have been mainly directed to mathematics. Here he began to give
evidence of that marvellous insight into the deep secrets of nature
which more than a century later led so dispassionate a judge as
Laplace to pronounce Newton's immortal work as pre-eminent above all
the productions of the human intellect. But though Newton was one of
the very greatest mathematicians that ever lived, he was never a
mathematician for the mere sake of mathematics. He employed his
mathematics as an instrument for discovering the laws of nature. His
industry and genius soon brought him under the notice of the
University authorities. It is stated in the University records that
he obtained a Scholarship in 1664. Two years later we find that
Newton, as well as many residents in the University, had to leave
Cambridge temporarily on account of the breaking out of the plague.
The philosopher retired for a season to his old home at Woolsthorpe,
and there he remained until he was appointed a Fellow of Trinity
College, Cambridge, in 1667. From this time onwards, Newton's
reputation as a mathematician and as a natural philosopher steadily
advanced, so that in 1669, while still but twenty-seven years of age,
he was appointed to the distinguished position of Lucasian Professor
of Mathematics at Cambridge. Here he found the opportunity to
continue and develop that marvellous career of discovery which formed
his life's work.
The earliest of Newton's great achievements in natural philosophy was
his detection of the composite character of light. That a beam of
ordinary sunlight is, in fact, a mixture of a very great number of
different-coloured lights, is a doctrine now familiar to every one
who has the slightest education in physical science. We must,
however, remember that this discovery was really a tremendous advance
in knowledge at the time when Newton announced it.
[PLATE: DIAGRAM OF A SUNBEAM.]
We here give the little diagram originally drawn by Newton, to
explain the experiment by which he first learned the composition of
light. A sunbeam is admitted into a darkened room through an
opening, H, in a shutter. This beam when not interfered with will
travel in a straight line to the screen, and there reproduce a bright
spot of the same shape as the hole in the shutter. If, however, a
prism of glass, A B C, be introduced so that the beam traverse it,
then it will be seen at once that the light is deflected from its
original track. There is, however, a further and most important
change which takes place. The spot of light is not alone removed to
another part of the screen, but it becomes spread out into a long
band beautifully coloured, and exhibiting the hues of the rainbow. At
the top are the violet rays, and then in descending order we have the
indigo, blue, green, yellow, orange, and red.
The circumstance in this phenomenon which appears to have
particularly arrested Newton's attention, was the elongation which
the luminous spot underwent in consequence of its passage through the
prism. When the prism was absent the spot was nearly circular, but
when the prism was introduced the spot was about five times as long
as it was broad. To ascertain the explanation of this was the first
problem to be solved. It seemed natural to suppose that it might be
due to the thickness of the glass in the prism which the light
traversed, or to the angle of incidence at which the light fell upon
the prism. He found, however, upon careful trial, that the phenomenon
could not be thus accounted for. It was not until after much patient
labour that the true explanation dawned upon him. He discovered that
though the beam of white light looks so pure and so simple, yet in
reality it is composed of differently coloured lights blended
together. These are, of course, indistinguishable in the compound
beam, but they are separated or disentangled, so to speak, by the
action of the prism. The rays at the blue end of the spectrum are
more powerfully deflected by the action of the glass than are the
rays at the red end. Thus, the rays variously coloured red, orange,
yellow, green, blue, indigo, violet, are each conducted to a
different part of the screen. In this way the prism has the effect
of exhibiting the constitution of the composite beam of light.
To us this now seems quite obvious, but Newton did not adopt it
hastily. With characteristic caution he verified the explanation by
many different experiments, all of which confirmed his discovery. One
of these may be mentioned. He made a hole in the screen at that part
on which the violet rays fell. Thus a violet ray was allowed to pass
through, all the rest of the light being intercepted, and on this
beam so isolated he was able to try further experiments. For
instance, when he interposed another prism in its path, he found, as
he expected, that it was again deflected, and he measured the amount
of the deflection. Again he tried the same experiment with one of
the red rays from the opposite end of the coloured band. He allowed
it to pass through the same aperture in the screen, and he tested the
amount by which the second prism was capable of producing deflection.
He thus found, as he had expected to find, that the second prism was
more efficacious in bending the violet rays than in bending the red
rays. Thus he confirmed the fact that the various hues of the
rainbow were each bent by a prism to a different extent, violet being
acted upon the most, and red the least.
[PLATE: ISAAC NEWTON.]
Not only did Newton decompose a white beam into its constituent
colours, but conversely by interposing a second prism with its angle
turned upwards, he reunited the different colours, and thus
reproduced the original beam of white light. In several other ways
also he illustrated his famous proposition, which then seemed so
startling, that white light was the result of a mixture of all hues
of the rainbow. By combining painters' colours in the right
proportion he did not indeed succeed in producing a mixture which
would ordinarily be called white, but he obtained a grey pigment.
