at the tops of the loftieft buildings, nor on the fummits of the highest mountains, it appeared to him reasonable to conclude, that this power, muft extend much farther than was ufually thought. Why not as high as the moon? faid he to himself; and, if fo, her motion mult be influenced by it; perhaps the is retained in her orbit thereby however, tho' the power of gravity is not fenfibly weakened in the little change of distance at which we can place ourfelves from the centre of the earth; yet it is very poffible, that, as high as the moon, this power may differ much in ftrength from what it is here.

To make an eftimate what might be the degree of this diminution, he confidered with himself, that, if the moon be retained in het orbit by the force of gravity, no doubt the primary planets are carried round the fun by the like power; and, by comparing the periods of the feveral planets with their di flances from the fun, he found, that, if any power like gravity held them in their courfes, its ftrength muft decrease in the duplicate proportion of the increafe of diflance.

This he concluded, by fuppofing them to move in perfect circles concentrical to the fun, from which the orbits of the greatest part of hem do not much differ. Suppofing therefore the power of gravity, when extended to the moon to decrease in the fame manner, he computed whether that force would be fufficient to keep the moon in her orbit.

Tn this computation, being abfent from books, he took the common ellimate, in ufe among geographers and our feamen before Norwood had measured the earth, that fixty English miles complete one degree of latitude; but, as this is a very faulty fuppofition, each degree containing about fixty-nine English miles and an half, his computation upon it did not make the power of gravity, decreafing in a duplicate proportion to the diftance, anfwera. ble to the power which retained the moon in her orbit; whence he concluded that fome other cause most at least join with the action of the power of gravity on the moon. For this reafon, he laid afide, for that time, any farther thoughts upon the matter.

An eafinefs fo refigned, as to give up a favourite opinion, founded upon the best astronomical obfervations of the whole planetary fyftěm, is an illuftrious proof of a temper exactly fitted for philofophical enquiries.

Mr. Voltaire relates it, as an anecdote of particular ufe in the hiftory of the human mind; as it fhews, at once, both how great an exactness is neceffary in thefe fciences, and likewife how difinterefed Mr. Newton was in his fearch after truth.

It is indeed a little furprifing, that he should not then be acquainted with Mr. Norwood's Menfuration, which was made in 1635; and feems to be more fo ftill, that he did not inform himfelf, when he returned to Cambridge,

which he did fhortly after; and, in the following year, 1667, was chofen fellow of his college, and took the degree of mafter of arts the fame year, having proceeded bachelor of arts three years before. But at this time he apparently thought it not poffible, that the old reckoning could be fo grofsly wide of the truth as it really is; and he was remarkably clear of that vanity, which in other eminent invento rs is ufeful, in making them forward to push the exercife of their inventive faculty. In reality, his thoughts were now engaged upon his newly-projected telescope by reflection; which, being a very useful invention, he was moft defirous to complete: and, in 1668, having confidered what Mr. James Gregory propofed in his Optica Promota, concerning fuch a telescope, with a hole in the inidft of the object-metal to tranfmit the light to an eye-glafs placed be hind it, he thought the difadvantages would be fo great, that he refolved, before he put any thing into practice, to alter Mr. Gregory's defign, and place the eye-glafs at the fide of the tube, rather than in the middle; he then made a fmall inftrument, with an object-metal fpherically concave but this was only a rude effay, the chief defect lay in wanting a good polifh for the metal. This therefore he fet himfelf to find out, when Dr. Barrow refigning the mathematical chair at Cambridge to him, on the eighth of November, in the year 1669, the bufinefs of that profefforship interrupted

rupted his attention to the tellescope for a while.

In the mean time, an unexpected occafion drew from our author a difcovery of the vast improvements he had made in geometry by the help of his new analysis.

Lord-vifcount Brouncker, the year before,, had published a quadrature of the hyperbola in an infinite feries; which, by the help of Dr. Wallis's divifion, was foon after demonftrated by Mr. Nicholas Mercator, in his Logarithmotechnica, in 1668.

This being the first appearance of a series of this fort, drawn from the particular nature of the curve expreffed in an abstracted algebraical equation, and that in a manner very new, the book prefently came into the hands of Dr. Barrow, then at Trinity-college; who hav ing, upon another occafion, been informed fome time before by Mr. Newton, that he had a general method of drawing tangents, communicated this invention of Morcator's to that fellow-collegian: upon fight of which, our author brought him thofe papers of his own, that contained his Analyfis per æquationes numero terminorum infinitas.

The doctor perufing it, stood amazed at the prodigious performance, and immediately acquainted his friend Mr. Collins with it; at whofe request he afterwards obtained leave of Mr. Newton to fend him the papers. Mr. Collins taking a copy before he returned the

treafure,

treafure, thence got the means of difperfing other tranfcripts to all the most eminent of his mathematical acquaintance. `But, notwithftanding this, it was not till many years afterwards, that the full extent to which our author had carried the invention came to be wellunderstood.

Mr. Fontenelle obferves, that it was natural to expect, that Mr. Newton, upon feeing Mercator's book, would have been forward to open his treafure, and thereby fecure to himfelf the glory of being the first discoverer. But this was not his way of thinking; on the contrary, we know, from his own words, that' be thought Mercator had entirely discovered His fecret; or that others would, before he was of a proper age for writing to the public. The empty name of barely doing what no body elfe could do, he looked upon as a child's bauble; his views were much higher, and more noble he thought to build his fame upon a more fubfantial foundation.

Thefe fpeculative inventions, therefore, however ingenious, were kept by him, as neceffary tools and implements in his researches into the works of nature; there he knew they would be of ufe to him, and he knew too how to use them there to advantage; and in thefe views only it was, that he fet any particular value upon them. Nay, he was now actually making this ufe of them, in difcovering the properties and unravelling the fubtle actions of light.

As