may be
+overlooked. A very important part of astronomical work is done
+away from telescopes and meridian circles and requires nothing but
+a good library for its prosecution. One who is devoted to this
+side of the subject may often feel that the public does not
+appreciate his work at its true relative value from the very fact
+that he has no great buildings or fine instruments to show. I may
+therefore be allowed to claim as an important factor in the
+American astronomy of the last half-century an institution of
+which few have heard and which has been overlooked because there
+was nothing about it to excite attention.
+
+In 1849 the American Nautical Almanac office was established by a
+Congressional appropriation. The title of this publication is
+somewhat misleading in suggesting a simple enlargement of the
+family almanac which the sailor is to hang up in his cabin for
+daily use. The fact is that what started more than a century ago
+as a nautical almanac has since grown into an astronomical
+ephemeris for the publication of everything pertaining to times,
+seasons, eclipses, and the motions of the heavenly bodies. It is
+the work in which astronomical observations made in all the great
+observatories of the world are ultimately utilized for scientific
+and public purposes. Each of the leading nations of western Europe
+issues such a publication. When the preparation and publication of
+the American ephemeris was decided upon the office was first
+established in Cambridge, the seat of Harvard University, because
+there could most readily be secured the technical knowledge of
+mathematics and theoretical astronomy necessary for the work.
+
+A field of activity was thus opened, of which a number of able
+young men who have since earned distinction in various walks of
+life availed themselves. The head of the office, Commander Davis,
+adopted a policy well fitted to promote their development. He
+translated the classic work of Gauss, Theoria Motus Corporum
+Celestium, and made the office a sort of informal school, not,
+indeed, of the modern type, but rather more like the classic grove
+of Hellas, where philosophers conducted their discussions and
+profited by mutual attrition. When, after a few years of
+experience, methods were well established and a routine adopted,
+the office was removed to Washington, where it has since remained.
+The work of preparing the ephemeris has, with experience, been
+reduced to a matter of routine which may be continued
+indefinitely, with occasional changes in methods and data, and
+improvements to meet the increasing wants of investigators.
+
+The mere preparation of the ephemeris includes but a small part of
+the work of mathematical calculation and investigation required in
+astronomy. One of the great wants of the science to-day is the
+reduction of the observations made during the first half of the
+present century, and even during the last half of the preceding
+one. The labor which could profitably be devoted to this work
+would be more than that required in any one astronomical
+observatory. It is unfortunate for this work that a great building
+is not required for its prosecution because its needfulness is
+thus very generally overlooked by that portion of the public
+interested in the progress of science. An organization especially
+devoted to it is one of the scientific needs of our time.
+
+In such an epoch-making age as the present it is dangerous to cite
+any one step as making a new epoch. Yet it may be that when the
+historian of the future reviews the science of our day he will
+find the most remarkable feature of the astronomy of the last
+twenty years of our century to be the discovery that this
+steadfast earth of which the poets have told us is not, after all,
+quite steadfast; that the north and south poles move about a very
+little, describing curves so complicated that they have not yet
+been fully marked out. The periodic variations of latitude thus
+brought about were first suspected about 1880, and announced with
+some modest assurance by Kustner, of Berlin, a few years later.
+The progress of the views of astronomical opinion from incredulity
+to confidence was extremely slow until, about 1890, Chandler, of
+the United States, by an exhaustive discussion of innumerable
+results of observations, showed that the latitude of every point
+on the earth was subject to a double oscillation, one having a
+period of a year, the other of four hundred and twenty-seven days.
+
+Notwithstanding the remarkable parallel between the growth of
+American astronomy and that of your city, one cannot but fear that
+if a foreign observer had been asked only half a dozen years ago
+at what point in the United States a great school of theoretical
+and practical astronomy, aided by an establishment for the
+exploration of the heavens, was likely to be established by the
+munificence of private citizens, he would have been wiser than
+most foreigners had he guessed Chicago. Had this place been
+suggested to him, I fear he would have replied that were it
+possible to utilize celestial knowledge in acquiring earthly
+wealth, here would be the most promising seat for such a school.
+But he would need to have been a little wiser than his generation
+to reflect that wealth is at the base of all progress in knowledge
+and the liberal arts; that it is only when men are relieved from
+the necessity of devoting all their energies to the immediate
+wants of life that they can lead the intellectual life, and that
+we should therefore look to the most enterprising commercial
+centre as the likeliest seat for a great scientific institution.
+
+Now we have the school, and we have the observatory, which we hope
+will in the near future do work that will cast lustre on the name
+of its founder as well as on the astronomers who may be associated
+with it. You will, I am sure, pardon me if I make some suggestions
+on the subject of the future needs of the establishment. We want
+this newly founded institution to be a great success, to do work
+which shall show that the intellectual productiveness of your
+community will not be allowed to lag behind its material growth
+The public is very apt to feel that when some munificent patron of
+science has mounted a great telescope under a suitable dome, and
+supplied all the apparatus which the astronomer wants to use,
+success is assured. But such is not the case. The most important
+requisite, one more difficult to command than telescopes or
+observatories, may still be wanting. A great telescope is of no
+use without a man at the end of it, and what the telescope may do
+depends more upon this appendage than upon the instrument itself.
+The place which telescopes and observatories have taken in
+astronomical history are by no means proportional to their
+dimensions. Many a great instrument has been a mere toy in the
+hands of its owner. Many a small one has become famous.
+
+Twenty years ago there was here in your own city a modest little
+instrument which, judged by its size, could not hold up its head
+with the great ones even of that day. It was the private property
+of a young man holding no scientific position and scarcely known
+to the public. And yet that little telescope is to-day among the
+famous ones of the world, having made memorable advances in the
+astronomy of double stars, and shown its owner to be a worthy
+successor of the Herschels and Struves in that line of work.
+
+A hundred observers might have used the appliances of the Lick
+Observatory for a whole generation without finding the fifth
+satellite of Jupiter; without successfully photographing the cloud
+forms of the Milky Way; without discovering the extraordinary
+patches of nebulous light, nearly or quite invisible to the human
+eye, which fill some regions of the heavens.
+
+When I was in Zurich last year I paid a visit to the little, but
+not unknown, observatory of its famous polytechnic school. The
+professor of astronomy was especially interested in the
+observations of the sun with the aid of the spectroscope, and
+among the ingenious devices which he described, not the least
+interesting was the method of photographing the sun by special
+rays of the spectrum, which had been worked out at the Kenwood
+Observatory in Chicago. The Kenwood Observatory is not, I believe,
+in the eye of the public, one of the noteworthy institutions of
+your city which every visitor is taken to see, and yet this
+invention has given it an important place in the science of our
+day.
+
+Should you ask me what are the most hopeful features in the great
+establishment which you are now dedicating, I would say that they
+are not alone to be found in the size of your unequalled
+telescope, nor in the cost of the outfit, but in the fact that
+your authorities have shown their appreciation of the requirements
+of success by adding to the material outfit of the establishment
+the three men whose works I have described.
+
+Gentlemen of the trustees, allow me to commend to your fostering
+care the men at the end of the telescope. The constitution of the
+astronomer shows curious and interesting features. If he is
+destined to advance the science by works of real genius, he must,
+like the poet, be born, not made. The born astronomer, when placed
+in command of a telescope, goes about using it as naturally and
+effectively as the babe avails itself of its mother's breast. He
+sees intuitively what less gifted men have to learn by long study
+and tedious experiment. He is moved to celestial knowledge by a
+passion which dominates his nature. He can no more avoid doing
+astronomical work, whether in the line of observations or
+research, than a poet can chain his Pegasus to earth. I do not
+mean by this that education and training will be of no use to him.
+They will certainly accelerate his early progress. If he is to
+become great on the mathematical side, not only must his genius
+have a bend in that direction, but he must have the means of
+pursuing his studies. And yet I have seen so many failures of men
+who had the best instruction, and so many successes of men who
+scarcely learned anything of their teachers, that I sometimes ask
+whether the great American celestial mechanician of the twentieth
+century will be a graduate of a university or of the backwoods.
+
+Is the man thus moved to the exploration of nature by an
+unconquerable passion more to be envied or pitied? In no other
+pursuit does success come with such certainty to him who deserves
+it. No life is so enjoyable as that whose energies are devoted to
+following out the inborn impulses of one's nature. The
+investigator of truth is little subject to the disappointments
+which await the ambitious man in other fields of activity. It is
+pleasant to be one of a brotherhood extending over the world, in
+which no rivalry exists except that which comes out of trying to
+do better work than any one else, while mutual admiration stifles
+jealousy. And yet, with all these advantages, the experience of
+the astronomer may have its dark side. As he sees his field
+widening faster than he can advance he is impressed with the
+littleness of all that can be done in one short life. He feels the
+same want of successors to pursue his work that the founder of a
+dynasty may feel for heirs to occupy his throne. He has no desire
+to figure in history as a Napoleon of science whose conquests must
+terminate with his life. Even during his active career his work
+may be such a kind as to require the co-operation of others and
+the active support of the public. If he is disappointed in
+commanding these requirements, if he finds neither co-operation
+nor support, if some great scheme to which he may have devoted
+much of his life thus proves to be only a castle in the air, he
+may feel that nature has dealt hardly with him in not endowing him
+with passions like to those of other men.