Some of this he put on the floor of his room for comparison with a
piece of white paper. He allowed a beam of bright sunlight to fall
upon the paper and the mixed colours side by side, and a friend he
called in for his opinion pronounced that under these circumstances
the mixed colours looked the whiter of the two.
By repeated demonstrations Newton thus established his great
discovery of the composite character of light. He at once perceived
that his researches had an important bearing upon the principles
involved in the construction of a telescope. Those who employed the
telescope for looking at the stars, had been long aware of the
imperfections which prevented all the various rays from being
conducted to the same focus. But this imperfection had hitherto been
erroneously accounted for. It had been supposed that the reason why
success had not been attained in the construction of a refracting
telescope was due to the fact that the object glass, made as it then
was of a single piece, had not been properly shaped. Mathematicians
had abundantly demonstrated that a single lens, if properly figured,
must conduct all rays of light to the same focus, provided all rays
experienced equal refraction in passing through the glass. Until
Newton's discovery of the composition of white light, it had been
taken for granted that the several rays in a white beam were equally
refrangible. No doubt if this had been the case, a perfect telescope
could have been produced by properly shaping the object glass. But
when Newton had demonstrated that light was by no means so simple as
had been supposed, it became obvious that a satisfactory refracting
telescope was an impossibility when only a single object lens was
employed, however carefully that lens might have been wrought. Such
an objective might, no doubt, be made to conduct any one group of
rays of a particular shade to the same focus, but the rays of other
colours in the beam of white light must necessarily travel somewhat
astray. In this way Newton accounted for a great part of the
difficulties which had hitherto beset the attempts to construct a
perfect refracting telescope.
We now know how these difficulties can be, to a great extent,
overcome, by employing for the objective a composite lens made of two
pieces of glass possessing different qualities. To these achromatic
object glasses, as they are called, the great development of
astronomical knowledge, since Newton's time, is due. But it must be
remarked that, although the theoretical possibility of constructing
an achromatic lens was investigated by Newton, he certainly came to
the conclusion that the difficulty could not be removed by employing
a composite objective, with two different kinds of glass. In this
his marvellous sagacity in the interpretation of nature seems for
once to have deserted him. We can, however, hardly regret that
Newton failed to discover the achromatic objective, when we observe
that it was in consequence of his deeming an achromatic objective to
be impossible that he was led to the invention of the reflecting
telescope. Finding, as he believed, that the defects of the
telescope could not be remedied by any application of the principle
of refraction he was led to look in quite a different direction for
the improvement of the tool on which the advancement of astronomy
depended. The REFRACTION of light depended as he had found, upon the
colour of the light. The laws of REFLECTION were, however, quite
independent of the colour. Whether rays be red or green, blue or
yellow, they are all reflected in precisely the same manner from a
mirror. Accordingly, Newton perceived that if he could construct a
telescope the action of which depended upon reflection, instead of
upon refraction, the difficulty which had hitherto proved an
insuperable obstacle to the improvement of the instrument would be
evaded.
[PLATE: SIR ISAAC NEWTON'S LITTLE REFLECTOR.]
For this purpose Newton fashioned a concave mirror from a mixture of
copper and tin, a combination which gives a surface with almost the
lustre of silver. When the light of a star fell upon the surface, an
image of the star was produced in the focus of this mirror, and then
this image was examined by a magnifying eye-piece. Such is the
principle of the famous reflecting telescope which bears the name of
Newton. The little reflector which he constructed, represented in
the adjoining figure, is still preserved as one of the treasures of
the Royal Society. The telescope tube had the very modest dimension
of one inch in diameter. It was, however, the precursor of a whole
series of magnificent instruments, each outstripping the other in
magnitude, until at last the culminating point was attained in 1845,
by the construction of Lord Rosse's mammoth reflector of six feet in
aperture.
Newton's discovery of the composition of light led to an embittered
controversy, which caused no little worry to the great Philosopher.
Some of those who attacked him enjoyed considerable and, it must be
admitted, even well-merited repute in the ranks of science. They
alleged, however, that the elongation of the coloured band which
Newton had noticed was due to this, to that, or to the other--to
anything, in fact, rather than to the true cause which Newton
assigned. With characteristic patience and love of truth, Newton
steadily replied to each such attack. He showed most completely how
utterly his adversaries had misunderstood the subject, and how slight
indeed was their acquaintance with the natural phenomenon in
question. In reply to each point raised, he was ever able to cite
fresh experiments and adduce fresh illustrations, until at last his
opponents retired worsted from the combat.
