but for whom the world would have remained in darkness. His first flashing
idea of gravitation deserves perhaps to be called an inspiration. But in
all his other labors, experimental as well as mathematical, he was but
following the spirit of the times. The love of science was abroad, and its
infinite curiosity. Each of Newton's discoveries was claimed also by other
men who had been working along similar lines. Of the dispute over the
gravitation theory Sir David Brewster, the great authority for the career
of Newton, gives some account. The controversy over the calculus was even
more bitter and prolonged.
It were well, however, to disabuse one's mind of the idea that Newton's
work was a finality, that it settled anything. As to why the law of
gravitation exists, why bodies tend to come together, the philosopher had
little suggestion to offer, and the present generation knows no more than
he. Before Copernicus and Newton men looked only with their eyes, and
accepted the apparent movements of sun and stars as real. Now, going one
step deeper, we look with our brains and see their real movements which
underlie appearances. Newton supplied us with the law and rate of the
movement--but not its cause. It is toward that cause, that great "Why?"
that science has ever since been dimly groping.
In the year 1666, when the plague had driven Newton from Cambridge, he was
sitting alone in the garden at Woolsthrope, and reflecting on the nature of
gravity, that remarkable power which causes all bodies to descend toward
the centre of the earth. As this power is not found to suffer any sensible
diminution at the greatest distance from the earth's centre to which we can
reach--being as powerful at the tops of the highest mountains as at the
bottom of the deepest mines--he conceived it highly probable that it must
extend much further than was usually supposed. No sooner had this happy
conjecture occurred to his mind than he considered what would be the effect
of its extending as far as the moon. That her motion must be influenced
by such a power he did not for a moment doubt; and a little reflection
convinced him that it might be sufficient for retaining that luminary in
her orbit round the earth.
Though the force of gravity suffers no sensible diminution at those small
distances from the earth's centre at which we can place ourselves, yet he
thought it very possible that, at the distance of the moon, it might differ
much in strength from what it is on the earth. In order to form some
estimate of the degree of its diminution, he considered that, if the moon
be retained in her orbit by the force of gravity, the primary planets must
also be carried round the sun by the same power; and by comparing the
periods of the different planets with their distances from the sun he found
that, if they were retained in their orbits by any power like gravity, its
force must decrease in the duplicate proportion, or as the squares of their
distances from the sun. In drawing this conclusion, he supposed the planets
to move in orbits perfectly circular, and having the sun in their centre.
Having thus obtained the law of the force by which the planets were drawn
to the sun, his next object was to ascertain if such a force emanating from
the earth, and directed to the moon, was sufficient, when diminished in the
duplicate ratio of the distance, to retain her in her orbit.
In performing this calculation it was necessary to compare the space
through which heavy bodies fall in a second at a given distance from the
centre of the earth, viz., at its surface, with the space through which the
moon, as it were, falls to the earth in a second of time while revolving
in a circular orbit. Being at a distance from books when he made this
computation, he adopted the common estimate of the earth's diameter then
in use among geographers and navigators, and supposed that each degree of
latitude contained sixty English miles.
In this way he found that the force which retains the moon in her orbit,
as deduced from the force which occasions the fall of heavy bodies to the
earth's surface, was one-sixth greater than that which is actually
observed in her circular orbit. This difference threw a doubt upon all his
speculations; but, unwilling to abandon what seemed to be otherwise so
plausible, he endeavored to account for the difference of the two forces
by supposing that some other cause must have been united with the force of
gravity in producing so great velocity of the moon in her circular orbit.
As this new cause, however, was beyond the reach of observation, he
discontinued all further inquiries into the subject, and concealed from his
friends the speculations in which he had been employed.
After his return to Cambridge in 1666 his attention was occupied with
optical discoveries; but he had no sooner brought them to a close than his
mind reverted to the great subject of the planetary motions. Upon the death
of Oldenburg in August, 1678, Dr. Hooke was appointed secretary to the
Royal Society; and as this learned body had requested the opinion of Newton
about a system of physical astronomy, he addressed a letter to Dr. Hooke
on November 28, 1679. In this letter he proposed a direct experiment for
verifying the motion of the earth, viz., by observing whether or not bodies
that fall from a considerable height descend in a vertical direction; for
if the earth were at rest the body would describe exactly a vertical line;
whereas if it revolved round its axis, the falling body must deviate from
the vertical line toward the east.
The Royal Society attached great value to the idea thus casually suggested,
and Dr. Hooke was appointed to put it to the test of experiment. Being
thus led to consider the subject more attentively, he wrote to Newton that
wherever the direction of gravity was oblique to the axis on which the
earth revolved, that is, in every part of the earth except the equator,
falling bodies should approach to the equator, and the deviation from the
vertical, in place of being exactly to the east, as Newton maintained,
should be to the southeast of the point from which the body began to move.
