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自然哲学的数学原理

_3 伊萨克·牛顿(英国)
ing and important, and had attracted considerable investigation.
He, however, was the first to determine the law of the produc
tion of these colours, arid, during the same year made known the
results of his researches herein to the Royal Society. His mode
of procedure in these experiments was simple and curious. He
placed a double convex lens of a large known radius of curvature,
the flat surface of a plano-convex object glass. Thus, from

UFE OF SIR ISAAC NEWTON. 25
their point of contact at the centre, to the circumference of the
lens, he obtained plates of air, or spaces varying from the extremest
possible thinness, by slow degrees, to a considerable thick
ness. Letting the light fall, every different thickness of this
plate of air gave different colours the point of contact of the
lens and glass forming the centre of numerous concentric colored
nags. Now the radius of curvature of the lens being known, the
thickness of the plate of air, at any given point, or where any par
ticular colour appeared, could be exactly determined. Carefully
noting, therefore, the order in which the different colours ap
peared, he measured, with the nicest accuracy, the different thick*
nesses at which the most luminous parts of the rings were pro
duced, whether the medium were air, water, or mica all these
substances giving the same colours at different thicknesses ; the
ratio of which he also ascertained. From the phenomena obser
ved in these experiments, Newton deduced his Theory of Fits of
EASY REFLECTION AND TRANSMISSION oflight. It consists in suppos
ing that every particle of light, from its first discharge from a lumi
nous body, possesses, at equally distant intervals, dispositions to
be reflected from, or transmitted through the surfaces of bodies
upon which it may fall. For instance, if the rays are in a Fit of
Easy Reflection, they are on reaching the surface, repelled,
thrown off] or reflected from it
; if, in a Fit of Easy Transmission,
they are attracted, drawn in, or transmitted through it. By this
Theory of Fits, our author likewise explained the colours of
thick plates.
He regarded light as consisting of small material particles
emitted from shining substances. He thought that these parti
cles could be re-combined into solid matter, so that "
gross bodies
and light, were convertible into one another ;" that the particles of
light and the particles of solid bodies acted mutually upon each
other ; those of light agitating and heating those of solid bodies,
and the latter attracting and repelling the former. Newton was
the first to suggest the idea of the POLARIZATION of light.
In the paper entitled An Hypothesis Explaining Properties of
Light, December, 1675, our author first introduced his opinions re
specting Ether opinions which he afterward abandoned and again

26 LIFE OF SIR S.\AC 1SEWTON.
permanently resumed " A most subtle spirit which pervades" ah
bodies, and is expanded through all the heavens. It is electric,
and almost, if not quite immeasurably elastic and rare. " By the
force and action of which spirit the particles of bodies mutually
attract one another, at near distances, and cohere, if contiguous ;
and electric bodies operate at greater distances, as well repelling
as attracting the neighbouring corpuscles ; and light is emitted,
-reflected, refracted, inflected and heats bodies ; and all sensation
is excited, and the members of animal bodies move at the com
mand of the will, namely, by the vibrations of this spirit, mutu
ally propagated along the solid filaments of the nerves, from the
outward organs of sense to the brain, and from the brain into the
muscles." This "
spirit" was no anima mundi ; nothing further
from the thought of Newton ; but was it not, on his part, a par
tial recognition of, or attempt to reach an ultimate material force,
or primary element, by means of which, " in the roaring loom of
time," this material universe, God s visible garment, may be
woven for us ?
The Royal Society were greatly interested in the results of
some experiments, which our author had, at the same time, com
municated to them relative to the excitation of electricity in glass ;
and they, after several attempts and further direction from him,
succeeded in re-producing the same phenomena.
One of the most curious of Newton s minor inquiries related to
the connexion between the refractive powers and chemical com
position of bodies. He found on comparing the refractive powers
and the densities of many different substances, that the former
were very nearly proportional to the latter, in the same bodies.
Unctuous and sulphureous bodies were noticed as remarkable excep
tions as well as the diamond their refractive powers being two
or three times greater in respect of their densities than in the
case of other substances, while, as among themselves, the one was
generally proportional to the other. He hence inferred as to the
diamond a great degree of combustibility ;
a conjecture which
the experiments of modern chemistry have shown to be true.
The chemical researches of our author were probably pursued
with more or less diligence from the time of his witnessing some

