_The first Idea of Gravity occurs to Newton in 1666—His first
Speculations upon it—Interrupted by his Optical Experiments—He
resumes the Subject in consequence of a Discussion with Dr. Hooke—
He discovers the true Law of Gravity and the Cause of the Planetary
Motions—Dr. Halley urges him to publish his Principia—His
Principles of Natural Philosophy—Proceedings of the Royal Society
on this Subject—The Principia appears in 1687—General Account
of it, and of the Discoveries it contains—They meet with great
Opposition, owing to the Prevalence of the Cartesian System—Account
of the Reception and Progress of the Newtonian Philosophy in foreign
Countries—Account of its Progress and Establishment in England._
Such is a brief sketch of the labours and lives of those illustrious
men who prepared the science of astronomy for the application of
Newton’s genius. Copernicus had determined the arrangement and general
movements of the planetary bodies: Kepler had proved that they moved
in elliptical orbits; that their _radii vectores_ described arcs
proportional to the times; and that their periodic times were related
to their distances. Galileo had added to the universe a whole system of
secondary planets; and several astronomers had distinctly referred the
motion of the heavenly bodies to the power of attraction.
In the year 1666, when the plague had driven Newton from Cambridge,
he was sitting alone in the garden at Woolsthorpe, and reflecting on
the nature of gravity,—that remarkable power which causes all bodies
to descend towards 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 farther 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,[41] 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 endeavoured to account for the difference of the two
forces, by supposing that some other cause[42] must have been united
with the force of gravity in producing so great a 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 those optical discoveries of which we have given an account in
a preceding chapter; 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 the 28th November, 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 towards 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
south-east 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.[43] 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.[44]
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,[45] 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.[46]
About this period other philosophers had been occupied with the same
subject. Sir Christopher Wren had many years before endeavoured to
explain the planetary motions “by the composition of a descent towards
the sun, and an impressed motion; but he at length gave it over,
not finding the means of doing it.” In January, 1683–4, 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 some 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 the 10th
of December, Dr. Halley announced to the society, that he had seen
at Cambridge Mr. 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 Mr. Newton of
his promise “for securing the invention to himself till such time as
he can be at leisure to publish it.” On the 25th February Mr. Aston,
the secretary, communicated a letter from Mr. 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 _Philosophiæ
Naturalis Principia Mathematica_, and dedicated to the society, was
presented by Dr. Vincent on the 28th April, 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 our author, on the 20th
June, 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 14th, 1672–3. “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 colours
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 the
14th July, 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.[47]
At the meeting of the 28th April, 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 the 19th May, it was resolved that the MSS. 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 the 22d May; and in Newton’s reply on the 20th
June 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 _Philosophiæ Naturalis
Principia Mathematica_; and therefore I had altered it to this, _De
Motu Corporum Libri duo_. But after second thoughts I retain the former
title. It will help the sale of the book, which I ought not to diminish
now ’tis yours.”
In replying to this letter on the 29th June, 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 the 2d March, 1686–7.
The third book was also transmitted, and presented on the 6th April,
and the whole work was completed and published in the month of May,
1687.
Such is a 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
endeavour 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 first two 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
description, 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 towards 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 hyperbolic orbit.
Notwithstanding the generality and importance of these results, it
still remained to be determined whether the force 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 surface, 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.
If the peculiar genius of Newton has been displayed in his
investigation of the law of universal gravitation, it shines with no
less lustre in the patience and sagacity with which he traced the
consequences of this fertile principle.