Newton acknowledged that this conclusion was correct in theory, and Dr.
Hooke is said to have given an experimental demonstration of it before the
Royal Society in December, 1679. Newton had erroneously concluded that the
path of the falling body would be a spiral; but Dr. Hooke, on the same
occasion on which he made the preceding experiment, read a paper to the
society in which he proved that the path of the body would be an eccentric
ellipse _in vacuo_, and an ellipti-spiral if the body moved in a resisting
medium.
This correction of Newton's error, and the discovery that a projectile
would move in an elliptical orbit when under the influence of a force
varying in the inverse ratio of the square of the distance, led Newton, as
he himself informs us in his letter to Halley, to discover "the theorem
by which he afterward examined the ellipsis," and to demonstrate the
celebrated proposition that a planet acted upon by an attractive force
varying inversely as the squares of the distances, will describe an
elliptical orbit in one of whose _foci_ the attractive force resides.
But though Newton had thus discovered the true cause of all the celestial
motions, he did not yet possess any evidence that such a force actually
resided in the sun and planets. The failure of his former attempt to
identify the law of falling bodies at the earth's surface with that which
guided the moon in her orbit, threw a doubt over all his speculations, and
prevented him from giving any account of them to the public.
An accident, however, of a very interesting nature induced him to resume
his former inquiries, and enabled him to bring them to a close. In June,
1682, when he was attending a meeting of the Royal Society of London, the
measurement of a degree of the meridian, executed by M. Picard in 1679,
became the subject of conversation. Newton took a memorandum of the result
obtained by the French astronomer, and having deduced from it the diameter
of the earth, he immediately resumed his calculation of 1665, and began to
repeat it with these new data. In the progress of the calculation he saw
that the result which he had formerly expected was likely to be produced,
and he was thrown into such a state of nervous irritability that he was
unable to carry on the calculation. In this state of mind he intrusted it
to one of his friends, and he had the high satisfaction of finding his
former views amply realized. The force of gravity which regulated the fall
of bodies at the earth's surface, when diminished as the square of the
moon's distance from the earth, was found to be almost exactly equal to the
centrifugal force of the moon as deduced from her observed distance and
velocity.
The influence of such a result upon such a mind may be more easily
conceived than described. The whole material universe was spread out before
him; the sun with all his attending planets; the planets with all their
satellites; the comets wheeling in every direction in their eccentric
orbits; and the systems of the fixed stars stretching to the remotest
limits of space. All the varied and complicated movements of the heavens,
in short, must have been at once presented to his mind as the necessary
result of that law which he had established in reference to the earth and
the moon.
After extending this law to the other bodies of the system, he composed a
series of propositions on the motion of the primary planets about the sun,
which were sent to London about the end of 1683, and were soon afterward
communicated to the Royal Society.
About this period other philosophers had been occupied with the same
subject. Sir Christopher Wren had many years before endeavored to explain
the planetary motions "by the composition of a descent toward the sun, and
an impressed motion; but he at length gave it over, not finding the means
of doing it." In January, 1683-1684, Dr. Halley had concluded from Kepler's
law of the periods and distances, that the centripetal force decreased in
the reciprocal proportion of the squares of the distances, and having one
day met Sir Christopher Wren and Dr. Hooke, the latter affirmed that he had
demonstrated upon that principle all the laws of the celestial motions. Dr.
Halley confessed that his attempts were unsuccessful, and Sir Christopher,
in order to encourage the inquiry, offered to present a book of forty
shillings value to either of the two philosophers who should, in the space
of two months, bring him a convincing demonstration of it. Hooke persisted
in the declaration that he possessed the method, but avowed it to be his
intention to conceal it for time. He promised, however, to show it to Sir
Christopher; but there is every reason to believe that this promise was
never fulfilled.
In August, 1684, Dr. Halley went to Cambridge for the express purpose of
consulting Newton on this interesting subject. Newton assured him that he
had brought this demonstration to perfection, and promised him a copy of
it. This copy was received in November by the doctor, who made a second
visit to Cambridge, in order to induce its author to have it inserted in
the register book of the society. On December 10th Dr. Halley announced
to the society that he had seen at Cambridge Newton's treatise _De Motu
Corporum_, which he had promised to send to the society to be entered upon
their register, and Dr. Halley was desired to unite with Mr. Paget, master
of the mathematical school in Christ's Hospital, in reminding Newton of his
promise, "for securing the invention to himself till such time as he can be
at leisure to publish it."