It has been often a matter for surprise that Newton, throughout his
whole career, should have taken so much trouble to expose the errors
of those who attacked his views. He used even to do this when it
plainly appeared that his adversaries did not understand the subject
they were discussing. A philosopher might have said, "I know I am
right, and whether others think I am right or not may be a matter of
concern to them, but it is certainly not a matter about which I need
trouble. If after having been told the truth they elect to remain in
error, so much the worse for them; my time can be better employed
than in seeking to put such people right." This, however, was not
Newton's method. He spent much valuable time in overthrowing
objections which were often of a very futile description. Indeed, he
suffered a great deal of annoyance from the persistency, and in some
cases one might almost say from the rancour, of the attacks which
were made upon him. Unfortunately for himself, he did not possess
that capacity for sublime indifference to what men may say, which is
often the happy possession of intellects greatly inferior to his.
The subject of optics still continuing to engross Newton's attention,
he followed up his researches into the structure of the sunbeam by
many other valuable investigations in connection with light. Every
one has noticed the beautiful colours manifested in a soap-bubble.
Here was a subject which not unnaturally attracted the attention of
one who had expounded the colours of the spectrum with such success.
He perceived that similar hues were produced by other thin plates of
transparent material besides soap-bubbles, and his ingenuity was
sufficient to devise a method by which the thicknesses of the
different films could be measured. We can hardly, indeed, say that a
like success attended his interpretation of these phenomena to that
which had been so conspicuous in his explanation of the spectrum. It
implies no disparagement to the sublime genius of Newton to admit
that the doctrines he put forth as to the causes of the colours in
the soap-bubbles can be no longer accepted. We must remember that
Newton was a pioneer in accounting for the physical properties of
light. The facts that he established are indeed unquestionable, but
the explanations which he was led to offer of some of them are seen
to be untenable in the fuller light of our present knowledge.
[PLATE: SIR ISAAC NEWTON'S SUN-DIAL.]
Had Newton done nothing beyond making his wonderful discoveries in
light, his fame would have gone down to posterity as one of the
greatest of Nature's interpreters. But it was reserved for him to
accomplish other discoveries, which have pushed even his analysis of
the sunbeam into the background; it is he who has expounded the
system of the universe by the discovery of the law of universal
gravitation.
The age had indeed become ripe for the advent of the genius of
Newton. Kepler had discovered with marvellous penetration the laws
which govern the movements of the planets around the sun, and in
various directions it had been more or less vaguely felt that the
explanation of Kepler's laws, as well as of many other phenomena,
must be sought for in connection with the attractive power of
matter. But the mathematical analysis which alone could deal with
this subject was wanting; it had to be created by Newton.
At Woolsthorpe, in the year 1666, Newton's attention appears to have
been concentrated upon the subject of gravitation. Whatever may be
the extent to which we accept the more or less mythical story as to
how the fall of an apple first directed the attention of the
philosopher to the fact that gravitation must extend through space,
it seems, at all events, certain that this is an excellent
illustration of the line of reasoning which he followed. He argued
in this way. The earth attracts the apple; it would do so, no matter
how high might be the tree from which that apple fell. It would then
seem to follow that this power which resides in the earth by which it
can draw all external bodies towards it, extends far beyond the
altitude of the loftiest tree. Indeed, we seem to find no limit to
it. At the greatest elevation that has ever been attained, the
attractive power of the earth is still exerted, and though we cannot
by any actual experiment reach an altitude more than a few miles
above the earth, yet it is certain that gravitation would extend to
elevations far greater. It is plain, thought Newton, that an apple
let fall from a point a hundred miles above this earth's surface,
would be drawn down by the attraction, and would continually gather
fresh velocity until it reached the ground. From a hundred miles it
was natural to think of what would happen at a thousand miles, or at
hundreds of thousands of miles. No doubt the intensity of the
attraction becomes weaker with every increase in the altitude, but
that action would still exist to some extent, however lofty might be
the elevation which had been attained.
It then occurred to Newton, that though the moon is at a distance of
two hundred and forty thousand miles from the earth, yet the
attractive power of the earth must extend to the moon. He was
particularly led to think of the moon in this connection, not only
because the moon is so much closer to the earth than are any other
celestial bodies, but also because the moon is an appendage to the
earth, always revolving around it. The moon is certainly attracted
to the earth, and yet the moon does not fall down; how is this to be
accounted for? The explanation was to be found in the character of
the moon's present motion. If the moon were left for a moment at
rest, there can be no doubt that the attraction of the earth would
begin to draw the lunar globe in towards our globe. In the course of
a few days our satellite would come down on the earth with a most
fearful crash. This catastrophe is averted by the circumstance that
the moon has a movement of revolution around the earth. Newton was
able to calculate from the known laws of mechanics, which he had
himself been mainly instrumental in discovering, what the attractive
power of the earth must be, so that the moon shall move precisely as
we find it to move. It then appeared that the very power which makes
an apple fall at the earth's surface is the power which guides the
moon in its orbit.
[PLATE: SIR ISAAC NEWTON'S TELESCOPE.]