The discovery of the spheroidal form of Jupiter by Cassini had probably
directed the attention of Newton to the determination of its cause, and
consequently to the investigation of the true figure of the earth. The
spherical form of the planets have been ascribed by Copernicus to the
gravity or natural appetency of their parts; but upon considering the
earth as a body revolving upon its axis, Newton quickly saw that the
figure arising from the mutual attraction of its parts must be modified
by another force arising from its rotation. When a body revolves upon
an axis, the velocity of rotation increases from the poles, where it
is nothing, to the equator, where it is a maximum. In consequence of
this velocity the bodies on the earth’s surface have a tendency to
fly off from it, and this tendency increases with the velocity. Hence
arises a centrifugal force which acts in combination with a force of
gravity, and which Newton found to be the 289th part of the force of
gravity at the equator, and decreasing, as the cosine of the latitude,
from the equator to the poles. The great predominance of gravity over
the centrifugal force prevents the latter from carrying off any bodies
from the earth’s surface, but the weight of all bodies is diminished
by the centrifugal force, so that the weight of any body is greater at
the poles than it is at the equator. If we now suppose the waters at
the pole to communicate with those at the equator by means of a canal,
one branch of which goes from the pole to the centre of the earth,
and the other from the centre of the earth to the equator, then the
polar branch of the canal will be heavier than the equatorial branch,
in consequence of its weight not being diminished by the centrifugal
force, and, therefore, in order that the two columns may be in
equilibrio, the equatorial one must be lengthened. Newton found that
the length of the polar must be to that of the equatorial canal as 229
to 230, or that the earth’s polar radius must be seventeen miles less
than its equatorial radius; that is, that the figure of the earth is
an oblate spheroid, formed by the revolution of an ellipse round its
lesser axis. Hence it follows, that the intensity of gravity at any
point of the earth’s surface is in the inverse ratio of the distance of
that point from the centre, and, consequently, that it diminishes from
the equator to the poles,—a result which he confirmed by the fact, that
clocks required to have their pendulums shortened in order to beat true
time when carried from Europe towards the equator.
The next subject to which Newton applied the principle of gravity was
the tides of the ocean. The philosophers of all ages have recognised
the connexion between the phenomena of the tides and the position
of the moon. The College of Jesuits at Coimbra, and subsequently
Antonio de Dominis and Kepler, distinctly referred the tides to the
attraction of the waters of the earth by the moon, but so imperfect was
the explanation which was thus given of the phenomena, that Galileo
ridiculed the idea of lunar attraction, and substituted for it a
fallacious explanation of his own. That the moon is the principal cause
of the tides is obvious from the well-known fact, that it is high water
at any given place about the time when she is in the meridian of that
place; and that the sun performs a secondary part in their production
may be proved from the circumstance, that the highest tides take place
when the sun, the moon, and the earth are in the same straight line,
that is, when the force of the sun conspires with that of the moon,
and that the lowest tides take place when the lines drawn from the
sun and moon to the earth are at right angles to each other, that is,
when the force of the sun acts in opposition to that of the moon. The
most perplexing phenomenon in the tides of the ocean, and one which
is still a stumbling-block to persons slightly acquainted with the
theory of attraction, is the existence of high water on the side of the
earth opposite to the moon, as well as on the side next the moon. To
maintain that the attraction of the moon at the same instant draws the
waters of the ocean towards herself, and also draws them from the earth
in an opposite direction, seems at first sight paradoxical; but the
difficulty vanishes when we consider the earth, or rather the centre of
the earth, and the water on each side of it as three distinct bodies
placed at different distances from the moon, and consequently attracted
with forces inversely proportional to the squares of their distances.