+
+In treating a theme of perennial interest one naturally tries to
+fancy what the future may have in store If the traveller,
+contemplating the ruins of some ancient city which in the long ago
+teemed with the life and activities of generations of men, sees
+every stone instinct with emotion and the dust alive with memories
+of the past, may he not be similarly impressed when he feels that
+he is looking around upon a seat of future empire--a region where
+generations yet unborn may take a leading part in moulding the
+history of the world? What may we not expect of that energy which
+in sixty years has transformed a straggling village into one of
+the world's great centres of commerce? May it not exercise a
+powerful influence on the destiny not only of the country but of
+the world? If so, shall the power thus to be exercised prove an
+agent of beneficence, diffusing light and life among nations, or
+shall it be the opposite?
+
+The time must come ere long when wealth shall outgrow the field in
+which it can be profitably employed. In what direction shall its
+possessors then look? Shall they train a posterity which will so
+use its power as to make the world better that it has lived in it?
+Will the future heir to great wealth prefer the intellectual life
+to the life of pleasure?
+
+We can have no more hopeful answer to these questions than the
+establishment of this great university in the very focus of the
+commercial activity of the West. Its connection with the
+institution we have been dedicating suggests some thoughts on
+science as a factor in that scheme of education best adapted to
+make the power of a wealthy community a benefit to the race at
+large. When we see what a factor science has been in our present
+civilization, how it has transformed the world and increased the
+means of human enjoyment by enabling men to apply the powers of
+nature to their own uses, it is not wonderful that it should claim
+the place in education hitherto held by classical studies. In the
+contest which has thus arisen I take no part but that of a peace-
+maker, holding that it is as important to us to keep in touch with
+the traditions of our race, and to cherish the thoughts which have
+come down to us through the centuries, as it is to enjoy and
+utilize what the present has to offer us. Speaking from this point
+of view, I would point out the error of making the utilitarian
+applications of knowledge the main object in its pursuit. It is an
+historic fact that abstract science--science pursued without any
+utilitarian end--has been at the base of our progress in the
+utilization of knowledge. If in the last century such men as
+Galvani and Volta had been moved by any other motive than love of
+penetrating the secrets of nature they would never have pursued
+the seemingly useless experiments they did, and the foundation of
+electrical science would not have been laid. Our present
+applications of electricity did not become possible until Ohm's
+mathematical laws of the electric current, which when first made
+known seemed little more than mathematical curiosities, had become
+the common property of inventors. Professional pride on the part
+of our own Henry led him, after making the discoveries which
+rendered the telegraph possible, to go no further in their
+application, and to live and die without receiving a dollar of the
+millions which the country has won through his agency.
+
+In the spirit of scientific progress thus shown we have patriotism
+in its highest form--a sentiment which does not seek to benefit
+the country at the expense of the world, but to benefit the world
+by means of one's country. Science has its competition, as keen as
+that which is the life of commerce. But its rivalries are over the
+question who shall contribute the most and the best to the sum
+total of knowledge; who shall give the most, not who shall take
+the most. Its animating spirit is love of truth. Its pride is to
+do the greatest good to the greatest number. It embraces not only
+the whole human race but all nature in its scope. The public
+spirit of which this city is the focus has made the desert blossom
+as the rose, and benefited humanity by the diffusion of the
+material products of the earth. Should you ask me how it is in the
+future to use its influence for the benefit of humanity at large,
+I would say, look at the work now going on in these precincts, and
+study its spirit. Here are the agencies which will make "the voice
+of law the harmony of the world." Here is the love of country
+blended with love of the race. Here the love of knowledge is as
+unconfined as your commercial enterprise. Let not your youth come
+hither merely to learn the forms of vertebrates and the properties
+of oxides, but rather to imbibe that catholic spirit which,
+animating their growing energies, shall make the power they are to
+wield an agent of beneficence to all mankind.
+
+
+
+
+
+XIX
+
+THE UNIVERSE AS AN ORGANISM
+
+[Footnote: Address before the Astronomical and Astrophysical
+Society of America, December 29, 1902]
+
+
+If I were called upon to convey, within the compass of a single
+sentence, an idea of the trend of recent astronomical and physical
+science, I should say that it was in the direction of showing the
+universe to be a connected whole. The farther we advance in
+knowledge, the clearer it becomes that the bodies which are
+scattered through the celestial spaces are not completely
+independent existences, but have, with all their infinite
+diversity, many attributes in common.
+
+In this we are going in the direction of certain ideas of the
+ancients which modern discovery long seemed to have contradicted.
+In the infancy of the race, the idea that the heavens were simply
+an enlarged and diversified earth, peopled by beings who could
+roam at pleasure from one extreme to the other, was a quite
+natural one. The crystalline sphere or spheres which contained all
+formed a combination of machinery revolving on a single plan. But
+all bonds of unity between the stars began to be weakened when
+Copernicus showed that there were no spheres, that the planets
+were isolated bodies, and that the stars were vastly more distant
+than the planets. As discovery went on and our conceptions of the
+universe were enlarged, it was found that the system of the fixed
+stars was made up of bodies so vastly distant and so completely
+isolated that it was difficult to conceive of them as standing in
+any definable relation to one another. It is true that they all
+emitted light, else we could not see them, and the theory of
+gravitation, if extended to such distances, a fact not then
+proved, showed that they acted on one another by their mutual
+gravitation. But this was all. Leaving out light and gravitation,
+the universe was still, in the time of Herschel, composed of
+bodies which, for the most part, could not stand in any known
+relation one to the other.
+
+When, forty years ago, the spectroscope was applied to analyze the
+light coming from the stars, a field was opened not less fruitful
+than that which the telescope made known to Galileo. The first
+conclusion reached was that the sun was composed almost entirely
+of the same elements that existed upon the earth. Yet, as the
+bodies of our solar system were evidently closely related, this
+was not remarkable. But very soon the same conclusion was, to a
+limited extent, extended to the fixed stars in general. Such
+elements as iron, hydrogen, and calcium were found not to belong
+merely to our earth, but to form important constituents of the
+whole universe. We can conceive of no reason why, out of the
+infinite number of combinations which might make up a spectrum,
+there should not be a separate kind of matter for each
+combination. So far as we know, the elements might merge into one
+another by insensible gradations. It is, therefore, a remarkable
+and suggestive fact when we find that the elements which make up
+bodies so widely separate that we can hardly imagine them having
+anything in common, should be so much the same.
+
+In recent times what we may regard as a new branch of astronomical
+science is being developed, showing a tendency towards unity of
+structure throughout the whole domain of the stars. This is what
+we now call the science of stellar statistics. The very conception
+of such a science might almost appall us by its immensity. The
+widest statistical field in other branches of research is that
+occupied by sociology. Every country has its census, in which the
+individual inhabitants are classified on the largest scale and the
+combination of these statistics for different countries may be
+said to include all the interest of the human race within its
+scope. Yet this field is necessarily confined to the surface of
+our planet. In the field of stellar statistics millions of stars
+are classified as if each taken individually were of no more
+weight in the scale than a single inhabitant of China in the scale
+of the sociologist. And yet the most insignificant of these suns
+may, for aught we know, have planets revolving around it, the
+interests of whose inhabitants cover as wide a range as ours do
+upon our own globe.
+
+The statistics of the stars may be said to have commenced with
+Herschel's gauges of the heavens, which were continued from time
+to time by various observers, never, however, on the largest
+scale. The subject was first opened out into an illimitable field
+of research through a paper presented by Kapteyn to the Amsterdam
+Academy of Sciences in 1893. The capital results of this paper
+were that different regions of space contain different kinds of
+stars and, more especially, that the stars of the Milky Way
+belong, in part at least, to a different class from those existing
+elsewhere. Stars not belonging to the Milky Way are, in large
+part, of a distinctly different class.
+
+The outcome of Kapteyn's conclusions is that we are able to
+describe the universe as a single object, with some characters of
+an organized whole. A large part of the stars which compose it may
+be considered as divisible into two groups. One of these comprises
+the stars composing the great girdle of the Milky Way. These are
+distinguished from the others by being bluer in color, generally
+greater in absolute brilliancy, and affected, there is some reason
+to believe, with rather slower proper motions The other classes
+are stars with a greater or less shade of yellow in their color,
+scattered through a spherical space of unknown dimensions, but
+concentric with the Milky Way. Thus a sphere with a girdle passing
+around it forms the nearest approach to a conception of the
+universe which we can reach to-day. The number of stars in the
+girdle is much greater than that in the sphere.
+
+The feature of the universe which should therefore command our
+attention is the arrangement of a large part of the stars which
+compose it in a ring, seemingly alike in all its parts, so far as
+general features are concerned. So far as research has yet gone,
+we are not able to say decisively that one region of this ring
+differs essentially from another. It may, therefore, be regarded
+as forming a structure built on a uniform plan throughout.
+
+All scientific conclusions drawn from statistical data require a
+critical investigation of the basis on which they rest. If we are
+going, from merely counting the stars, observing their magnitudes
+and determining their proper motions, to draw conclusions as to
+the structure of the universe in space, the question may arise how
+we can form any estimate whatever of the possible distance of the
+stars, a conclusion as to which must be the very first step we
+take. We can hardly say that the parallaxes of more than one
+hundred stars have been measured with any approach to certainty.
