Newtonian law of gravitation. It appears all things possess the
remarkable property of attracting or pulling each other. Newton
declared that all substances, solid, liquid or even gaseous, from the
massive cliff of rock down to the invisible air--all matter can no more
help pulling than it can help existing. His law further formulates
certain conditions governing the manner in which this gravitational
attraction is exerted; but these are mere matters of detail; interest
centers about the mysterious fact of attraction itself. How can one
thing pull another with no connecting link through which the pull can
act? Just here we touch the point that has never yet been explained.
Nature withholds from science her ultimate secrets. They that have
pondered longest, that have descended farthest of all men into the
clear well of knowledge, have done so but to sound the depths beyond,
never touching bottom.
This inability of ours to give a good physical explanation of
gravitation has led numerous paradoxers to doubt or even deny that
there is any such thing. But fortunately we have a simple laboratory
experiment that helps us. Unexplained it may ever remain, but that
there can be attraction between physical objects connected by no
visible link is proved by the behavior of an ordinary magnet. Place
a small piece of steel or iron near a magnetized bar, and it will at
once be so strongly attracted that it will actually fly to the magnet.
Any one who has seen this simple experiment can never again deny the
possibility at least of the law of attraction as stated by Newton. Its
possibility once admitted, the fact that it can predict the motions
of all the planets, even shown to the minutest details, transforms
the possibility of its birth into a certainty as strong as any human
certainty can ever be.
But this demonstration of Newton’s law is limited strictly to the
solar system itself. We may indeed reason by analogy, and take for
granted that a law which holds within our immediate neighborhood is
extremely likely to be true also of the entire visible universe. But
men of science are loath to reason thus; and hence the fascination
of researches in cosmic astronomy. Analogy points out the path. The
astronomer is not slow to follow; but he seeks ever to establish upon
incontrovertible evidence those truths which at first only his daring
imagination had led him to half suspect. If we are to extend the law
of gravitation to the utmost, we must be careful to consider the law
itself in its most complete form. A heavenly body like the sun is
often said to govern the motions of its family of planets; but such a
statement is not strictly accurate. The governing body is no despot;
’tis an abject slave of law and order, as much as the tiniest of
attendant planets. The action of gravitation is mutual, and no cosmic
body can attract another without being itself in turn subject to that
other’s gravitational action. If there were in our solar system but
two bodies, sun and planet, we should find each one pursuing a path
in space under the influence of the other’s attraction. These two
paths or orbits would be oval, and if the sun and planet were equally
massive, the orbits would be exactly alike, both in shape and size.
But if the sun were far larger than the planet, the orbits would still
be similar in form, but the one traversed by the larger body would
be small. For it is not reasonable to expect a little planet to keep
the big sun moving with a velocity as great as that derived by itself
from the attraction of the larger orb. Whenever the preponderance of
the larger body is extremely great, its orbit will be correspondingly
insignificant in size. This is in fact the case with our own sun.
So massive is it in comparison with the planets, that the orbit is
too small to reveal its actual existence without the aid of our most
refined instruments. The path traced out by the sun’s center would not
fill a space as large as the sun’s own bulk. Nevertheless, true orbital
motion is there.
So we may conclude that as a necessary consequence of the law of
gravitation every object within the solar system is in motion. To
say that planets revolve about the sun is to neglect as unimportant
the small orbit of the sun itself. This may be sufficiently accurate
for ordinary purposes; but it is unquestionably necessary to neglect
no factor, however small, if we propose to extend our reasoning to a
consideration of the stellar universe. For we shall then have to deal
with systems in which the planets are of a size comparable with the
sun; and in such systems all the orbits will also be of comparatively
equal importance.
Mathematical analysis has derived another fact from discussion of
the law of gravitation which perhaps transcends in simple grandeur
everything we have as yet mentioned. It matters not how great may
be the number of massive orbs threading their countless interlacing
curved paths in space, there yet must be in every cosmic system one
single point immovable. This point is called the Center of Gravity. If
it should so happen that in the beginning of things, some particle of
matter were situated at this center, then would that atom ever remain
unmoved and imperturbable throughout all the successive vicissitudes
of cosmic evolution. It is doubtful whether the mind of man can form a
conception of anything grander than such an immovable atom within the
mysterious intricacies of cosmic motion.
But in general, we can not suppose that the centers of gravity in the
various stellar systems are really occupied by actual physical bodies.
The center may be a mere mathematical point in space, situated among
the several bodies composing the system, but nevertheless endowed with
the same remarkable property of relative immobility.