The water nearest the moon will be much more powerfully attracted than
the centre of the earth, and the centre of the earth more powerfully
than the water farthest from the moon. The consequence of this must be,
that the waters nearest the moon will be drawn away from the centre
of the earth, and will consequently rise from their level, while the
centre of the earth will be drawn away from the waters opposite the
moon, which will, as it were, be left behind, and consequently be in
the same situation as if they were raised from the earth in a direction
opposite to that in which they are attracted by the moon. Hence the
effect of the moon’s action upon the earth is to draw its fluid parts
into the form of an oblong spheroid, the axis of which passes through
the moon. As the action of the sun will produce the very same effect,
though in a smaller degree, the tide at any place will depend on the
relative position of these two spheroids, and will be always equal
either to the sum or to the difference of the effects of the two
luminaries. At the time of new and full moon the two spheroids will
have their axes coincident, and the height of the tide, which will then
be a _spring_ one, will be equal to the sum of the elevations produced
in each spheroid considered separately, while at the first and third
quarters the axes of the spheroids will be at right angles to each
other, and the height of the tide, which will then be a _neap_ one,
will be equal to the difference of the elevations produced in each
separate spheroid. By comparing the spring and neap tides, Newton found
that the force with which the sun acted upon the waters of the earth
was to that with which the sun acted upon them as 4.48 to 1;—that the
force of the moon produced a tide of 8.63 feet;—that of the sun one of
1.93 feet;—and both of them combined, one of 10½ French feet,—a result
which in the open sea does not deviate much from observation. Having
thus ascertained the force of the moon on the waters of our globe, he
found that the quantity of matter in the moon was to that in the earth
as 1 to 40, and the density of the moon to that of the earth as 11 to 9.
The motions of the moon, so much within the reach of our own
observation, presented a fine field for the application of the theory
of universal gravitation. The irregularities exhibited in the lunar
motions had been known in the time of Hipparchus and Ptolemy. Tycho
had discovered the great inequality called the _variation_, amounting
to 37′, and depending on the alternate acceleration and retardation of
the moon in every quarter of a revolution, and he had also ascertained
the existence of the annual equation. Of these two inequalities Newton
gave a most satisfactory explanation. The action of the sun upon the
moon may be always resolved into two, one acting in the direction
of the line joining the moon and earth, and consequently tending to
increase or diminish the moon’s gravity to the earth, and the other
in a direction at right angles to this, and consequently tending to
accelerate or retard the motion in her orbit. Now, it was found by
Newton that this last force was reduced to nothing, or vanished at
the syzigies or quadratures, so that at these four points the moon
described areas proportional to the times. The instant, however, that
the moon quits these positions, the force under consideration, which
we may call the tangential force, begins, and it reaches its maximum
in the four octants. The force, therefore, compounded of these two
elements of the solar force, or the diagonal of the parallelogram
which they form, is no longer directed to the earth’s centre, but
deviates from it at a maximum about 30 minutes, and therefore affects
the angular motion of the moon, the motion being accelerated in passing
from the quadratures to the syzigies, and retarded in passing from
the syzigies to the quadratures. Hence the velocity is in its mean
state in the octants, a maximum in the syzigies, and a minimum in the
quadratures.
Upon considering the influence of the solar force in diminishing
or increasing the moon’s gravity to the earth, Newton saw that her
distance and her periodic time must from this cause be subject to
change, and in this way he accounted for the annual equation observed
by Tycho. By the application of similar principles, he explained the
cause of the motion of the apsides, or of the greater axis of the
moon’s orbit, which has an angular progressive motion of 3° 4′ nearly
in the course of one lunation; and he showed that the retrogradation of
the nodes, amounting to 3′ 10″ daily, arose from one of the elements
of the solar force being exerted in the plane of the ecliptic, and not
in the plane of the moon’s orbit, the effect of which was to draw the
moon down to the plane of the ecliptic, and thus cause the line of the
nodes, or the intersection of these two planes, to move in a direction
opposite to that of the moon. The lunar theory thus blocked out by
Newton, required for its completion the labours of another century. The
imperfections of the fluxionary calculus prevented him from explaining
the other inequalities of the moon’s motions, and it was reserved to
Euler, D’Alembert, Clairaut, Mayer, and Laplace to bring the lunar
tables to a high degree of perfection, and to enable the navigator to
determine his longitude at sea with a degree of precision which the
most sanguine astronomer could scarcely have anticipated.