+The individuals of this one hundred are situated at very different
+distances from. us. We hope, by long and repeated observations, to
+make a fairly approximate determination of the parallaxes of all
+the stars whose distance is less than twenty times that of a
+Centauri. But how can we know anything about the distance of stars
+outside this sphere? What can we say against the view of Kepler
+that the space around our sun is very much thinner in stars than
+it is at a greater distance; in fact, that, the great mass of the
+stars may be situated between the surfaces of two concentrated
+spheres not very different in radius. May not this universe of
+stars be somewhat in the nature of a hollow sphere?
+
+This objection requires very careful consideration on the part of
+all who draw conclusions as to the distribution of stars in space
+and as to the extent of the visible universe. The steps to a
+conclusion on the subject are briefly these: First, we have a
+general conclusion, the basis of which I have already set forth,
+that, to use a loose expression, there are likenesses throughout
+the whole diameter of the universe. There is, therefore, no reason
+to suppose that the region in which our system is situated differs
+in any essential degree from any other region near the central
+portion. Again, spectroscopic examinations seem to show that all
+the stars are in motion, and that we cannot say that those in one
+part of the universe move more rapidly than those in another. This
+result is of the greatest value for our purpose, because, when we
+consider only the apparent motions, as ordinarily observed, these
+are necessarily dependent upon the distance of the star. We
+cannot, therefore, infer the actual speed of a star from ordinary
+observations until we know its distance. But the results of
+spectroscopic measurements of radial velocity are independent of
+the distance of the star.
+
+But let us not claim too much. We cannot yet say with certainty
+that the stars which form the agglomerations of the Milky Way
+have, beyond doubt, the same average motion as the stars in other
+regions of the universe. The difficulty is that these stars appear
+to us so faint individually, that the investigation of their
+spectra is still beyond the powers of our instruments. But the
+extraordinary feat performed at the Lick Observatory of measuring
+the radial motion of 1830 Groombridge, a star quite invisible to
+the naked eye, and showing that it is approaching our system with
+a speed of between fifty and sixty miles a second, may lead us to
+hope for a speedy solution of this question. But we need not await
+this result in order to reach very probable conclusions. The
+general outcome of researches on proper motions tends to
+strengthen the conclusions that the Keplerian sphere, if I may use
+this expression, has no very well marked existence. The laws of
+stellar velocity and the statistics of proper motions, while
+giving some color to the view that the space in which we are
+situated is thinner in stars than elsewhere, yet show that, as a
+general rule, there are no great agglomerations of stars elsewhere
+than in the region of the Milky Way.
+
+With unity there is always diversity; in fact, the unity of the
+universe on which I have been insisting consists in part of
+diversity. It is very curious that, among the many thousands of
+stars which have been spectroscopically examined, no two are known
+to have absolutely the same physical constitution. It is true that
+there are a great many resemblances. a Centauri, our nearest
+neighbor, if we can use such a word as "near" in speaking of its
+distance, has a spectrum very like that of our sun, and so has
+Capella. But even in these cases careful examination shows
+differences. These differences arise from variety in the
+combinations and temperature of the substances of which the star
+is made up. Quite likely also, elements not known on the earth may
+exist on the stars, but this is a point on which we cannot yet
+speak with certainty.
+
+Perhaps the attribute in which the stars show the greatest variety
+is that of absolute luminosity. One hundred years ago it was
+naturally supposed that the brighter stars were the nearest to us,
+and this is doubtless true when we take the general average. But
+it was soon found that we cannot conclude that because a star is
+bright, therefore it is near. The most striking example of this is
+afforded by the absence of measurable parallaxes in the two bright
+stars, Canopus and Rigel, showing that these stars, though of the
+first magnitude, are immeasurably distant. A remarkable fact is
+that these conclusions coincide with that which we draw from the
+minuteness of the proper motions. Rigel has no motion that has
+certainly been shown by more than a century of observation, and it
+is not certain that Canopus has either. From this alone we may
+conclude, with a high degree of probability, that the distance of
+each is immeasurably great. We may say with certainty that the
+brightness of each is thousands of times that of the sun, and with
+a high degree of probability that it is hundreds of thousands of
+times. On the other hand, there are stars comparatively near us of
+which the light is not the hundredth part of the sun.
+
+[Illustration with caption: Star Spectra]
+
+The universe may be a unit in two ways. One is that unity of
+structure to which our attention has just been directed. This
+might subsist forever without one body influencing another. The
+other form of unity leads us to view the universe as an organism.
+It is such by mutual action going on between its bodies. A few
+years ago we could hardly suppose or imagine that any other agents
+than gravitation and light could possibly pass through spaces so
+immense as those which separate the stars.
+
+The most remarkable and hopeful characteristic of the unity of the
+universe is the evidence which is being gathered that there are
+other agencies whose exact nature is yet unknown to us, but which
+do pass from one heavenly body to another. The best established
+example of this yet obtained is afforded in the case of the sun
+and the earth.
+
+The fact that the frequency of magnetic storms goes through a
+period of about eleven years, and is proportional to the frequency
+of sun-spots, has been well established. The recent work of
+Professor Bigelow shows the coincidence to be of remarkable
+exactness, the curves of the two phenomena being practically
+coincident so far as their general features are concerned. The
+conclusion is that spots on the sun and magnetic storms are due to
+the same cause. This cause cannot be any change in the ordinary
+radiation of the sun, because the best records of temperature show
+that, to whatever variations the sun's radiation may be subjected,
+they do not change in the period of the sun-spots. To appreciate
+the relation, we must recall that the researches of Hale with the
+spectro-heliograph show that spots are not the primary phenomenon
+of solar activity, but are simply the outcome of processes going
+on constantly in the sun which result in spots only in special
+regions and on special occasions. It does not, therefore,
+necessarily follow that a spot does cause a magnetic storm. What
+we should conclude is that the solar activity which produces a
+spot also produces the magnetic storm.
+
+When we inquire into the possible nature of these relations
+between solar activity and terrestrial magnetism, we find
+ourselves so completely in the dark that the question of what is
+really proved by the coincidence may arise. Perhaps the most
+obvious explanation of fluctuations in the earth's magnetic field
+to be inquired into would be based on the hypothesis that the
+space through which the earth is moving is in itself a varying
+magnetic field of vast extent. This explanation is tested by
+inquiring whether the fluctuations in question can be explained by
+supposing a disturbing force which acts substantially in the same
+direction all over the globe. But a very obvious test shows that
+this explanation is untenable. Were it the correct one, the
+intensity of the force in some regions of the earth would be
+diminished and in regions where the needle pointed in the opposite
+direction would be increased in exactly the same degree. But there
+is no relation traceable either in any of the regular fluctuations
+of the magnetic force, or in those irregular ones which occur
+during a magnetic storm. If the horizontal force is increased in
+one part of the earth, it is very apt to show a simultaneous
+increase the world over, regardless of the direction in which the
+needle may point in various localities. It is hardly necessary to
+add that none of the fluctuations in terrestrial magnetism can be
+explained on the hypothesis that either the moon or the sun acts
+as a magnet. In such a case the action would be substantially in
+the same direction at the same moment the world over.
+
+Such being the case, the question may arise whether the action
+producing a magnetic storm comes from the sun at all, and whether
+the fluctuations in the sun's activity, and in the earth's
+magnetic field may not be due to some cause external to both. All
+we can say in reply to this is that every effort to find such a
+cause has failed and that it is hardly possible to imagine any
+cause producing such an effect. It is true that the solar spots
+were, not many years ago, supposed to be due in some way to the
+action of the planets. But, for reasons which it would be tedious
+to go into at present, we may fairly regard this hypothesis as
+being completely disproved. There can, I conclude, be little doubt
+that the eleven-year cycle of change in the solar spots is due to
+a cycle going on in the sun itself. Such being the case, the
+corresponding change in the earth's magnetism must be due to the
+same cause.
+
+We may, therefore, regard it as a fact sufficiently established to
+merit further investigation that there does emanate from the sun,
+in an irregular way, some agency adequate to produce a measurable
+effect on the magnetic needle. We must regard it as a singular
+fact that no observations yet made give us the slightest
+indication as to what this emanation is. The possibility of
+defining it is suggested by the discovery within the past few
+years, that under certain conditions, heated matter sends forth
+entities known as Rontgen rays, Becquerel corpuscles and
+electrons. I cannot speak authoritatively on this subject, but, so
+far as I am aware, no direct evidence has yet been gathered
+showing that any of these entities reach us from the sun. We must
+regard the search for the unknown agency so fully proved as among
+the most important tasks of the astronomical physicist of the
+present time. From what we know of the history of scientific
+discovery, it seems highly probable that, in the course of his
+search, he will, before he finds the object he is aiming at,
+discover many other things of equal or greater importance of which
+he had, at the outset, no conception.
+
+The main point I desire to bring out in this review is the
+tendency which it shows towards unification in physical research.