Having thus defined the center of gravity in its relation to the
constituent parts of any cosmic system, we can pass easily to its
characteristic properties in connection with the inter-relation of
stellar systems with one another. It can be proved mathematically that
our solar system will pull upon distant stars just as though the sun
and all the planets were concentrated into one vast sphere having its
center in the center of gravity of the whole. It is this property of
the center of gravity which makes it preëminently important in cosmic
researches. For, while we know that center to be at rest relatively to
all the planets in the system, it may, nevertheless, in its quality as
a sort of concentrated essence of them all, be moving swiftly through
space under the pull of distant stars. In that case, the attendant
bodies will go with it--but they will pursue their evolutions within
the system, all unconscious that the center of gravity is carrying them
on a far wider circuit.
What is the nature of that circuit? This question has been for many
years the subject of earnest study by the clearest minds among
astronomers. The greatest difficulty in the way is the comparatively
brief period during which men have been able to make astronomical
observations of precision. Space and time are two conceptions that
transcend the powers of definition possessed by any man. But we can at
least form a notion of how vast is the extent of time, if we remember
that the period covered by man’s written records is registered but
as a single moment upon the great revolving dial of heaven’s dome.
One hundred and fifty years have elapsed since James Bradley built
the foundations of sidereal astronomy upon his masterly series of
star-observations at the Royal Observatory of Greenwich, in England.
Yet so slowly do the movements of the stars unroll themselves upon the
firmament, that even to this day no one of them has been seen by men
to trace out more than an infinitesimal fraction of its destined path
through the voids of space.
Travelers upon a railroad can not tell at any given moment whether they
are moving in a straight line, or whether the train is turning upon
some curve of huge size. The St. Gothard railway has several so-called
‘corkscrew’ tunnels, within which the rails make a complete turn in a
spiral, the train finally emerging from the tunnel at a point almost
vertically over the entrance. In this way the train is lifted to a
higher level. Passengers are wont to amuse themselves while in these
tunnels by watching the needle of an ordinary pocket compass. This
needle, of course, always points to the north; and as the train turns
upon its curve, the needle will make a complete revolution. But the
passenger could not know without the compass that the train was not
moving in a perfectly straight line. Just so we passengers on the earth
are unaware of the kind of path we are traversing, until, like the
compass, the astronomer’s instruments shall reveal to us the truth.
But as we have seen, astronomical observations of precision have not as
yet extended through a period of time corresponding to the few minutes
during which the St. Gothard traveler watches the compass. We are still
in the dark, and do not know as yet whether mankind shall last long
enough upon the earth to see the compass needle make its revolution.
We are compelled to believe that the motion in space of our sun is
progressing upon a curved path; but so far as precise observations
allow us to speak, we can but say that we have as yet moved through
an infinitesimal element only of that mighty curve. However, we know
the point upon the sky towards which this tiny element of our path is
directed, and we have an approximate knowledge of the speed at which we
move.
More than a century ago Sir William Herschel was able to fix roughly
what we call the Apex of the sun’s way in space, or the point among the
stars towards which that way is for the moment directed. We say for the
moment, but we mean that moment of which Bradley saw the beginning in
1750, and upon whose end no man of those now living shall ever look.
Herschel found that a comparison of old stellar observations seemed
to indicate that the stars in a certain part of the sky were opening
out, as it were, and that the constellations in the opposite part of
the heavens seemed to be drawing in, or becoming smaller. There can be
but one reasonable explanation of this. We must be moving towards that
part of the sky where the stars are separating. Just so a man watching
a regiment of soldiers approaching, will see at first only a confused
body of men. But as they come nearer the individual soldiers will seem
to separate, until at length each one is seen distinct from all the
others.
Herschel fixed the position of the apex at a point in the constellation
Hercules. The most recent investigations of Newcomb, published only a
few months ago, have, on the whole, verified Herschel’s conclusions.
With the intuitive power of rare genius, Herschel had been able to
sift truth out of error. The observational data at his disposal would
now be called rude, but they disclosed to the scrutiny of his acute
understanding the germ of truth that was in them. Later investigators
have increased the precision of our knowledge, until we can now say
that the present direction of the solar motion is known within very
narrow limits. A tiny circle might be drawn on the sky, to which an
astronomer might point his hand and say: Yonder little circle contains
the goal towards which the sun and planets are hastening to-day. Even
the speed of this motion has been subjected to measurement, and found
to be about ten miles per second.