On February 25th Mr. Aston, the secretary, communicated a letter from
Newton in which he expressed his willingness "to enter in the register
his notions about motion, and his intentions to fit them suddenly for the
press." The progress of his work was, however, interrupted by a visit of
five or six weeks which he made in Lincolnshire; but he proceeded with such
diligence on his return that he was able to transmit the manuscript to
London before the end of April. This manuscript, entitled _Philosophic
Naturalis Principia Mathematics_ and dedicated to the society, was
presented by Dr. Vincent on April 28, 1686, when Sir John Hoskins, the
vice-president and the particular friend of Dr. Hooke, was in the chair.
Dr. Vincent passed a just encomium on the novelty and dignity of the
subject; and another member added that "Mr. Newton had carried the thing
so far that there was no more to be added." To these remarks the
vice-president replied that the method "was so much the more to be prized
as it was both invented and perfected at the same time." Dr. Hooke took
offence at these remarks, and blamed Sir John for not having mentioned
"what he had discovered to him"; but the vice-president did not seem to
recollect any such communication, and the consequence of this discussion
was that "these two, who till then were the most inseparable cronies, have
since scarcely seen one another, and are utterly fallen out." After the
breaking up of the meeting, the society adjourned to the coffee house,
where Dr. Hooke stated that he not only had made the same discovery, but
had given the first hint of it to Newton.
An account of these proceedings was communicated to Newton through two
different channels. In a letter dated May 22d Dr. Halley wrote to him
"that Mr. Hooke has some pretensions upon the invention of the rule of the
decrease of gravity being reciprocally as the squares of the distances
from the centre. He says you had the notion from him, though he owns the
demonstration of the curves generated thereby to be wholly your own. How
much of this is so you know best, as likewise what you have to do in this
matter; only Mr. Hooke seems to expect you would make some mention of him
in the preface, which it is possible you may see reason to prefix."
This communication from Dr. Halley induced the author, on June 20th,
to address a long letter to him, in which he gives a minute and able
refutation of Hooke's claims; but before this letter was despatched another
correspondent, who had received his information from one of the members
that were present, informed Newton "that Hooke made a great stir,
pretending that he had all from him, and desiring they would see that
he had justice done him." This fresh charge seems to have ruffled the
tranquillity of Newton; and he accordingly added an angry and satirical
postscript, in which he treats Hooke with little ceremony, and goes so far
as to conjecture that Hooke might have acquired his knowledge of the law
from a letter of his own to Huygens, directed to Oldenburg, and dated
January 14,1672-1673. "My letter to Hugenius was directed to Mr. Oldenburg,
who used to keep the originals. His papers came into Mr. Hooke's
possession. Mr. Hooke, knowing my hand, might have the curiosity to look
into that letter, and there take the notion of comparing the forces of the
planets arising from their circular motion; and so what he wrote to me
afterward about the rate of gravity might be nothing but the fruit of my
own garden."
In replying to this letter Dr. Halley assured him that Hooke's "manner of
claiming the discovery had been represented to him in worse colors than
it ought, and that he neither made public application to the society for
justice nor pretended that you had all from him." The effect of this
assurance was to make Newton regret that he had written the angry
postscript to his letter; and in replying to Halley on July 14, 1686, he
not only expresses his regret, but recounts the different new ideas which
he had acquired from Hooke's correspondence, and suggests it as the best
method "of compromising the present dispute" to add a _scholium_ in which
Wren, Hooke, and Halley are acknowledged to have independently deduced the
law of gravity from the second law of Kepler.
At the meeting of April 28th, at which the manuscript of the _Principia_
was presented to the Royal Society, it was agreed that the printing of
it should be referred to the council: that a letter of thanks should be
written to its author; and at a meeting of the council on May 19th it was
resolved that the manuscript should be printed at the society's expense,
and that Dr. Halley should superintend it while going through the press.
These resolutions were communicated by Dr. Halley in a letter dated May
22d; and in Newton's reply on June 20th, already mentioned, he makes the
following observations:
"The proof you sent me I like very well. I designed the whole to consist
of three books; the second was finished last summer, being short, and only
wants transcribing and drawing the cuts fairly. Some new propositions I
have since thought on which I can as well let alone. The third wants the
theory of comets. In autumn last I spent two months in calculation to no
purpose, for want of a good method, which made me afterward return to the
first book and enlarge it with diverse propositions, some relating to
comets, others to other things found out last winter. The third I now
design to suppress. Philosophy is such an impertinently litigious lady that
a man had as good be engaged in lawsuits as have to do with her. I found it
so formerly, and now I can no sooner come near her again but she gives me
warning. The first two books, without the third, will not so well bear the
title of _Philosophies Naturalis Principia Mathematica_; and therefore I
had altered it to this: _de Moti Corporum, Libri duo_. But after second
thoughts I retain the former title. 'Twill help the sale of the book, which
I ought not to diminish now 'tis yours."