+Heretofore differentiation--the subdivision of workers into a
+continually increasing number of groups of specialists--has been
+the rule. Now we see a coming together of what, at first sight,
+seem the most widely separated spheres of activity. What two
+branches could be more widely separated than that of stellar
+statistics, embracing the whole universe within its scope, and the
+study of these newly discovered emanations, the product of our
+laboratories, which seem to show the existence of corpuscles
+smaller than the atoms of matter? And yet, the phenomena which we
+have reviewed, especially the relation of terrestrial magnetism to
+the solar activity, and the formation of nebulous masses around
+the new stars, can be accounted for only by emanations or forms of
+force, having probably some similarity with the corpuscles,
+electrons, and rays which we are now producing in our
+laboratories. The nineteenth century, in passing away, points with
+pride to what it has done. It has become a word to symbolize what
+is most important in human progress Yet, perhaps its greatest
+glory may prove to be that the last thing it did was to lay a
+foundation for the physical science of the twentieth century. What
+shall be discovered in the new fields is, at present, as far
+without our ken as were the modern developments of electricity
+without the ken of the investigators of one hundred years ago. We
+cannot guarantee any special discovery. What lies before us is an
+illimitable field, the existence of which was scarcely suspected
+ten years ago, the exploration of which may well absorb the
+activities of our physical laboratories, and of the great mass of
+our astronomical observers and investigators for as many
+generations as were required to bring electrical science to its
+present state. We of the older generation cannot hope to see more
+than the beginning of this development, and can only tender our
+best wishes and most hearty congratulations to the younger school
+whose function it will be to explore the limitless field now
+before it.
+
+
+
+
+
+XX
+
+THE RELATION OF SCIENTIFIC METHOD TO SOCIAL PROGRESS
+[Footnote: An address before the Washington Philosophical Society]
+
+
+Among those subjects which are not always correctly apprehended,
+even by educated men, we may place that of the true significance
+of scientific method and the relations of such method to practical
+affairs. This is especially apt to be the case in a country like
+our own, where the points of contact between the scientific world
+on the one hand, and the industrial and political world on the
+other, are fewer than in other civilized countries. The form which
+this misapprehension usually takes is that of a failure to
+appreciate the character of scientific method, and especially its
+analogy to the methods of practical life. In the judgment of the
+ordinary intelligent man there is a wide distinction between
+theoretical and practical science. The latter he considers as that
+science directly applicable to the building of railroads, the
+construction of engines, the invention of new machinery, the
+construction of maps, and other useful objects. The former he
+considers analogous to those philosophic speculations in which men
+have indulged in all ages without leading to any result which he
+considers practical. That our knowledge of nature is increased by
+its prosecution is a fact of which he is quite conscious, but he
+considers it as terminating with a mere increase of knowledge, and
+not as having in its method anything which a person devoted to
+material interests can be expected to appreciate.
+
+This view is strengthened by the spirit with which he sees
+scientific investigation prosecuted. It is well understood on all
+sides that when such investigations are pursued in a spirit really
+recognized as scientific, no merely utilitarian object is had in
+view. Indeed, it is easy to see how the very fact of pursuing such
+an object would detract from that thoroughness of examination
+which is the first condition of a real advance. True science
+demands in its every research a completeness far beyond what is
+apparently necessary for its practical applications. The precision
+with which the astronomer seeks to measure the heavens and the
+chemist to determine the relations of the ultimate molecules of
+matter has no limit, except that set by the imperfections of the
+instruments of research. There is no such division recognized as
+that of useful and useless knowledge. The ultimate aim is nothing
+less than that of bringing all the phenomena of nature under laws
+as exact as those which govern the planetary motions.
+
+Now the pursuit of any high object in this spirit commands from
+men of wide views that respect which is felt towards all exertion
+having in view more elevated objects than the pursuit of gain.
+Accordingly, it is very natural to classify scientists and
+philosophers with the men who in all ages have sought after
+learning instead of utility. But there is another aspect of the
+question which will show the relations of scientific advance to
+the practical affairs of life in a different light. I make bold to
+say that the greatest want of the day, from a purely practical
+point of view, is the more general introduction of the scientific
+method and the scientific spirit into the discussion of those
+political and social problems which we encounter on our road to a
+higher plane of public well being. Far from using methods too
+refined for practical purposes, what most distinguishes scientific
+from other thought is the introduction of the methods of practical
+life into the discussion of abstract general problems. A single
+instance will illustrate the lesson I wish to enforce.
+
+The question of the tariff is, from a practical point of view, one
+of the most important with which our legislators will have to deal
+during the next few years. The widest diversity of opinion exists
+as to the best policy to be pursued in collecting a revenue from
+imports. Opposing interests contend against one another without
+any common basis of fact or principle on which a conclusion can be
+reached. The opinions of intelligent men differ almost as widely
+as those of the men who are immediately interested. But all will
+admit that public action in this direction should be dictated by
+one guiding principle--that the greatest good of the community is
+to be sought after. That policy is the best which will most
+promote this good. Nor is there any serious difference of opinion
+as to the nature of the good to be had in view; it is in a word
+the increase of the national wealth and prosperity. The question
+on which opinions fundamentally differ is that of the effects of a
+higher or lower rate of duty upon the interests of the public. If
+it were possible to foresee, with an approach to certainty, what
+effect a given tariff would have upon the producers and consumers
+of an article taxed, and, indirectly, upon each member of the
+community in any way interested in the article, we should then
+have an exact datum which we do not now possess for reaching a
+conclusion. If some superhuman authority, speaking with the voice
+of infallibility, could give us this information, it is evident
+that a great national want would be supplied. No question in
+practical life is more important than this: How can this desirable
+knowledge of the economic effects of a tariff be obtained?
+
+The answer to this question is clear and simple. The subject must
+be studied in the same spirit, and, to a certain extent, by the
+same methods which have been so successful in advancing our
+knowledge of nature. Every one knows that, within the last two
+centuries, a method of studying the course of nature has been
+introduced which has been so successful in enabling us to trace
+the sequence of cause and effect as almost to revolutionize
+society. The very fact that scientific method has been so
+successful here leads to the belief that it might be equally
+successful in other departments of inquiry.
+
+The same remarks will apply to the questions connected with
+banking and currency; the standard of value; and, indeed, all
+subjects which have a financial bearing. On every such question we
+see wide differences of opinion without any common basis to rest
+upon.
+
+It may be said, in reply, that in these cases there are really no
+grounds for forming an opinion, and that the contests which arise
+over them are merely those between conflicting interests. But this
+claim is not at all consonant with the form which we see the
+discussion assume. Nearly every one has a decided opinion on these
+several subjects; whereas, if there were no data for forming an
+opinion, it would be unreasonable to maintain any whatever.
+Indeed, it is evident that there must be truth somewhere, and the
+only question that can be open is that of the mode of discovering
+it. No man imbued with a scientific spirit can claim that such
+truth is beyond the power of the human intellect. He may doubt his
+own ability to grasp it, but cannot doubt that by pursuing the
+proper method and adopting the best means the problem can be
+solved. It is, in fact, difficult to show why some exact results
+could not be as certainly reached in economic questions as in
+those of physical science. It is true that if we pursue the
+inquiry far enough we shall find more complex conditions to
+encounter, because the future course of demand and supply enters
+as an uncertain element. But a remarkable fact to be considered is
+that the difference of opinion to which we allude does not depend
+upon different estimates of the future, but upon different views
+of the most elementary and general principles of the subject. It
+is as if men were not agreed whether air were elastic or whether
+the earth turns on its axis. Why is it that while in all subjects
+of physical science we find a general agreement through a wide
+range of subjects, and doubt commences only where certainty is not
+attained, yet when we turn to economic subjects we do not find the
+beginning of an agreement?
+
+No two answers can be given. It is because the two classes of
+subjects are investigated by different instruments and in a
+different spirit. The physicist has an exact nomenclature; uses
+methods of research well adapted to the objects he has in view;
+pursues his investigations without being attacked by those who
+wish for different results; and, above all, pursues them only for
+the purpose of discovering the truth. In economic questions the
+case is entirely different. Only in rare cases are they studied
+without at least the suspicion that the student has a preconceived
+theory to support. If results are attained which oppose any
+powerful interest, this interest can hire a competing investigator
+to bring out a different result. So far as the public can see, one
+man's result is as good as another's, and thus the object is as
+far off as ever. We may be sure that until there is an intelligent
+and rational public, able to distinguish between the speculations
+of the charlatan and the researches of the investigator, the
+present state of things will continue. What we want is so wide a
+diffusion of scientific ideas that there shall be a class of men
+engaged in studying economic problems for their own sake, and an
+intelligent public able to judge what they are doing. There must
+be an improvement in the objects at which they aim in education,
+and it is now worth while to inquire what that improvement is.
+
+It is not mere instruction in any branch of technical science that
+is wanted. No knowledge of chemistry, physics, or biology, however
+extensive, can give the learner much aid in forming a correct
+opinion of such a question as that of the currency. If we should
+claim that political economy ought to be more extensively studied,
+we would be met by the question, which of several conflicting
+systems shall we teach? What is wanted is not to teach this system
+or that, but to give such a training that the student shall be
+able to decide for himself which system is right.
+
+It seems to me that the true educational want is ignored both by
+those who advocate a classical and those who advocate a scientific
+education. What is really wanted is to train the intellectual
+powers, and the question ought to be, what is the best method of
+doing this? Perhaps it might be found that both of the conflicting
+methods could be improved upon. The really distinctive features,
+which we should desire to see introduced, are two in number: the
+one the scientific spirit; the other the scientific discipline.