By the consideration of the retrograde motion of the moon’s nodes,
Newton was led to discover the cause of the remarkable phenomenon of
the precession of the equinoctial points, which moved 50″ annually,
and completed the circuit of the heavens in 25,920 years. Kepler had
declared himself incapable of assigning any cause for this motion, and
we do not believe that any other astronomer ever made the attempt.
From the spheroidal form of the earth, it may be regarded as a sphere
with a spheroidal ring surrounding its equator, one-half of the ring
being above the plane of the ecliptic and the other half below it.
Considering this excess of matter as a system of satellites adhering
to the earth’s surface, Newton saw that the combined actions of the
sun and moon upon these satellites tended to produce a retrogradation
in the nodes of the circles which they described in their diurnal
rotation, and that the sum of all the tendencies being communicated to
the whole mass of the planet, ought to produce a slow retrogradation of
the equinoctial points. The effect produced by the motion of the sun he
found to be 40″, and that produced by the action of the moon 10″.
Although there could be little doubt that the comets were retained
in their orbits by the same laws which regulated the motions of the
planets, yet it was difficult to put this opinion to the test of
observation. The visibility of comets only in a small part of their
orbits rendered it difficult to ascertain their distance and periodic
times, and as their periods were probably of great length, it was
impossible to correct approximate results by repeated observation.
Newton, however, removed this difficulty, by showing how to determine
the orbit of a comet, namely, the form and position of the orbit and
the periodic time, by three observations. By applying this method to
the comet of 1680, he calculated the elements of its orbit, and from
the agreement of the computed places with those which were observed,
he justly inferred that the motions of comets were regulated by the
same laws as those of the planetary bodies. This result was one of
great importance; for as the comets enter our system in every possible
direction, and at all angles with the ecliptic, and as a great part
of their orbits extend far beyond the limits of the solar system, it
demonstrated the existence of gravity in spaces far removed beyond the
planet, and proved that the law of the inverse ratio of the squares of
the distance was true in every possible direction, and at very remote
distances from the centre of our system.[48]
Such is a brief view of the leading discoveries which the _Principia_
first announced to the world. The grandeur of the subjects of which
it treats, the beautiful simplicity of the system which it unfolds,
the clear and concise reasoning by which that system is explained, and
the irresistible evidence by which it is supported might have ensured
it the warmest admiration of contemporary mathematicians, and the
most welcome reception in all the schools of philosophy throughout
Europe. This, however, is not the way in which great truths are
generally received. Though the astronomical discoveries of Newton were
not assailed by the class of ignorant pretenders who attacked his
optical writings, yet they were every where resisted by the errors and
prejudices which had taken a deep hold even of the strongest minds. The
philosophy of Descartes was predominant throughout Europe. Appealing
to the imagination, and not to the reason of mankind, it was quickly
received into popular favour, and the same causes which facilitated
its introduction extended its influence, and completed its dominion
over the human mind. In explaining all the movements of the heavenly
bodies by a system of vortices in a fluid medium diffused through the
universe, Descartes had seized upon an analogy of the most alluring
and deceitful kind. Those who had seen heavy bodies revolving in the
eddies of a whirlpool, or in the gyrations of a vessel of water thrown
into a circular motion, had no difficulty in conceiving how the planets
might revolve round the sun by analogous movements. The mind instantly
grasped at an explanation of so palpable a character, and which
required for its development neither the exercise of patient thought
nor the aid of mathematical skill. The talent and perspicuity with
which the Cartesian system was expounded, and the show of experiments
with which it was sustained, contributed powerfully to its adoption,
while it derived a still higher sanction from the excellent character
and the unaffected piety of its author.
Thus intrenched, as the Cartesian system was, in the strongholds of
the human mind, and fortified by its most obstinate prejudices, it
was not to be wondered at that the pure and sublime doctrines of the
Principia were distrustfully received and perseveringly resisted. The
uninstructed mind could not readily admit the idea, that the great
masses of the planets were suspended in empty space, and retained
in their orbits by an invisible influence residing in the sun; and
even those philosophers who had been accustomed to the rigour of true
scientific research, and who possessed sufficient mathematical skill
for the examination of the Newtonian doctrines, viewed them at first
as reviving the occult qualities of the ancient physics, and resisted
their introduction with a pertinacity which it is not easy to explain.