The objective point and the rate of motion thus stated, exact science
holds her peace. Here genuine knowledge stops; and we can proceed
further only by the aid of that imagination which men of science need
to curb at every moment. But let no one think that the sun will ever
reach the so-called apex. To do so would mean cosmic motion upon a
straight line, while every consideration of celestial mechanics points
to motion upon a curve. When shall we turn sufficiently upon that
curve to detect its bending? ’Tis a problem we must leave as a rich
heritage to later generations that are to follow us. The visionary
theorist’s notion of a great central sun, controlling our own sun’s way
in space, must be dismissed as far too daring. But for such a central
sun we may substitute a central center of gravity belonging to a great
system of which our sun is but an insignificant member. Then we reach a
conception that has lost nothing in the grandeur of its simplicity, and
is yet in accord with the probabilities of sober mechanical science.
We cease to be a lonely world, and stretch out the bonds of a common
relationship to yonder stars within the firmament.
A BIOGRAPHICAL SKETCH OF AN INFANT[H].
BY CHARLES DARWIN.
[H] Reprinted from _Mind_, July, 1877.
[Child-study has recently become a most active department of
psychology. It is the serious pursuit of men of science and the
fad of women’s clubs; a late accession to the magazines devoted
to it comes from Japan. In spite of this wide-spread zeal, few of
the followers of child-study have ever heard of one of the most
valuable contributions to it. And in spite of the eminence of the
author, Darwin’s observations on the mental growth of his child are
practically unknown to most zoölogists and psychologists.
It is a witness to the breadth of Darwin’s interests that he should
have been among the few men who anticipated by a generation or more
what is now so wide a movement in psychology. His retention of his
notes for thirty-seven years before publishing them is thoroughly
characteristic. In this respect there is a notable difference
between Darwin and the present-day enthusiasts for child-study.]
M. Taine’s very interesting account of the mental development of an
infant, translated in the last number of _Mind_ (p. 252), has led me
to look over a diary which I kept thirty-seven years ago with respect
to one of my own infants. I had excellent opportunities for close
observation, and wrote down at once whatever was observed. My chief
object was expression, and my notes were used in my book on this
subject; but as I attended to some other points, my observations may
possibly possess some little interest in comparison with those by
M. Taine, and others which hereafter no doubt will be made. I feel
sure, from what I have seen with my own infants, that the period
of development of the several faculties will be found to differ
considerably in different infants.
During the first seven days various reflex actions, namely sneezing,
hickuping, yawning, stretching, and, of course, sucking and screaming,
were well performed by my infant. On the seventh day, I touched the
naked sole of his foot with a bit of paper, and he jerked it away,
curling at the same time his toes, like a much older child when
tickled. The perfection of these reflex movements shows that the
extreme imperfection of the voluntary ones is not due to the state
of the muscles or of the co-ordinating centers, but to that of the
seat of the will. At this time, though so early, it seemed clear to
me that a warm, soft hand applied to his face excited a wish to suck.
This must be considered as a reflex or an instinctive action, for
it is impossible to believe that experience and association with
the touch of his mother’s breast could so soon have come into play.
During the first fortnight he often started on hearing any sudden
sound, and blinked his eyes. The same fact was observed with some of
my other infants within the first fortnight. Once, when he was 66 days
old, I happened to sneeze, and he started violently, frowned, looked
frightened, and cried rather badly; for an hour afterwards he was in
a state which would be called nervous in an older person, for every
slight noise made him start. A few days before this same date, he first
started at an object suddenly seen; but for a long time afterwards
sounds made him start and wink his eyes much more frequently than did
sight; thus, when 114 days old, I shook a pasteboard box with comfits
in it near his face and he started, whilst the same box when empty or
any other object shaken as near or much nearer to his face produced no
effect. We may infer from these several facts that the winking of the
eyes, which manifestly serves to protect them, had not been acquired
through experience. Although so sensitive to sound in a general way, he
was not able even when 124 days old, easily to recognize whence a sound
proceeded so as to direct his eyes to the source.
With respect to vision--his eyes were fixed on a candle as early as the
9th day, and up to the 45th day nothing else seemed thus to fix them;
but on the 49th day his attention was attracted by a bright-colored
tassel, as was shown by his eyes becoming fixed and the movements of
his arms ceasing. It was surprising how slowly he acquired the power of
following with his eyes an object if swinging at all rapidly; for he
could not do this well when seven and a half months old. At the age of
32 days he perceived his mother’s bosom when three or four inches from
it, as was shown by the protrusion of his lips and his eyes becoming
fixed; but I much doubt whether this had any connection with vision;
he certainly had not touched the bosom. Whether he was guided through
smell or the sensation of warmth or through association with the
position in which he was held, I do not at all know.