+Although many details may be classified under each of these heads,
+yet there is one of pre-eminent importance on which we should
+insist.
+
+The one feature of the scientific spirit which outweighs all
+others in importance is the love of knowledge for its own sake. If
+by our system of education we can inculcate this sentiment we
+shall do what is, from a public point of view, worth more than any
+amount of technical knowledge, because we shall lay the foundation
+of all knowledge. So long as men study only what they think is
+going to be useful their knowledge will be partial and
+insufficient. I think it is to the constant inculcation of this
+fact by experience, rather than to any reasoning, that is due the
+continued appreciation of a liberal education. Every business-man
+knows that a business-college training is of very little account
+in enabling one to fight the battle of life, and that college-bred
+men have a great advantage even in fields where mere education is
+a secondary matter. We are accustomed to seeing ridicule thrown
+upon the questions sometimes asked of candidates for the civil
+service because the questions refer to subjects of which a
+knowledge is not essential. The reply to all criticisms of this
+kind is that there is no one quality which more certainly assures
+a man's usefulness to society than the propensity to acquire
+useless knowledge. Most of our citizens take a wide interest in
+public affairs, else our form of government would be a failure.
+But it is desirable that their study of public measures should be
+more critical and take a wider range. It is especially desirable
+that the conclusions to which they are led should be unaffected by
+partisan sympathies. The more strongly the love of mere truth is
+inculcated in their nature the better this end will be attained.
+
+The scientific discipline to which I ask mainly to call your
+attention consists in training the scholar to the scientific use
+of language. Although whole volumes may be written on the logic of
+science there is one general feature of its method which is of
+fundamental significance. It is that every term which it uses and
+every proposition which it enunciates has a precise meaning which
+can be made evident by proper definitions. This general principle
+of scientific language is much more easily inculcated by example
+than subject to exact description; but I shall ask leave to add
+one to several attempts I have made to define it. If I should say
+that when a statement is made in the language of science the
+speaker knows what he means, and the hearer either knows it or can
+be made to know it by proper definitions, and that this community
+of understanding is frequently not reached in other departments of
+thought, I might be understood as casting a slur on whole
+departments of inquiry. Without intending any such slur, I may
+still say that language and statements are worthy of the name
+scientific as they approach this standard; and, moreover, that a
+great deal is said and written which does not fulfil the
+requirement. The fact that words lose their meaning when removed
+from the connections in which that meaning has been acquired and
+put to higher uses, is one which, I think, is rarely recognized.
+There is nothing in the history of philosophical inquiry more
+curious than the frequency of interminable disputes on subjects
+where no agreement can be reached because the opposing parties do
+not use words in the same sense. That the history of science is
+not free from this reproach is shown by the fact of the long
+dispute whether the force of a moving body was proportional to the
+simple velocity or to its square. Neither of the parties to the
+dispute thought it worth while to define what they meant by the
+word "force," and it was at length found that if a definition was
+agreed upon the seeming difference of opinion would vanish.
+Perhaps the most striking feature of the case, and one peculiar to
+a scientific dispute, was that the opposing parties did not differ
+in their solution of a single mechanical problem. I say this is
+curious, because the very fact of their agreeing upon every
+concrete question which could have been presented ought to have
+made it clear that some fallacy was lacking in the discussion as
+to the measure of force. The good effect of a scientific spirit is
+shown by the fact that this discussion is almost unique in the
+history of science during the past two centuries, and that
+scientific men themselves were able to see the fallacy involved,
+and thus to bring the matter to a conclusion.
+
+If we now turn to the discussion of philosophers, we shall find at
+least one yet more striking example of the same kind. The question
+of the freedom of the human will has, I believe, raged for
+centuries. It cannot yet be said that any conclusion has been
+reached. Indeed, I have heard it admitted by men of high
+intellectual attainments that the question was insoluble. Now a
+curious feature of this dispute is that none of the combatants, at
+least on the affirmative side, have made any serious attempt to
+define what should be meant by the phrase freedom of the will,
+except by using such terms as require definition equally with the
+word freedom itself. It can, I conceive, be made quite clear that
+the assertion, "The will is free," is one without meaning, until
+we analyze more fully the different meanings to be attached to the
+word free. Now this word has a perfectly well-defined
+signification in every-day life. We say that anything is free when
+it is not subject to external constraint. We also know exactly
+what we mean when we say that a man is free to do a certain act.
+We mean that if he chooses to do it there is no external
+constraint acting to prevent him. In all cases a relation of two
+things is implied in the word, some active agent or power, and the
+presence or absence of another constraining agent. Now, when we
+inquire whether the will itself is free, irrespective of external
+constraints, the word free no longer has a meaning, because one of
+the elements implied in it is ignored.
+
+To inquire whether the will itself is free is like inquiring
+whether fire itself is consumed by the burning, or whether
+clothing is itself clad. It is not, therefore, at all surprising
+that both parties have been able to dispute without end, but it is
+a most astonishing phenomenon of the human intellect that the
+dispute should go on generation after generation without the
+parties finding out whether there was really any difference of
+opinion between them on the subject. I venture to say that if
+there is any such difference, neither party has ever analyzed the
+meaning of the words used sufficiently far to show it. The daily
+experience of every man, from his cradle to his grave, shows that
+human acts are as much the subject of external causal influences
+as are the phenomena of nature. To dispute this would be little
+short of the ludicrous. All that the opponents of freedom, as a
+class, have ever claimed is the assertion of a causal connection
+between the acts of the will and influences independent of the
+will. True, propositions of this sort can be expressed in a
+variety of ways connoting an endless number of more or less
+objectionable ideas, but this is the substance of the matter.
+
+To suppose that the advocates on the other side meant to take
+issue on this proposition would be to assume that they did not
+know what they were saying. The conclusion forced upon us is that
+though men spend their whole lives in the study of the most
+elevated department of human thought it does not guard them
+against the danger of using words without meaning. It would be a
+mark of ignorance, rather than of penetration, to hastily denounce
+propositions on subjects we are not well acquainted with because
+we do not understand their meaning. I do not mean to intimate that
+philosophy itself is subject to this reproach. When we see a
+philosophical proposition couched in terms we do not understand,
+the most modest and charitable view is to assume that this arises
+from our lack of knowledge. Nothing is easier than for the
+ignorant to ridicule the propositions of the learned. And yet,
+with every reserve, I cannot but feel that the disputes to which I
+have alluded prove the necessity of bringing scientific precision
+of language into the whole domain of thought. If the discussion
+had been confined to a few, and other philosophers had analyzed
+the subject, and showed the fictitious character of the
+discussion, or had pointed out where opinions really might differ,
+there would be nothing derogatory to philosophers. But the most
+suggestive circumstance is that although a large proportion of the
+philosophic writers in recent times have devoted more or less
+attention to the subject, few, or none, have made even this modest
+contribution. I speak with some little confidence on this subject,
+because several years ago I wrote to one of the most acute
+thinkers of the country, asking if he could find in philosophic
+literature any terms or definitions expressive of the three
+different senses in which not only the word freedom, but nearly
+all words implying freedom were used. His search was in vain.
+
+Nothing of this sort occurs in the practical affairs of life. All
+terms used in business, however general or abstract, have that
+well-defined meaning which is the first requisite of the
+scientific language. Now one important lesson which I wish to
+inculcate is that the language of science in this respect
+corresponds to that of business; in that each and every term that
+is employed has a meaning as well defined as the subject of
+discussion can admit of. It will be an instructive exercise to
+inquire what this peculiarity of scientific and business language
+is. It can be shown that a certain requirement should be fulfilled
+by all language intended for the discovery of truth, which is
+fulfilled only by the two classes of language which I have
+described. It is one of the most common errors of discourse to
+assume that any common expression which we may use always conveys
+an idea, no matter what the subject of discourse. The true state
+of the case can, perhaps, best be seen by beginning at the
+foundation of things and examining under what conditions language
+can really convey ideas.
+
+Suppose thrown among us a person of well-developed intellect, but
+unacquainted with a single language or word that we use. It is
+absolutely useless to talk to him, because nothing that we say
+conveys any meaning to his mind. We can supply him no dictionary,
+because by hypothesis he knows no language to which we have
+access. How shall we proceed to communicate our ideas to him?
+Clearly there is but one possible way--namely, through his senses.
+Outside of this means of bringing him in contact with us we can
+have no communication with him. We, therefore, begin by showing
+him sensible objects, and letting him understand that certain
+words which we use correspond to those objects. After he has thus
+acquired a small vocabulary, we make him understand that other
+terms refer to relations between objects which he can perceive by
+his senses. Next he learns, by induction, that there are terms
+which apply not to special objects, but to whole classes of
+objects. Continuing the same process, he learns that there are
+certain attributes of objects made known by the manner in which
+they affect his senses, to which abstract terms are applied.
+Having learned all this, we can teach him new words by combining
+words without exhibiting objects already known. Using these words
+we can proceed yet further, building up, as it were, a complete
+language. But there is one limit at every step. Every term which
+we make known to him must depend ultimately upon terms the meaning
+of which he has learned from their connection with special objects
+of sense.
