82 NEWTON. 
the primary planets are carried round the fun by the like 
power; and, by comparing the periods of the feveral 
planets with their diftances from the fun, he found, that, 
if any power like gravity held them in their courfes, its 
ftrength multdecreafe in the duplicate proportion of the 
increafe of diftance. 
Soon after this, Newton returned to Cambridge, where, 
in the year 1667, he was elefted fellow of his college, and 
admitted to the degree of M. A. In 1669, Dr. Barrow 
refigned to him the buiinefs connected with the profefior- 
fhip of mathematics. However, as his thoughts had for 
fome time been chiefly employed upon optics, he made his 
difcoveries in that fcience the fubjedl of his leftures for 
the three firlt years after his appointment to the mathe¬ 
matical chair. 
In the mean time, an unexpected occafion drew from 
him a difcovery of the vaft improvements which he had 
made in geometry by means of his new analyfls. During 
the year 1668, lord Brouncker had publiflied a quadra¬ 
ture of the hyperbola in an infinite feries, which, with the 
aid of Dr. Wallis’s diviflon, was loon afterwards demon- 
ftrated by Nicholas Mercator, in his Logarithmo technica. 
This, being the firlt appearance of a feries of this fort, drawn 
from the particular nature of the curve exprefi'ed in an 
abltraCted algebraical equation, and that in a new man¬ 
ner, foon came into the hands of Dr. Barrow, then at 
Trinity-college. This learned mathematician, recollect¬ 
ing that he had met with a fimilar feries in the writings of 
Newton, and not confined to the hyperbola only, but 
extended by general forms to all forts of curves, even 
fuch as are mechanical, communicated to him. this work 
of Mercator. Upon the fight of it, our author brought 
to him thofe papers of his own which contained his 
“ Analyfls per HJquationes Numero Terminorum infini- 
tas.” When the doCtor had perufed it, he was aftonilhed 
at the prodigious performance, and immediately acquain¬ 
ted his friend Mr. Collins with it; at wdiofe requeft he 
afterwards obtained our author’s leave to fend him the 
papers. Thefe were tranfcribed by Mr. Collins, who fent 
copies of them to fome of the moll eminent of his ma¬ 
thematical acquaintance. It was not, however, till many 
years afterwards, that the full extent to which our author 
had carried his invention came to be w r ell underftood. 
In his eloge upon our author, Fontenelle obferves, that 
it was natural to expeCt that, upon feeing Mercator’s 
book, he would have been forward to open his treafure, 
and thereby fecure to himfelf the glory of being the firft 
difcoverer: but this was not his way of thinking; on 
the contrary, we know from himfelf, that he thought 
that Mercator had difcovered his fecret, or that others 
would, before his modefty would allow him to confider 
himfelf of a proper age to adarefs the public. 
In the year 1672, Newton was chofen a fellow of the 
Royal Society ; and, having now brought his “Theory of 
Light and Colours” to a confiderable degree of perfection, 
he communicated it to the fociety, who publiflied it in 
the Philofophical TranfaCtions for that year. But, not- 
withftanding ail the precaution which the author had 
taken in preparing it for public view, it was fo new and 
unexpected, and fo totally fubverfive of all men’s fettled 
opinions on the fubjeCt; while, at the fame time, fuch a 
great degree of accuracy was necefiary in making the ex¬ 
periments upon which it was founded, and the reafoning 
alfo upon thofe experiments was fo very fubtleand pene¬ 
trating ; that it no fooner made its appearance, than it 
■met with opponents from all quarters. Our author was 
thus unexpectedly drawn into difputes concerning the 
truth of it, which, as he had a great averfion to contro- 
verfy, were very unpleafant to him, and determined him 
not to publifin any thing further upon the fubjeCt for 
fome time. On this account he laid by his Optical Lec¬ 
tures, after he had prepared them for the preis, and his 
Analyfls by Infinite Series, which was intended to accom¬ 
pany them. In this conduct he evidently aCted againft 
his own fame; but that confideration had little weight 
with him, when oppofed to the enjoyment of unruffled 
ferenity of thought: a blefling which he valued above all 
the glory that mathematics or philofophy could confer 
upon him. Our author now refumed his endeavours to 
perfeCt his reflecting telefcope; and, obferving that there 
was no abfolute neceflity for the parabolical figure of the 
glafles, fince, if metals could be ground truly fpherical, 
they would bear as great apertures as men would be able 
to polifli, he completed another inftrument of the fame- 
kind. This anfwered his purpofe fo well, that, though 
it was only fix inches long, he had feen Jupiter with it 
diltinCtly round, with the four fatellites then difcovered; 
and alfo Venus horned. This telefcope he fent to the 
Royal Society, at their requeff, together with a defcrip- 
tion of it, and further particulars ; which were publiflied 
in the Philolophical TranfaCtions for 1672. Several aS- 
tempts were alfo made by the fociety to bring it to per¬ 
fection ; but, for w'ant of a proper compofition of metal, 
and a good polifli, they failed of fuccefs; and the inven¬ 
tion lay dormant till Hailey made his Newtonian telefcope 
in 1723. 