In replying to this letter on June 29th Dr. Halley regrets that our
author's tranquillity should have been thus disturbed by envious rivals,
and implores him in the name of the society not to suppress the third book.
"I must again beg you," says he, "not to let your resentments run so high
as to deprive us of your third book, wherein your applications of your
mathematical doctrine to the theory of comets, and several curious
experiments which, as I guess by what you write ought to compose it,
will undoubtedly render it acceptable to those who will call themselves
philosophers without mathematics, which are much the greater number."
To these solicitations Newton seems to have readily yielded. His second
book was sent to the society, and presented on March 2, 1687. The third
book was also transmitted, and presented on April 6th, and the whole work
was completed and published in the month of May, 1687.
Such is the brief account of the publication of a work which is memorable
not only in the annals of one science or of one country, but which will
form an epoch in the history of the world, and will ever be regarded as the
brightest page in the records of human reason. We shall endeavor to convey
to the reader some idea of its contents, and of the brilliant discoveries
which it disseminated over Europe.
The _Principia_ consists of three books. The first and second, which occupy
three-fourths of the work, are entitled _On the Motion of Bodies_, and the
third bears the title _On the System of the World_. The two first books
contain the mathematical principles of philosophy, namely, the laws and
conditions of motions and forces; and they are illustrated with several
philosophical _scholia_ which treat of some of the most general and
best-established points in philosophy, such as the density and resistance
of bodies, spaces void of matter, and the motion of sound and light.
The object of the third book is to deduce from these principles the
constitution of the system of the world; and this book has been drawn up in
as popular a style as possible, in order that it may be generally read.
The great discovery which characterizes the _Principia_ is that of the
principle of universal gravitation, as deduced from the motion of the moon,
and from the three great facts or laws discovered by Kepler. This principle
is: _That every particle of matter is attracted by or gravitates to every
other particle of matter, with a force inversely proportional to the
squares of their distances_. From the first law of Kepler, namely, the
proportionality of the areas to the times of their revolution, Newton
inferred that the force which kept the planet in its orbit was always
directed to the sun; and from the second law of Kepler, that every planet
moves in an ellipse with the sun in one of its foci, he drew the still more
general inference that the force by which the planet moves round that focus
varies inversely as the square of its distance from the focus. As this law
was true in the motion of satellites round their primary planets Newton
deduced the equality of gravity in all the heavenly bodies toward the sun,
upon the supposition that they are equally distant from its centre; and
in the case of terrestrial bodies he succeeded in verifying this truth by
numerous and accurate experiments.
By taking a more general view of the subject Newton demonstrated that a
conic section was the only curve in which a body could move when acted
upon by a force varying inversely as the square of the distance; and he
established the conditions depending on the velocity and the primitive
position of the body, which were requisite to make it describe a circular,
an elliptical, a parabolic, or a hyberbolic orbit.
Notwithstanding the generality and importance of these results, it still
remained to be determined whether the forces resided in the centres of
the planets or belonged to each individual particle of which they were
composed. Newton removed this uncertainty by demonstrating that if a
spherical body acts upon a distant body with a force varying as the
distance of this body from the centre of the sphere, the same effect
will be produced as if each of its particles acted upon the distant body
according to the same law. And hence it follows that the spheres, whether
they are of uniform density or consist of concentric layers, with densities
varying according to any law whatever, will act upon each other in the same
manner as if their force resided in their centres alone.
But as the bodies of the solar system are very nearly spherical they will
all act upon one another, and upon bodies placed on their surfaces, as if
they were so many centres of attraction; and therefore we obtain the law of
gravity which subsists between spherical bodies, namely, that one sphere
will act upon another with a force directly proportional to the quantity of
matter, and inversely as the square of the distance between the centres
of the spheres. From the equality of action and reaction, to which no
exception can be found, Newton concluded that the sun gravitated to the
planets, and the planets to their satellites; and the earth itself to
the stone which falls upon its surface, and, consequently, that the two
mutually gravitating bodies approached to one another with velocities
inversely proportional to their quantities of matter.
Having established this universal law, Newton was enabled not only to
determine the weight which the same body would have at the surface of the
sun and the planets, but even to calculate the quantity of matter in the
sun, and in all the planets that had satellites, and even to determine the
density or specific gravity of the matter of which they were composed. In
this way he found that the weight of the same body would be twenty-three
times greater at the surface of the sun than at the surface of the earth,
and that the density of the earth was four times greater than that of the
sun, the planets increasing in density as they receded from the centre of
the system.