+
+To communicate to him a knowledge of words expressive of mental
+states it is necessary to assume that his own mind is subject to
+these states as well as our own, and that we can in some way
+indicate them by our acts. That the former hypothesis is
+sufficiently well established can be made evident so long as a
+consistency of different words and ideas is maintained. If no such
+consistency of meaning on his part were evident, it might indicate
+that the operations of his mind were so different from ours that
+no such communication of ideas was possible. Uncertainty in this
+respect must arise as soon as we go beyond those mental states
+which communicate themselves to the senses of others.
+
+We now see that in order to communicate to our foreigner a
+knowledge of language, we must follow rules similar to those
+necessary for the stability of a building. The foundation of the
+building must be well laid upon objects knowable by his five
+senses. Of course the mind, as well as the external object, may be
+a factor in determining the ideas which the words are intended to
+express; but this does not in any manner invalidate the conditions
+which we impose. Whatever theory we may adopt of the relative part
+played by the knowing subject, and the external object in the
+acquirement of knowledge, it remains none the less true that no
+knowledge of the meaning of a word can be acquired except through
+the senses, and that the meaning is, therefore, limited by the
+senses. If we transgress the rule of founding each meaning upon
+meanings below it, and having the whole ultimately resting upon a
+sensuous foundation, we at once branch off into sound without
+sense. We may teach him the use of an extended vocabulary, to the
+terms of which he may apply ideas of his own, more or less vague,
+but there will be no way of deciding that he attaches the same
+meaning to these terms that we do.
+
+What we have shown true of an intelligent foreigner is necessarily
+true of the growing child. We come into the world without a
+knowledge of the meaning of words, and can acquire such knowledge
+only by a process which we have found applicable to the
+intelligent foreigner. But to confine ourselves within these
+limits in the use of language requires a course of severe mental
+discipline. The transgression of the rule will naturally seem to
+the undisciplined mind a mark of intellectual vigor rather than
+the reverse. In our system of education every temptation is held
+out to the learner to transgress the rule by the fluent use of
+language to which it is doubtful if he himself attaches clear
+notions, and which he can never be certain suggests to his hearer
+the ideas which he desires to convey. Indeed, we not infrequently
+see, even among practical educators, expressions of positive
+antipathy to scientific precision of language so obviously opposed
+to good sense that they can be attributed only to a failure to
+comprehend the meaning of the language which they criticise.
+
+Perhaps the most injurious effect in this direction arises from
+the natural tendency of the mind, when not subject to a scientific
+discipline, to think of words expressing sensible objects and
+their relations as connoting certain supersensuous attributes.
+This is frequently seen in the repugnance of the metaphysical mind
+to receive a scientific statement about a matter of fact simply as
+a matter of fact. This repugnance does not generally arise in
+respect to the every-day matters of life. When we say that the
+earth is round we state a truth which every one is willing to
+receive as final. If without denying that the earth was round, one
+should criticise the statement on the ground that it was not
+necessarily round but might be of some other form, we should
+simply smile at this use of language. But when we take a more
+general statement and assert that the laws of nature are
+inexorable, and that all phenomena, so far as we can show, occur
+in obedience to their requirements, we are met with a sort of
+criticism with which all of us are familiar, but which I am unable
+adequately to describe. No one denies that as a matter of fact,
+and as far as his experience extends, these laws do appear to be
+inexorable. I have never heard of any one professing, during the
+present generation, to describe a natural phenomenon, with the
+avowed belief that it was not a product of natural law; yet we
+constantly hear the scientific view criticised on the ground that
+events MAY occur without being subject to natural law. The word
+"may," in this connection, is one to which we can attach no
+meaning expressive of a sensuous relation.
+
+The analogous conflict between the scientific use of language and
+the use made by some philosophers is found in connection with the
+idea of causation. Fundamentally the word cause is used in
+scientific language in the same sense as in the language of common
+life. When we discuss with our neighbors the cause of a fit of
+illness, of a fire, or of cold weather, not the slightest
+ambiguity attaches to the use of the word, because whatever
+meaning may be given to it is founded only on an accurate analysis
+of the ideas involved in it from daily use. No philosopher objects
+to the common meaning of the word, yet we frequently find men of
+eminence in the intellectual world who will not tolerate the
+scientific man in using the word in this way. In every explanation
+which he can give to its use they detect ambiguity. They insist
+that in any proper use of the term the idea of power must be
+connoted. But what meaning is here attached to the word power, and
+how shall we first reduce it to a sensible form, and then apply
+its meaning to the operations of nature? Whether this can be done,
+I do not inquire. All I maintain is that if we wish to do it, we
+must pass without the domain of scientific statement.
+
+Perhaps the greatest advantage in the use of symbolic and other
+mathematical language in scientific investigation is that it
+cannot possibly be made to connote anything except what the
+speaker means. It adheres to the subject matter of discourse with
+a tenacity which no criticism can overcome. In consequence,
+whenever a science is reduced to a mathematical form its
+conclusions are no longer the subject of philosophical attack. To
+secure the same desirable quality in all other scientific language
+it is necessary to give it, so far as possible, the same
+simplicity of signification which attaches to mathematical
+symbols. This is not easy, because we are obliged to use words of
+ordinary language, and it is impossible to divest them of whatever
+they may connote to ordinary hearers.
+
+I have thus sought to make it clear that the language of science
+corresponds to that of ordinary life, and especially of business
+life, in confining its meaning to phenomena. An analogous
+statement may be made of the method and objects of scientific
+investigation. I think Professor Clifford was very happy in
+defining science as organized common-sense. The foundation of its
+widest general creations is laid, not in any artificial theories,
+but in the natural beliefs and tendencies of the human mind. Its
+position against those who deny these generalizations is quite
+analogous to that taken by the Scottish school of philosophy
+against the scepticism of Hume.
+
+It may be asked, if the methods and language of science correspond
+to those of practical life, why is not the every-day discipline of
+that life as good as the discipline of science? The answer is,
+that the power of transferring the modes of thought of common life
+to subjects of a higher order of generality is a rare faculty
+which can be acquired only by scientific discipline. What we want
+is that in public affairs men shall reason about questions of
+finance, trade, national wealth, legislation, and administration,
+with the same consciousness of the practical side that they reason
+about their own interests. When this habit is once acquired and
+appreciated, the scientific method will naturally be applied to
+the study of questions of social policy. When a scientific
+interest is taken in such questions, their boundaries will be
+extended beyond the utilities immediately involved, and one
+important condition of unceasing progress will be complied with.
+
+
+
+
+
+XXI
+
+THE OUTLOOK FOR THE FLYING-MACHINE
+
+
+Mr. Secretary Langley's trial of his flying-machine, which seems
+to have come to an abortive issue for the time, strikes a
+sympathetic chord in the constitution of our race. Are we not the
+lords of creation? Have we not girdled the earth with wires
+through which we speak to our antipodes? Do we not journey from
+continent to continent over oceans that no animal can cross, and
+with a speed of which our ancestors would never have dreamed? Is
+not all the rest of the animal creation so far inferior to us in
+every point that the best thing it can do is to become completely
+subservient to our needs, dying, if need be, that its flesh may
+become a toothsome dish on our tables? And yet here is an
+insignificant little bird, from whose mind, if mind it has, all
+conceptions of natural law are excluded, applying the rules of
+aerodynamics in an application of mechanical force to an end we
+have never been able to reach, and this with entire ease and
+absence of consciousness that it is doing an extraordinary thing.
+Surely our knowledge of natural laws, and that inventive genius
+which has enabled us to subordinate all nature to our needs, ought
+also to enable us to do anything that the bird can do. Therefore
+we must fly. If we cannot yet do it, it is only because we have
+not got to the bottom of the subject. Our successors of the not
+distant future will surely succeed.
+
+This is at first sight a very natural and plausible view of the
+case. And yet there are a number of circumstances of which we
+should take account before attempting a confident forecast. Our
+hope for the future is based on what we have done in the past. But
+when we draw conclusions from past successes we should not lose
+sight of the conditions on which success has depended. There is no
+advantage which has not its attendant drawbacks; no strength which
+has not its concomitant weakness. Wealth has its trials and health
+its dangers. We must expect our great superiority to the bird to
+be associated with conditions which would give it an advantage at
+some point. A little study will make these conditions clear.
+
+We may look on the bird as a sort of flying-machine complete in
+itself, of which a brain and nervous system are fundamentally
+necessary parts. No such machine can navigate the air unless
+guided by something having life. Apart from this, it could be of
+little use to us unless it carried human beings on its wings. We
+thus meet with a difficulty at the first step--we cannot give a
+brain and nervous system to our machine. These necessary adjuncts
+must be supplied by a man, who is no part of the machine, but
+something carried by it. The bird is a complete machine in itself.
+Our aerial ship must be machine plus man. Now, a man is, I
+believe, heavier than any bird that flies. The limit which the
+rarity of the air places upon its power of supporting wings, taken
+in connection with the combined weight of a man and a machine,
+make a drawback which we should not too hastily assume our ability
+to overcome. The example of the bird does not prove that man can
+fly. The hundred and fifty pounds of dead weight which the manager
+of the machine must add to it over and above that necessary in the
+bird may well prove an insurmountable obstacle to success.
+
+I need hardly remark that the advantage possessed by the bird has
+its attendant drawbacks when we consider other movements than
+flying. Its wings are simply one pair of its legs, and the human
+race could not afford to abandon its arms for the most effective
+wings that nature or art could supply.
