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Title: Side-Lights On Astronomy

Author: Simon Newcomb

Release Date: May, 2003  [Etext #4065]
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[The actual date this file first posted = 10/30/01]

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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