LIFE OF .SIR ISAAC NEWTON. 27
?t the uractical operations in that science at the Apothecary s at
Grantham. DE NATURA ACIDORUM is a short chemical paper, on
various topics, and published in Dr. Horsley s Edition of his
works. TABULA QUANTITATUM E r GRADUUM COLORIS was in
serted iii the Philosophical Transactions ;
it contains a compara
tive scale of temperature from that of melting ice to that of a
small kitchen coal-fire. He regarded fire as a body heated so hot
as to emit light copiously ; and flame as a vapour, fume, or ex
halation heated so hot as to shine. To elective attraction, by
the operation of which the small particles of bodies, as he con
ceived, act upon one another, at distances so minute as to escape
observation, he ascribed all the various chemical phenomena ot
precipitation, combination, solution, and crystallization, and the
mechanical phenomena of cohesion and capillary attraction. New
ton s chemical views were illustrated and confirmed, in part, at
least, in his own life-time. As to the structure of bodies, he was
of opinion
" that the smallest particles of matter may cohere by
the strongest attractions, and compose bigger particles of weaker
virtue
; and many of these may cohere and compose bigger par
tides whose virtue is still weaker ; and so on for divers succes
sions, until the progression end in the biggest particles, on which
the operations in chemistry and the colours of natural bodies de
pend, and which by adhering, compose bodies of sensible magni
tude."
There is good reason to suppose that our author was a diligent
student of the writings of Jacob Behmen ; and that in conjunction
with a relative, Dr. Newton, he was busily engaged, for several
months in the earlier part of life, in quest of the philosopher s
tincture. " Great Alchymist," however, very imperfectly de
scribes the character of Behmen, whose researches into things
material and things spiritual, things human and things divine, aiford
the strongest evidence of a great and original mind.
More appropriately here, perhaps, than elsewhere, may be
given Newton s account of some curious experiments, made in his
own person, on the action of light upon the retina, Locke, who
was an intimate friend of our author, wrote to him for his opinion
on a certain fact stated in Boyle s Book of Colours. Newton, in

2S LIFE OF SIR ISAAC NEWTON.
his reply, dated June 30th, 16(
Jl, narrates the following circum
stances, which probably took place in the course of his optical
researches. Thus :
" The observation you mention in Mr. Boyle s Book of Colours
I once tried upon myself with the hazard of my eyes. The
manner was this
;
I looked a very little while upon the sun in the
looking-glass with my right eye, and then turned my eyes into a
dark corner of my chamber, arid winked, to observe the impres
sion made, and the circles of colours which encompassed it, and
how they decayed by degrees, and at last vanished. This I re
peated a second and a third time. At the third time, when the
phantasm of light and colours about it were almost vanished, in
tending my fancy upon them to see their last appearance, I found,
to my amazement, that they began to return, and by little and
little to become as lively and vivid as when I had newly looked
upon the sun. But when I ceased to intend my fancy upon them,
they vanished again. After this, I found, that as often as I went
into the dark, and intended my mind upon them, as when a man
looks earnestly to see anything which is difficult to be seen, I
could make the phantasm return without looking any more upon
the sun ; and the oftener I made it return, the more easily I could
make it return again. And, at length, by repeating this, without
looking any more upon the sun, I made such an impression on my
eye, that, if I looked upon the clouds, or a book, or any bright
object, I saw upon it a round bright spot of light like the sun,
and, which is still stranger, though I looked upon the sun with
my right eye only, and not with my left, yet my fancy began *o
make an impression upon my left eye, as well us upon my right.
For if I shut my right eye, or looked upon a book, or the clouds,
with my left eye, I could see the spectrum of the sun almost as
plain as with my right eye, if I did but intend my fancy a little
while upon it
;
for at first, if I shut my right eye, and looked with
my left, the spectrum of the sun did not appear till I intended my
fancy upon it
; but by repeating, this appeared every time more
easily. And now, in a few hours time, I had brought my eyes
to such a pass, that I could look upon no blight object with either
eye, but I saw the sun before me, so that I durst neither write