+
+Another point to be considered is that the bird operates by the
+application of a kind of force which is peculiar to the animal
+creation, and no approach to which has ever been made in any
+mechanism. This force is that which gives rise to muscular action,
+of which the necessary condition is the direct action of a nervous
+system. We cannot have muscles or nerves for our flying-machine.
+We have to replace them by such crude and clumsy adjuncts as
+steam-engines and electric batteries. It may certainly seem
+singular if man is never to discover any combination of substances
+which, under the influence of some such agency as an electric
+current, shall expand and contract like a muscle. But, if he is
+ever to do so, the time is still in the future. We do not see the
+dawn of the age in which such a result will be brought forth.
+
+Another consideration of a general character may be introduced. As
+a rule it is the unexpected that happens in invention as well as
+discovery. There are many problems which have fascinated mankind
+ever since civilization began which we have made little or no
+advance in solving. The only satisfaction we can feel in our
+treatment of the great geometrical problems of antiquity is that
+we have shown their solution to be impossible. The mathematician
+of to-day admits that he can neither square the circle, duplicate
+the cube or trisect the angle. May not our mechanicians, in like
+manner, be ultimately forced to admit that aerial flight is one of
+that great class of problems with which man can never cope, and
+give up all attempts to grapple with it?
+
+[Illustration with caption: PROFESSOR LANGLEY'S AIR-SHIP]
+
+The fact is that invention and discovery have, notwithstanding
+their seemingly wide extent, gone on in rather narrower lines than
+is commonly supposed. If, a hundred years ago, the most sagacious
+of mortals had been told that before the nineteenth century closed
+the face of the earth would be changed, time and space almost
+annihilated, and communication between continents made more rapid
+and easy than it was between cities in his time; and if he had
+been asked to exercise his wildest imagination in depicting what
+might come--the airship and the flying-machine would probably have
+had a prominent place in his scheme, but neither the steamship,
+the railway, the telegraph, nor the telephone would have been
+there. Probably not a single new agency which he could have
+imagined would have been one that has come to pass.
+
+It is quite clear to me that success must await progress of a
+different kind from that which the inventors of flying-machines
+are aiming at. We want a great discovery, not a great invention.
+It is an unfortunate fact that we do not always appreciate the
+distinction between progress in scientific discovery and ingenious
+application of discovery to the wants of civilization. The name of
+Marconi is familiar to every ear; the names of Maxwell and Herz,
+who made the discoveries which rendered wireless telegraphy
+possible, are rarely recalled. Modern progress is the result of
+two factors: Discoveries of the laws of nature and of actions or
+possibilities in nature, and the application of such discoveries
+to practical purposes. The first is the work of the scientific
+investigator, the second that of the inventor.
+
+In view of the scientific discoveries of the past ten years,
+which, after bringing about results that would have seemed
+chimerical if predicted, leading on to the extraction of a
+substance which seems to set the laws and limits of nature at
+defiance by radiating a flood of heat, even when cooled to the
+lowest point that science can reach--a substance, a few specks of
+which contain power enough to start a railway train, and embody
+perpetual motion itself, almost--he would be a bold prophet who
+would set any limit to possible discoveries in the realm of
+nature. We are binding the universe together by agencies which
+pass from sun to planet and from star to star. We are determined
+to find out all we can about the mysterious ethereal medium
+supposed to fill all space, and which conveys light and heat from
+one heavenly body to another, but which yet evades all direct
+investigation. We are peering into the law of gravitation itself
+with the full hope of discovering something in its origin which
+may enable us to evade its action. From time to time philosophers
+fancy the road open to success, yet nothing that can be
+practically called success has yet been reached or even
+approached. When it is reached, when we are able to state exactly
+why matter gravitates, then will arise the question how this
+hitherto unchangeable force may be controlled and regulated. With
+this question answered the problem of the interaction between
+ether and matter may be solved. That interaction goes on between
+ethers and molecules is shown by the radiation of heat by all
+bodies. When the molecules are combined into a mass, this
+interaction ceases, so that the lightest objects fly through the
+ether without resistance. Why is this? Why does ether act on the
+molecule and not the mass? When we can produce the latter, and
+when the mutual action can be controlled, then may gravitation be
+overcome and then may men build, not merely airships, but ships
+which shall fly above the air, and transport their passengers from
+continent to continent with the speed of the celestial motions.
+
+The first question suggested to the reader by these considerations
+is whether any such result is possible; whether it is within the
+power of man to discover the nature of luminiferous ether and the
+cause of gravitation. To this the profoundest philosopher can only
+answer, "I do not know." Quite possibly the gates at which he is
+beating are, in the very nature of things, incapable of being
+opened. It may be that the mind of man is incapable of grasping
+the secrets within them. The question has even occurred to me
+whether, if a being of such supernatural power as to understand
+the operations going on in a molecule of matter or in a current of
+electricity as we understand the operations of a steam-engine
+should essay to explain them to us, he would meet with any more
+success than we should in explaining to a fish the engines of a
+ship which so rudely invades its domain. As was remarked by
+William K. Clifford, perhaps the clearest spirit that has ever
+studied such problems, it is possible that the laws of geometry
+for spaces infinitely small may be so different from those of
+larger spaces that we must necessarily be unable to conceive them.
+
+Still, considering mere possibilities, it is not impossible that
+the twentieth century may be destined to make known natural forces
+which will enable us to fly from continent to continent with a
+speed far exceeding that of the bird.
+
+But when we inquire whether aerial flight is possible in the
+present state of our knowledge, whether, with such materials as we
+possess, a combination of steel, cloth, and wire can be made
+which, moved by the power of electricity or steam, shall form a
+successful flying-machine, the outlook may be altogether
+different. To judge it sanely, let us bear in mind the
+difficulties which are encountered in any flying-machine. The
+basic principle on which any such machine must be constructed is
+that of the aeroplane. This, by itself, would be the simplest of
+all flyers, and therefore the best if it could be put into
+operation. The principle involved may be readily comprehended by
+the accompanying figure. A M is the section of a flat plane
+surface, say a thin sheet of metal or a cloth supported by wires.
+It moves through the air, the latter being represented by the
+horizontal rows of dots. The direction of the motion is that of
+the horizontal line A P. The aeroplane has a slight inclination
+measured by the proportion between the perpendicular M P and the
+length A P. We may raise the edge M up or lower it at pleasure.
+Now the interesting point, and that on which the hopes of
+inventors are based, is that if we give the plane any given
+inclination, even one so small that the perpendicular M P is only
+two or three per cent of the length A M, we can also calculate a
+certain speed of motion through the air which, if given to the
+plane, will enable it to bear any required weight. A plane ten
+feet square, for example, would not need any great inclination,
+nor would it require a speed higher than a few hundred feet a
+second to bear a man. What is of yet more importance, the higher
+the speed the less the inclination required, and, if we leave out
+of consideration the friction of the air and the resistance
+arising from any object which the machine may carry, the less the
+horse-power expended in driving the plane.
+
+[Illustration]
+
+Maxim exemplified this by experiment several years ago. He found
+that, with a small inclination, he could readily give his
+aeroplane, when it slid forward upon ways, such a speed that it
+would rise from the ways of itself. The whole problem of the
+successful flying-machine is, therefore, that of arranging an
+aeroplane that shall move through the air with the requisite
+speed.
+
+The practical difficulties in the way of realizing the movement of
+such an object are obvious. The aeroplane must have its
+propellers. These must be driven by an engine with a source of
+power. Weight is an essential quality of every engine. The
+propellers must be made of metal, which has its weakness, and
+which is liable to give way when its speed attains a certain
+limit. And, granting complete success, imagine the proud possessor
+of the aeroplane darting through the air at a speed of several
+hundred feet per second! It is the speed alone that sustains him.
+How is he ever going to stop? Once he slackens his speed, down he
+begins to fall. He may, indeed, increase the inclination of his
+aeroplane. Then he increases the resistance to the sustaining
+force. Once he stops he falls a dead mass. How shall he reach the
+ground without destroying his delicate machinery? I do not think
+the most imaginative inventor has yet even put upon paper a
+demonstratively successful way of meeting this difficulty. The
+only ray of hope is afforded by the bird. The latter does succeed
+in stopping and reaching the ground safely after its flight. But
+we have already mentioned the great advantages which the bird
+possesses in the power of applying force to its wings, which, in
+its case, form the aeroplanes. But we have already seen that there
+is no mechanical combination, and no way of applying force, which
+will give to the aeroplanes the flexibility and rapidity of
+movement belonging to the wings of a bird. With all the
+improvements that the genius of man has made in the steamship, the
+greatest and best ever constructed is liable now and then to meet
+with accident. When this happens she simply floats on the water
+until the damage is repaired, or help reaches her. Unless we are
+to suppose for the flying-machine, in addition to everything else,
+an immunity from accident which no human experience leads us to
+believe possible, it would be liable to derangements of machinery,
+any one of which would be necessarily fatal. If an engine were
+necessary not only to propel a ship, but also to make her float--
+if, on the occasion of any accident she immediately went to the
+bottom with all on board--there would not, at the present day, be
+any such thing as steam navigation. That this difficulty is
+insurmountable would seem to be a very fair deduction, not only
+from the failure of all attempts to surmount it, but from the fact
+that Maxim has never, so far as we are aware, followed up his
+seemingly successful experiment.