During the year 1672, likewife, our author publiflied, 
at Cambridge, “Bernardi Varenii Geographia generalis, 
in qua affeCtiones generales Telluris explicantur; auCta 
et illuftrata ab If. Newton;” oClavo. This edition was 
reprinted in 1687; and at a later period with larger addi¬ 
tions, chiefly taken from our author’s writings, by Dr. 
James Jurin. From this time till 1679, our author main¬ 
tained a correfpondence, by letters, with Mr. Henry 
Oldenburg, fecretary of the Royal Society, Mr. John 
Collins, Mr. John Flamfteed, and Dr. Edmund Halley; 
which letters contain a variety of curious and ufeful ob- 
fervations. In the year 1675, Mr. Hooke having laid 
claim to fome of his inventions in his New Theory of 
Light and Colours, our author vindicated his right to 
them, with becoming fpirit, and complete fuccefs. Du¬ 
ring the following year, at the requeft: of Mr. Leibnita, 
lie wrote two letters, to be communicated to that gen¬ 
tleman, containing an explanation of his invention of 
infinite feries, and took notice how far he had improved 
it by his Method of Fluxions. That method, however, 
he ltill concealed, and particularly on this occafion, by 
the tranlpofition of the letters that make up the two fun¬ 
damental propofitions of it, into an alphabetical order. 
Thefe letters are inferred in Collins’s Commercium Epif- 
tolicum. 
In the winter between 1676 and 1677, Newton found 
out the grand propofition, that, by a centripetal force 
adling reciprocally as the fquare of the diftance, a planet 
mult revolve in an elliplis about the centre of force 
placed in its lower focus, and, with a radius drawn to 
that centre, defcribe areas proportional to the times. In 
1680, he made feveral aftronomical obfervations on the 
comet that then appeared; which, for fome time, he took, 
not to be one and the fame, but two different comets, 
contrary to the opinion of Mr. Flamfteed. While he 
continued under this miftake, he received a letter from 
Mr. Hooke, explaining the nature of the line defcribed 
by a falling body, fuppofed to be moved circularly by the 
diurnal motion of the earth, and perpendicularly by the 
power of gravity. This letter led him to enquire anew 
what was the real figure in which fuch a body moved; 
and this enquiry gave occafion to his refuming his former 
thoughts concerning the moon. As Picart had meafured 
a degree of the earth in 1679, by ufing his mealures our 
author concluded, that the moon is retained in her orbit 
folely by the power of gravity ; and, confequently, that 
this power decreafes in the duplicate proportion of the 
diftance, as he had formerly conjectured. Upon this 
principle, he found the line defcribed by a falling body 
to be an elliplis, having one focus in the centre of the 
earth ; and, finding by this means that the primary planets 
really moved in fuch orbits as Kepler had fuppofed, he 
had the latisfaCtion to fee that this enquiry, which he 
had undertaken at firft from motives of mere curiofity, 
was 