Prejudiced, no doubt, in favour of his own metaphysical views, Leibnitz
himself misapprehended the principles of the Newtonian philosophy,
and endeavoured to demonstrate the truths in the Principia by the
application of different principles. Huygens, who above all other men
was qualified to appreciate the new philosophy, rejected the doctrine
of gravitation as existing between the individual particles of matter,
and received it only as an attribute of the planetary masses. John
Bernouilli, one of the first mathematicians of his age, opposed the
philosophy of Newton. Mairan, in the early part of his life, was a
strenuous defender of the system of vortices. Cassini and Maraldi were
quite ignorant of the Principia, and occupied themselves with the
most absurd methods of calculating the orbits of comets long after
the Newtonian method had been established on the most impregnable
foundation; and even Fontenelle, a man of liberal views and extensive
information, continued, throughout the whole of his life, to maintain
the doctrines of Descartes.
The Chevalier Louville of Paris had adopted the Newtonian philosophy
before 1720. S’Gravesande had introduced it into the Dutch universities
at a somewhat earlier period, and Maupertuis, in consequence of a visit
which he paid to England in 1728, became a zealous defender of it; but
notwithstanding these and some other examples that might be quoted,
we must admit the truth of the remark of Voltaire, that though Newton
survived the publication of the Principia more than forty years, yet
at the time of his death he had not above _twenty_ followers out of
England.
With regard to the progress of the Newtonian philosophy in England,
some difference of opinion has been entertained. Professor Playfair
gives the following account of it. “In the universities of England,
though the Aristotelian physics had made an obstinate resistance, they
had been supplanted by the Cartesian, which became firmly established
about the time when their foundation began to be sapped by the general
progress of science, and particularly by the discoveries of Newton. For
more than thirty years after the publication of these discoveries, the
system of vortices kept its ground; and a translation from the French
into Latin of the _Physics_ of Rohault, a work entirely Cartesian,
continued at Cambridge to be the text for philosophical instruction.
About the year 1718, a new and more elegant translation of the same
book was published by Dr. Samuel Clarke, with the addition of notes, in
which that profound and ingenious writer explained the views of Newton
on the principal objects of discussion, so that the notes contained
virtually a refutation of the text; they did so, however, only
virtually, all appearance of argument and controversy being carefully
avoided. Whether this escaped the notice of the learned doctor or not
is uncertain, but the new translation, from its better Latinity, and
the name of the editor, was readily admitted to all the academical
honours which the old one had enjoyed. Thus the stratagem of Dr. Clarke
completely succeeded; the tutor might prelect from the text, but the
pupil would sometimes look into the notes; and error is never so sure
of being exposed as when the truth is placed close to it, side by side,
without any thing to alarm prejudice, or awaken from its lethargy
the dread of innovation. Thus, therefore, the Newtonian philosophy
first entered the university of Cambridge under the protection of the
Cartesian.” To this passage Professor Playfair adds the following as a
note:—
“The universities of St. Andrew’s and Edinburgh were, I believe, the
first in Britain where the Newtonian philosophy was made the subject
of the academical prelections. For this distinction they are indebted
to James and David Gregory, the first in some respects the rival, but
both the friends of Newton. Whiston bewails, in the anguish of his
heart, the difference, in this respect, between those universities and
his own. David Gregory taught in Edinburgh for several years prior to
1690, when he removed to Oxford; and Whiston says, ‘He had already
caused several of his scholars to keep acts, as we call them, upon
several branches of the Newtonian philosophy, while we at Cambridge,
poor wretches, were ignominiously studying the fictitious hypotheses
of the Cartesians.’[49] I do not, however, mean to say, that from this
date the Cartesian philosophy was expelled from those universities;
the _Physics_ of Rohault were still in use as a text-book,—at least
occasionally, to a much later period than this, and a great deal, no
doubt, depended on the character of the individual. Professor Keill
introduced the Newtonian philosophy in his lectures at Oxford in 1697;
but the instructions of the tutors, which constitute the real and
efficient system of the university, were not cast in that mould till
long afterward.” Adopting the same view of the subject, Mr. Dugald
Stewart has stated, “that the philosophy of Newton was publicly taught
by David Gregory at Edinburgh, and by his brother, James Gregory,
at St. Andrew’s,[50] before it was able to supplant the vortices of
Descartes in that very university of which Newton was a member. It was
in the Scottish universities that the philosophy of Locke, as well as
that of Newton, was first adopted as a branch of academical education.”