Once this step had been taken, the whole scheme of the universe might
almost be said to have become unrolled before the eye of the
philosopher. It was natural to suppose that just as the moon was
guided and controlled by the attraction of the earth, so the earth
itself, in the course of its great annual progress, should be guided
and controlled by the supreme attractive power of the sun. If this
were so with regard to the earth, then it would be impossible to
doubt that in the same way the movements of the planets could be
explained to be consequences of solar attraction.
It was at this point that the great laws of Kepler became especially
significant. Kepler had shown how each of the planets revolves in an
ellipse around the sun, which is situated on one of the foci. This
discovery had been arrived at from the interpretation of
observations. Kepler had himself assigned no reason why the orbit of
a planet should be an ellipse rather than any other of the infinite
number of closed curves which might be traced around the sun. Kepler
had also shown, and here again he was merely deducing the results
from observation, that when the movements of two planets were
compared together, the squares of the periodic times in which each
planet revolved were proportional to the cubes of their mean
distances from the sun. This also Kepler merely knew to be true as a
fact, he gave no demonstration of the reason why nature should have
adopted this particular relation between the distance and the
periodic time rather than any other. Then, too, there was the law by
which Kepler with unparalleled ingenuity, explained the way in which
the velocity of a planet varies at the different points of its track,
when he showed how the line drawn from the sun to the planet
described equal areas around the sun in equal times. These were the
materials with which Newton set to work. He proposed to infer from
these the actual laws regulating the force by which the sun guides
the planets. Here it was that his sublime mathematical genius came
into play. Step by step Newton advanced until he had completely
accounted for all the phenomena.
In the first place, he showed that as the planet describes equal
areas in equal times about the sun, the attractive force which the
sun exerts upon it must necessarily be directed in a straight line
towards the sun itself. He also demonstrated the converse truth,
that whatever be the nature of the force which emanated from a sun,
yet so long as that force was directed through the sun's centre, any
body which revolved around it must describe equal areas in equal
times, and this it must do, whatever be the actual character of the
law according to which the intensity of the force varies at different
parts of the planet's journey. Thus the first advance was taken in
the exposition of the scheme of the universe.
The next step was to determine the law according to which the force
thus proved to reside in the sun varied with the distance of the
planet. Newton presently showed by a most superb effort of
mathematical reasoning, that if the orbit of a planet were an ellipse
and if the sun were at one of the foci of that ellipse, the intensity
of the attractive force must vary inversely as the square of the
planet's distance. If the law had any other expression than the
inverse square of the distance, then the orbit which the planet must
follow would not be an ellipse; or if an ellipse, it would, at all
events, not have the sun in the focus. Hence he was able to show
from Kepler's laws alone that the force which guided the planets was
an attractive power emanating from the sun, and that the intensity of
this attractive power varied with the inverse square of the distance
between the two bodies.
These circumstances being known, it was then easy to show that the
last of Kepler's three laws must necessarily follow. If a number of
planets were revolving around the sun, then supposing the materials
of all these bodies were equally affected by gravitation, it can be
demonstrated that the square of the periodic time in which each
planet completes its orbit is proportional to the cube of the
greatest diameter in that orbit.
[PLATE: SIR ISAAC NEWTON'S ASTROLABE.]
These superb discoveries were, however, but the starting point from
which Newton entered on a series of researches, which disclosed many
of the profoundest secrets in the scheme of celestial mechanics. His
natural insight showed that not only large masses like the sun and
the earth, and the moon, attract each other, but that every particle
in the universe must attract every other particle with a force which
varies inversely as the square of the distance between them. If, for
example, the two particles were placed twice as far apart, then the
intensity of the force which sought to bring them together would be
reduced to one-fourth. If two particles, originally ten miles
asunder, attracted each other with a certain force, then, when the
distance was reduced to one mile, the intensity of the attraction
between the two particles would be increased one-hundred-fold. This
fertile principle extends throughout the whole of nature. In some
cases, however, the calculation of its effect upon the actual
problems of nature would be hardly possible, were it not for another
discovery which Newton's genius enabled him to accomplish. In the
case of two globes like the earth and the moon, we must remember that
we are dealing not with particles, but with two mighty masses of
matter, each composed of innumerable myriads of particles. Every
particle in the earth does attract every particle in the moon with a
force which varies inversely as the square of their distance. The
calculation of such attractions is rendered feasible by the following
principle. Assuming that the earth consists of materials
symmetrically arranged in shells of varying densities, we may then,
in calculating its attraction, regard the whole mass of the globe as
concentrated at its centre. Similarly we may regard the moon as
concentrated at the centre of its mass. In this way the earth and
the moon can both be regarded as particles in point of size, each
particle having, however, the entire mass of the corresponding
globe. The attraction of one particle for another is a much more
simple matter to investigate than the attraction of the myriad
different points of the earth upon the myriad different points of the
moon.