The movements of his limbs and body were for a long time vague and
purposeless, and usually performed in a jerking manner; but there was
one exception to this rule, namely, that from a very early period,
certainly long before he was 40 days old, he could move his hands to
his own mouth. When 77 days old, he took the sucking bottle (with
which he was partly fed) in his right hand, whether he was held on
the left or right arm of his nurse, and he would not take it in his
left hand until a week later, although I tried to make him do so; so
that the right hand was a week in advance of the left. Yet this infant
afterwards proved to be left-handed, the tendency being no doubt
inherited--his grandfather, mother, and a brother having been or being
left-handed. When between 80 and 90 days old, he drew all sorts of
objects into his mouth, and in two or three weeks’ time could do this
with some skill; but he often first touched his nose with the object
and then dragged it down into his mouth. After grasping my finger and
drawing it to his mouth, his own hand prevented him from sucking it;
but on the 114th day, after acting in this manner, he slipped his own
hand down so that he could get the end of my finger into his mouth.
This action was repeated several times, and evidently was not a chance
but a rational one. The intentional movements of the hands and arms
were thus much in advance of those of the body and legs; though the
purposeless movements of the latter were from a very early period
usually alternate, as in the act of walking. When four months old he
often looked intently at his own hands and other objects close to him,
and in doing so the eyes were turned much inwards, so that he often
squinted frightfully. In a fortnight after this time (i. e., 132 days
old), I observed that if an object was brought as near to his face as
his own hands were, he tried to seize it, but often failed; and he did
not try to do so in regard to more distant objects. I think there can
be little doubt that the convergence of his eyes gave him the clue
and excited him to move his arms. Although this infant thus began to
use his hands at an early period, he showed no special aptitude in
this respect, for when he was two years and four months old, he held
pencils, pens, and other objects far less neatly and efficiently than
did his sister, who was then only fourteen months old, and who showed
great inherent aptitude in handling anything.
ANGER.--It was difficult to decide at how early an age anger was felt;
on his eighth day he frowned and wrinkled the skin round his eyes
before a crying fit, but this may have been due to pain or distress,
and not to anger. When about ten weeks old, he was given some rather
cold milk, and he kept a slight frown on his forehead all the time
that he was sucking, so that he looked like a grown-up person made
cross from being compelled to do something which he did not like. When
nearly four months old, and perhaps much earlier, there could be no
doubt, from the manner in which the blood gushed into his whole face
and scalp, that he easily got into a violent passion. A small cause
sufficed; thus, when a little over seven months old, he screamed with
rage because a lemon slipped away and he could not seize it with his
hands. When eleven months old, if a wrong plaything was given him,
he would push it away and beat it; I presume that the beating was an
instinctive sign of anger, like the snapping of the jaws by a young
crocodile just out of the egg, and not that he imagined he could hurt
the plaything. When two years and three months old, he became a great
adept at throwing books or sticks, etc., at any one who offended him;
and so it was with some of my other sons. On the other hand, I could
never see a trace of such aptitude in my infant daughters; and this
makes me think that a tendency to throw objects is inherited by boys.
FEAR.--This feeling probably is one of the earliest which is
experienced by infants, as shown by their starting at any sudden sound
when only a few weeks old, followed by crying. Before the present one
was four and a half months old, I had been accustomed to make close to
him many strange and loud noises, which were all taken as excellent
jokes, but at this period I one day made a loud snoring noise, which
I had never done before; he instantly looked grave and then burst out
crying. Two or three days afterwards I made, through forgetfulness,
the same noise, with the same result. About the same time (viz., on
the 137th day), I approached with my back towards him and then stood
motionless; he looked very grave and much surprised, and would soon
have cried, had I not turned round; then his face instantly relaxed
into a smile. It is well known how intensely older children suffer
from vague and undefined fears, as from the dark, or in passing an
obscure corner in a large hall, etc. I may give as an instance that I
took the child in question, when two and one fourth years old, to the
Zoölogical Gardens, and he enjoyed looking at all the animals which
were like those that he knew, such as deer, antelope, etc., and all the
birds, even the ostriches, but was much alarmed at the various larger
animals in cages. He often said afterwards that he wished to go again,
but not to see ‘beasts in houses’; and we could in no manner account
for this fear. May we not suspect that the vague but very real fears of
children, which are quite independent of experience, are the inherited
effects of real dangers and abject superstitions during ancient savage
times? It is quite conformable with what we know of the transmission of
formerly well-developed characters, that they should appear at an early
period of life, and afterwards disappear.