LIFE OF SIR ISAAC NEWTON. 29
nor read ; but to recover the use of my eyes, shut myself up in
my chamber made dark, for three days together, and used all
means to divert my imagination from the sun. For if I thought
upon him, I presently saw his picture, though I was in the dark.
But by keeping in the dark, and employing my mind about other
things, I began in three or four days to have some use of my eyes
again ; and by forbearing to look upon bright objects, recovered
them pretty well, though not so well but that, for some months
after, the spectrum of the sun began to return as often as I began
to meditate upon the phenomena, even though I lay in bed at mid
night with my curtains drawn. But now I have been very well
for many years, though I am apt to think, if I durst venture my
eyes, I could still make the phantasm return by the power of my
fancy. This story I tell you, to let you understand, thaj; in the
observation related by Mr. Boyle, the man s fancy probably con
curred with the impression made by the sun s light to produce
that phantasm of the sun which he constantly saw in bright ob
jects. And so your question about the cause of phantasm in
volves another about the power of fancy, which I must confess is
too hard a knot for me to untie. To place this effect in a constant
motion is hard, because the sun ought then to appear perpetually.
It seems rather to consist in a disposition of the sensorium to
move the imagination strongly, and to be easily moved, both by
the imagination and by the light, as often as bright objects are
looked upon."
J
Though Newton had continued silent, yet his thoughts were
by no means inactive upon the vast subject of the planetary mo
tions. The idea of Universal Gravitation, first caught sight of, so
to speak, in the garden at Woolsthorpe, years ago, had gradually
expanded upon him. We find him, in a letter to Dr. Hooke,
Secretary of the Royal Society, dated in November, 1679, pro
posing to verify the motion of the earth by direct experiment,
namely, by the observation of the path pursued by a body falling
from a considerable height. He had concluded that the path
would be spiral ; but Dr. Hooke maintained that it would be an
eccentric ellipse iu vacuo, and an ellipti-spiral in a resisting me
dium. Our author, aided by this correction of his error, and by

30 LIFE OF SIR ISAAC NEWTON.
the discovery that a projectile would move in an elliptical orbil
when under the influence of a force varying inversely as the
square of the distance, was led to discover " the theorem bj
which he afterwards examined the ellipsis ;" and to demonstrate
the celebrated proposition that a planet acted upon by an attrac
tive force varying inversely as the squares of the distances will
describe an elliptical orbit, in one of whose foci the attractive
force resides.
When he was attending a meeting of the Royal Society, in
June 1682, the conversation fell upon the subject of the measure
ment of a degree of the meridian, executed by M. Picard, a
French Astronomer, in 1679. Newton took a memorandum oi
the result
; and afterward, at the earliest opportunity, computed
from it the diameter of the earth : furnished with these new data,
he resumed his calculation of 1666. As he proceeded therein,
he saw that his early expectations were now likely to be realized ;
the thick rushing, stupendous results overpowered him ; he be
came unable to carry on the process of calculation, and intrusted
its completion to one of his friends. The discoverer had, indeed,
grasped the master-fact. The law of falling bodies at the earth s
surface was at length identified with that which guided the moon
in her orbit. And so his GREAT THOUGHT, that had for sixteen
years loomed up in dim, gigantic outline, amid the first dawn of a
plausible hypothesis, now stood forth, radiant and not less grand,
in the mid-day light of demonstrated truth.
It were difficult, nay impossible to imagine, even, the influence
of a result like this upon a mind like Newton s. It was as if the
keystone had been fitted to the glorious arch by which his spirit
should ascend to the outskirts of infinite space spanning the immea
surable weighing the imponderable computing the incalculable
mapping out the marchings of the planets, and the far-wander
ings of the comef
s, and catching, bring back to earth some clearer
notes of that higher melody which, as a sounding voice, bears
perpetual witness to the design and omnipotence of a creating
Deity.
Newton, extending the law thus obtained, composed a series
of about twelve propositions on the motion of the primary planets

LIFE OF SIR ISAAC NEWTON. 31
about the sun. These were sent to London, and communicated
to the Royal Society about the end of 1683. At or near this pe
riod, other philosophers, as Sir Christopher Wren, Dr. Halley,
and Dr. Hooke, were engaged in investigating the same subject ;
but with no definite or satisfactory results. Dr. Halley, having
seen, it is presumed, our author s propositions, went in August,
1684, to Cambridge to consult with him upon the subject.
Newton assured him that he had brought the demonstration to
perfection. In November, Dr. Halley received a copy of the
work ; and, in the following month^ announced . it to the Royal
Society, with the author s promise to have it entered upon their
Register. Newton, subsequently reminded by the Society of his
promise, proceeded in the diligent preparation of the work, and.
though suffering an interruption of six weeks, transmitted the
manuscript of the first book to London before the end of April.
The work was entitled PHILOSOPHI/E NATURALIS PRINCIPIA
MATHEMATICA, dedicated to the Royal Society, and presented
thereto on the 28th of April, 1685-6. The highest encomiums
were passed upon it
; and the council resolved, on the 19th of
May, to print it at the expense of the Society, and under the di
rection of Dr. Halley. The latter, a few days afterward, com
municated these steps to Newton, who, in a reply, dated the 20th
of June, holds the following language :
" 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 ouf last winter. The third I now design to sup
press. Philosophy is such an impertinently litigious lady, that a
man had as good be engaged in liw-suits 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 P/iilosophicc Naturalis
3