Anxious as we should have been to have awarded to Scotland the honour
of having first adopted the Newtonian philosophy, yet a regard for
historical truth compels us to take a different view of the subject.
It is well known that Sir Isaac Newton delivered lectures on his own
philosophy from the Lucasian chair before the publication of the
Principia; and in the very page of Whiston’s life quoted by Professor
Playfair, he informs us that he had heard him read such lectures in the
public schools, though at that time he did not at all understand them.
Newton continued to lecture till 1699, and occasionally, we presume,
till 1703, when Whiston became his successor, having been appointed
his deputy in 1699. In both of these capacities Whiston delivered in
the public schools a course of lectures on astronomy, and a course of
physico-mathematical lectures, in which the mathematical philosophy
of Newton was explained and demonstrated, and both these courses
were published, the one in 1707, and the other in 1710, “for the use
of the young men in the university.” In 1707, the celebrated blind
mathematician Nicholas Saunderson took up his residence in Christ’s
College without being admitted a member of that body. The society
not only allotted to him apartments, but gave him the free use of
their library. With the concurrence of Whiston he delivered a course
of lectures “on the Principia, Optics, and Universal Arithmetic of
Newton,” and the popularity of these lectures was so great, that Sir
Isaac corresponded on the subject of them with their author; and on the
ejection of Whiston from the Lucasian chair in 1711, Saunderson was
appointed his successor. In this important office he continued to teach
the Newtonian philosophy till the time of his death, which took place
in 1739.
But while the Newtonian philosophy was thus regularly taught in
Cambridge, after the publication of the Principia, there were not
wanting other exertions for accelerating its progress. About 1694, the
celebrated Dr. Samuel Clarke, while an under-graduate, defended, in the
public schools, a question taken from the Newtonian philosophy; and
his translation of Rohault’s Physics, which contains references in the
notes to the Principia, and which was published in 1697 (and not in
1718, as stated by Professor Playfair), shows how early the Cartesian
system was attacked by the disciples of Newton. The author of the Life
of Saunderson informs us, that public exercises or acts founded on
every part of the Newtonian system were very common about 1707, and so
general were such studies in the university, that the Principia rose to
four times its original price.[51] One of the most ardent votaries of
the Newtonian philosophy was Dr. Laughton, who had been tutor in Clare
Hall from 1694, and it is probable that during the whole, or at least
a greater part, of his tutorship he had inculcated the same doctrines.
