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´╗┐Title: Side-Lights on Astronomy and Kindred Fields of Popular Science
Author: Newcomb, Simon, 1835-1909
Language: English
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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 OF THE CORONA OF 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. 1]

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 in 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. Alpha 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.





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