32 LIFE OF SIR ISAAC NEWTON.
Principia Mathematicia ; and thereupon I had altered it to this,
De Motu Corporum Libri duo. But after second thought I re
tain the former title. It will help the sale of the book, which I
ought not to diminish now tis
yours."
This "
warning" arose from some pretensions put forth by Dr.
Hooke. And though Newton gave a minute and positive refuta
tions of such claims, yet, to reconcile all differences, he gener
ously added to Prop. IV. Cor. 6, Book I, a Scholium, in which
Wren, Hooke and Halley are acknowledged to have indepen
dently deduced the law of gravity from the second law of
Kepler.
The suppression of the third book Dr. Halley could not endure
to see. " I must again beg you" says he,
" not to let your re
sentments run so high as to deprive us of your third book, where
in 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 yielded. There were no "resentments," how
ever, as we conceive, in his "
design to suppress." He sought
peace ;
for he loved and valued it above all applause. But, in
spite of his efforts for tranquillity s sake, his course of discovery
was all along molested by ignorance or presumptuous rivalry.
The publication of the great work now went rapidly forwards,
The second book was sent to the Society, and presented on the
2d March ; the third, on the 6th April ; and the whole was com
pleted and published in the month of May, 1686-7. In the sec
ond Lemma of the second book, the fundamental principle of his
fiuxionary calculus was, for the first time, given to the world ; but
its algorithm or notation did not appear till published in the
second volume nf Dr. Wallis s works, in 1693.
And thus was ushered into existence The PRINCIPIA a work
to which pre-eminence above all the productions of the human
intellect has been awarded a work that must be esteemed of
priceless worth so long as Science has a votary, or a single wor
shipper be left to kneel at the altar of Truth.

LIFE OF SIR ISAAC NEWTON. 33
The entire work bears the general title of THE MATHEMATICAL
PRINCIPLES OF NATURAL PHILOSOPHY. It consists of three books:
the first two, entitled, OF THE MOTION OF BODIES, are occupied
with the laws and conditions of motions and forces, and are illus
trated with many scholia treating 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. From these principles, there is deduced, in the
third book, drawn up in as popular a style as possible and entitled,
OF THE SYSTEM OF THE WORLD, the constitution of the system of
i he world. In regard to this book, the author say^
" I had, indeed,
composed the third Book in a popular method, that it might be read
by many ; but afterwards, considering that such as had not sufficently
entered into the principles could not easily discover the
strength of the consequences, nor lay aside the prejudices to which
they had been many years accustomed, therefore, to prevent dis
putes which might be raised upon such accounts, I chose to reduce
the substance of this Book into the form of Propositions (in the
mathematical way), which should be read by those only who had
first made themselves masters of the principles established in the
preceding Books : not that I would advise any one to the previous
study of every Proposition of those Books." "It is enough it
one carefully reads the Definitions, the Laws of Motion, and the
three first Sections of the first Book. He may then pass on to
this Book, and consult such of the remaining Propositions of the
first two Books, as the references in this, and his occasions shall re
quire." So that " The System of the World" is composed both
" in a popular method," and in the form of mathematical Propo
sitions.
The principle of Universal Gravi ition, namely, that every
particle of matter is attracted by, or gravitates to, every other
particle of matter, icith a force inversely proportional to the
squares of their distances is the discovery w? ich characterizes
The PRINCIPIA. This principle the author deduced from the mo
tion of the moon, and the three laws of Kepler laws, which
Newton, in turn, by his greater law, demonstrated to be true.
From the first law of Kepler, namely, the proportionality of

LIFE OF SIR ISAAC NEWTON.
the areas to t\ie times of their description, our author inferred
that the force which retained the planet in its orbit was always
directed to the sun ; and from the second, namely, that every
planet moves in an ellipse with the sun in one of its foci, he drew
the more general inference that the force by which the planet
moves round that focus varies inversely as the square of its dis
tance therefrom : and he demonstrated that a planet acted upon
by such a force could not move in any other curve than a conic
section ; showing when the moving body would describe a circu
lar, an elliptical, a parabolic, or hyperbolic orbit. He demon
strated, too, that this force, or attracting, gravitating power re
sided in every, the least particle ; but that, in spherical masses, it
operated as if confined to their centres ; so that, one sphere or
body will act upon another sphere or body, with a force directly
proportional to the quantity of matter, and inversely as the square
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