In 1709–10, when he was proctor of that college, instead of appointing
a moderator, he discharged the office himself, and devoted his most
active exertions to the promotion of mathematical knowledge. Previous
to this, he had even published a paper of questions on the Newtonian
philosophy, which appear to have been used as theses for disputations;
and such was his ardour and learning that they powerfully contributed
to the popularity of his college. Between 1706 and 1716, the year
of his death, the celebrated Roger Cotes, the friend and disciple
of Newton, filled the Plumian chair of astronomy and experimental
philosophy at Cambridge. During this period he edited the second
edition of the Principia, which he enriched with an admirable preface,
and thus contributed, by his writings as well as by his lectures, to
advance the philosophy of his master. About the same time, the learned
Dr. Bentley, who first made known the philosophy of his friend to
the readers of general literature, filled the high office of master
of Trinity College, and could not fail to have exerted his utmost
influence in propagating doctrines which he so greatly admired. Had any
opposition been offered to the introduction of the true system of the
universe, the talents and influence of these individuals would have
immediately suppressed it; but no such opposition seems to have been
made; and though there may have been individuals at Cambridge ignorant
of mathematical science, who adhered to the system of Descartes, and
patronised the study of the Physics of Rohault, yet it is probable
that similar persons existed in the universities of Edinburgh and St.
Andrew’s; and we cannot regard their adherence to error as disproving
the general fact, that the philosophy of Newton was quickly introduced
into all the universities of Great Britain.
But while the mathematical principles of the Newtonian system were ably
expounded in our seats of learning, its physical truths were generally
studied, and were explained and communicated to the public by various
lecturers on experimental philosophy. The celebrated Locke, who was
incapable of understanding the Principia from his want of mathematical
knowledge, inquired of Huygens if all the mathematical propositions
in that work were true. When he was assured that he might depend upon
their certainty, he took them for granted, and carefully examined
the reasonings and corollaries deduced from them. In this manner he
acquired a knowledge of the physical truths in the Principia, and
became a firm believer in the discoveries which it contained. In the
same manner he studied the treatise on Optics, and made himself master
of every part of it which was not mathematical.[52] From a manuscript
of Sir Isaac Newton’s, entitled “A demonstration that the planets, by
their gravity towards the sun, may move in ellipses,[53] found among
the papers of Mr. Locke, and published by Lord King,” it would appear
that he himself had been at considerable trouble in explaining to his
friend that interesting doctrine. This manuscript is endorsed, “Mr.
Newton, March, 1689.” It begins with three hypotheses (the first
two being the two laws of motion, and the third the parallelogram
of motion), which introduce the proposition of the proportionality
of the areas to the times in motions round an immoveable centre of
attraction.[54] Three lemmas, containing properties of the ellipse,
then prepare the reader for the celebrated proposition, that when a
body moves in an ellipse,[55] the attraction is reciprocally as the
square of the distance of the body from the focus to which it is
attracted. These propositions are demonstrated in a more popular manner
than in the Principia, but there can be no doubt that, even in their
present modified form, they were beyond the capacity of Mr. Locke.
Dr. John Keill was the first person who publicly taught natural
philosophy by experiments. Desaguliers informs us that this author
“laid down very simple propositions, which he proved by experiments,
and from these he deduced others more compound, which he still
confirmed by experiments, till he had instructed his auditors in the
laws of motion, the principles of hydrostatics and optics, and some
of the chief propositions of Sir Isaac Newton concerning light and
colours. He began these courses in Oxford about the year 1704 or 1705,
and in that way introduced the love of the Newtonian philosophy.” When
Dr. Keill left the university, Desaguliers began to teach the Newtonian
philosophy by experiments. He commenced his lectures at Harthall in
Oxford, in 1710, and delivered more than a hundred and twenty courses;
and when he went to settle in London in 1713, he informs us that he
found “the Newtonian philosophy generally received among persons of
all ranks and professions, and even among the ladies by the help of
experiments.” Such were the steps by which the Newtonian philosophy
was established in Great Britain. From the time of the publication
of the Principia, its mathematical doctrines formed a regular part of
academical education; and before twenty years had elapsed, its physical
truths were communicated to the public in popular lectures illustrated
by experiments, and accommodated to the capacities of those who were
not versed in mathematical knowledge. The Cartesian system, though it
may have lingered for a while in the recesses of our universities, was
soon overturned; and long before his death, Newton enjoyed the high
satisfaction of seeing his philosophy triumphant in his native land.