+
+There is, indeed, a way of attacking it which may, at first sight,
+seem plausible. In order that the aeroplane may have its full
+sustaining power, there is no need that its motion be continuously
+forward. A nearly horizontal surface, swinging around in a circle,
+on a vertical axis, like the wings of a windmill moving
+horizontally, will fulfil all the conditions. In fact, we have a
+machine on this simple principle in the familiar toy which, set
+rapidly whirling, rises in the air. Why more attempts have not
+been made to apply this system, with two sets of sails whirling in
+opposite directions, I do not know. Were there any possibility of
+making a flying-machine, it would seem that we should look in this
+direction.
+
+The difficulties which I have pointed out are only preliminary
+ones, patent on the surface. A more fundamental one still, which
+the writer feels may prove insurmountable, is based on a law of
+nature which we are bound to accept. It is that when we increase
+the size of any flying-machine without changing its model we
+increase the weight in proportion to the cube of the linear
+dimensions, while the effective supporting power of the air
+increases only as the square of those dimensions. To illustrate
+the principle let us make two flying-machines exactly alike, only
+make one on double the scale of the other in all its dimensions.
+We all know that the volume and therefore the weight of two
+similar bodies are proportional to the cubes of their dimensions.
+The cube of two is eight. Hence the large machine will have eight
+times the weight of the other. But surfaces are as the squares of
+the dimensions. The square of two is four. The heavier machine
+will therefore expose only four times the wing surface to the air,
+and so will have a distinct disadvantage in the ratio of
+efficiency to weight.
+
+Mechanical principles show that the steam pressures which the
+engines would bear would be the same, and that the larger engine,
+though it would have more than four times the horse-power of the
+other, would have less than eight times. The larger of the two
+machines would therefore be at a disadvantage, which could be
+overcome only by reducing the thickness of its parts, especially
+of its wings, to that of the other machine. Then we should lose in
+strength. It follows that the smaller the machine the greater its
+advantage, and the smallest possible flying-machine will be the
+first one to be successful.
+
+We see the principle of the cube exemplified in the animal
+kingdom. The agile flea, the nimble ant, the swift-footed
+greyhound, and the unwieldy elephant form a series of which the
+next term would be an animal tottering under its own weight, if
+able to stand or move at all. The kingdom of flying animals shows
+a similar gradation. The most numerous fliers are little insects,
+and the rising series stops with the condor, which, though having
+much less weight than a man, is said to fly with difficulty when
+gorged with food.
+
+Now, suppose that an inventor succeeds, as well he may, in making
+a machine which would go into a watch-case, yet complete in all
+its parts, able to fly around the room. It may carry a button, but
+nothing heavier. Elated by his success, he makes one on the same
+model twice as large in every dimension. The parts of the first,
+which are one inch in length, he increases to two inches. Every
+part is twice as long, twice as broad, and twice as thick. The
+result is that his machine is eight times as heavy as before. But
+the sustaining surface is only four times as great. As compared
+with the smaller machine, its ratio of effectiveness is reduced to
+one-half. It may carry two or three buttons, but will not carry
+over four, because the total weight, machine plus buttons, can
+only be quadrupled, and if he more than quadruples the weight of
+the machine, he must less than quadruple that of the load. How
+many such enlargements must he make before his machine will cease
+to sustain itself, before it will fall as an inert mass when we
+seek to make it fly through the air? Is there any size at which it
+will be able to support a human being? We may well hesitate before
+we answer this question in the affirmative.
+
+Dr. Graham Bell, with a cheery optimism very pleasant to
+contemplate, has pointed out that the law I have just cited may be
+evaded by not making a larger machine on the same model, but
+changing the latter in a way tantamount to increasing the number
+of small machines. This is quite true, and I wish it understood
+that, in laying down the law I have cited, I limit it to two
+machines of different sizes on the same model throughout. Quite
+likely the most effective flying-machine would be one carried by a
+vast number of little birds. The veracious chronicler who escaped
+from a cloud of mosquitoes by crawling into an immense metal pot
+and then amused himself by clinching the antennae of the insects
+which bored through the pot until, to his horror, they became so
+numerous as to fly off with the covering, was more scientific than
+he supposed. Yes, a sufficient number of humming-birds, if we
+could combine their forces, would carry an aerial excursion party
+of human beings through the air. If the watch-maker can make a
+machine which will fly through the room with a button, then, by
+combining ten thousand such machines he may be able to carry a
+man. But how shall the combined forces be applied?
+
+The difficulties I have pointed out apply only to the flying-
+machine properly so-called, and not to the dirigible balloon or
+airship. It is of interest to notice that the law is reversed in
+the case of a body which is not supported by the resistance of a
+fluid in which it is immersed, but floats in it, the ship or
+balloon, for example. When we double the linear dimensions of a
+steamship in all its parts, we increase not only her weight but
+her floating power, her carrying capacity, and her engine capacity
+eightfold. But the resistance which she meets with when passing
+through the water at a given speed is only multiplied four times.
+Hence, the larger we build the steamship the more economical the
+application of the power necessary to drive it at a given speed.
+It is this law which has brought the great increase in the size of
+ocean steamers in recent times. The proportionately diminishing
+resistance which, in the flying-machine, represents the floating
+power is, in the ship, something to be overcome. Thus there is a
+complete reversal of the law in its practical application to the
+two cases.
+
+The balloon is in the same class with the ship. Practical
+difficulties aside, the larger it is built the more effective it
+will be, and the more advantageous will be the ratio of the power
+which is necessary to drive it to the resistance to be overcome.
+
+If, therefore, we are ever to have aerial navigation with our
+present knowledge of natural capabilities, it is to the airship
+floating in the air, rather than the flying-machine resting on the
+air, to which we are to look. In the light of the law which I have
+laid down, the subject, while not at all promising, seems worthy
+of more attention than it has received. It is not at all unlikely
+that if a skilful and experienced naval constructor, aided by an
+able corps of assistants, should design an airship of a diameter
+of not less than two hundred feet, and a length at least four or
+five times as great, constructed, possibly, of a textile substance
+impervious to gas and borne by a light framework, but, more
+likely, of exceedingly thin plates of steel carried by a frame
+fitted to secure the greatest combination of strength and
+lightness, he might find the result to be, ideally at least, a
+ship which would be driven through the air by a steam-engine with
+a velocity far exceeding that of the fleetest Atlantic liner. Then
+would come the practical problem of realizing the ship by
+overcoming the mechanical difficulties involved in the
+construction of such a huge and light framework. I would not be at
+all surprised if the result of the exact calculation necessary to
+determine the question should lead to an affirmative conclusion,
+but I am quite unable to judge whether steel could be rolled into
+parts of the size and form required in the mechanism.
+
+In judging of the possibility of commercial success the cheapness
+of modern transportation is an element in the case that should not
+be overlooked. I believe the principal part of the resistance
+which a limited express train meets is the resistance of the air.
+This would be as great for an airship as for a train. An important
+fraction of the cost of transporting goods from Chicago to London
+is that of getting them into vehicles, whether cars or ships, and
+getting them out again. The cost of sending a pair of shoes from a
+shop in New York to the residence of the wearer is, if I mistake
+not, much greater than the mere cost of transporting them across
+the Atlantic. Even if a dirigible balloon should cross the
+Atlantic, it does not follow that it could compete with the
+steamship in carrying passengers and freight.
+
+I may, in conclusion, caution the reader on one point. I should be
+very sorry if my suggestion of the advantage of the huge airship
+leads to the subject being taken up by any other than skilful
+engineers or constructors, able to grapple with all problems
+relating to the strength and resistance of materials. As a single
+example of what is to be avoided I may mention the project, which
+sometimes has been mooted, of making a balloon by pumping the air
+from a very thin, hollow receptacle. Such a project is as futile
+as can well be imagined; no known substance would begin to resist
+the necessary pressure. Our aerial ship must be filled with some
+substance lighter than air. Whether heated air would answer the
+purpose, or whether we should have to use a gas, is a question for
+the designer.
+
+To return to our main theme, all should admit that if any hope for
+the flying-machine can be entertained, it must be based more on
+general faith in what mankind is going to do than upon either
+reasoning or experience. We have solved the problem of talking
+between two widely separated cities, and of telegraphing from
+continent to continent and island to island under all the oceans--
+therefore we shall solve the problem of flying. But, as I have
+already intimated, there is another great fact of progress which
+should limit this hope. As an almost universal rule we have never
+solved a problem at which our predecessors have worked in vain,
+unless through the discovery of some agency of which they have had
+no conception. The demonstration that no possible combination of
+known substances, known forms of machinery, and known forms of
+force can be united in a practicable machine by which men shall
+fly long distances through the air, seems to the writer as
+complete as it is possible for the demonstration of any physical
+fact to be. But let us discover a substance a hundred times as
+strong as steel, and with that some form of force hitherto
+unsuspected which will enable us to utilize this strength, or let
+us discover some way of reversing the law of gravitation so that
+matter may be repelled by the earth instead of attracted--then we
+may have a flying-machine. But we have every reason to believe
+that mere ingenious contrivances with our present means and forms
+of force will be as vain in the future as they have been in the
+past.
+
+
+
+End of Project Gutenberg's Side-Lights On Astronomy, by Simon Newcomb
+
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