tima, infinitè magna and the like; which, though not rendered according to the original import of the words, are yet explained in that fenfe, and with thofe limitations, under which the author cautions his readers to understand them. This is the more neceffary, as the terms infinite, infinitefimal, leaft poffible, and the like, have been grofsly mifapplied and abufed: and it would contribute much to the accuracy required in mathematical knowledge, if they were entirely rejected from all reafonings on fuch fubjects.

The fubftance of many of the notes is taken from Maclaurin, Saunderson, Keill, Morgan's notes on Rohault, Excerpta quædam e Newtoni Principiis Philofophiæ Naturalis, cum notis variorum, and feveral other writings, in which particular parts of the Principia are elucidated.'

From this fhort ftate, which feems to be juft, the nature of this work may be easily known; we may however obferve, that Mr. Thorp has prefixed to this volume a large introduction of his own, containing general and pertinent reflections on fome of the principal fubjects treated of in the Principia, together with Dr. Halley's Latin poem, and tranflations of fir Ifaac Newton's three prefaces to the three different editions of it, as alfo that of the very ingenious and learned Mr. Cotes, the editor of the fecond edition, published in the year 1713.

This work is well printed, the text in a large type, and the comment on a smaller one at the bottoms of the fame pages.We wish that the ufual mode of printing the fchemes with wooden cuts, on the pages with the letter-prefs, had been retained, inftead of the feparate fleets of copper-plates here introduced, as a distinction would thus have been preserved between the original figures belonging to the text and those added by the tranflator to illuftrate his commentary, which are mixed in the fame folding sheets.

The nature of fir Ifaac Newton's Principia is too well known to render a description of its contents neceffary. And as neither it nor the commentary are proper fubjects to make extra&s from, we shall select a specimen from the popular introduction of the ingenious editor.

No part of aftronomy was more imperfect, before fir Ifaac Newton's time, than the theory of the comets. The appearance of a few of the most remarkable had indeed been recorded in history. But the prevailing opinion was, that they were only meteors, floating in the atmosphere of the earth. He therefore begins by fhewing, that they are above the moon, and in the planetary regions. He proceeds to trace out their orbits and finds, that they revolve round the fun, like planets, in very ec

centrical

as de.

:

centrical ellipfes, approaching nearly to the form of parabolas • and he fhews, how fuch trajectories may be determined from three obfervations. From the examples to which he has applied his theory it appears, that the motions of comets, duced from the computations of their orbits, agree as nearly with their real motions, derived from obfervation, as the theory of the planets agrees with their motions. But few of the comets have yet been obferved with care and accuracy; though their number is probably very great. The improvement therefore of this important part of aftronomical fcience must be left to the labours of future ages; when, by long and accurate obfervations on fuch as may appear at nearly equal intervals, their periods and orbits may be determined; and their theory, by the application of the principles here laid down, may at last be brought to the fame perfection as that of the planets. For though they cannot be expected to return in the fame orbits, and at equal intervals, accurately, on account of the disturbances arifing from their mutual gravitations, and various other refiftances; yet it must be observed, that their motions are fo contrived, as to diminish these inequalities as much as poffible. For that no inconvenience may arife from their mutual gravitations, the planes of their orbits are inclined to each other, and to the plane of the ecliptic in large angles; fo that they can never approach very near either to each other, or to the planets, except they happen to be at the fame time in the interfections of thofe planes. And to prevent the errors in the higher parts of their orbits, where the effects of their disturbing forces on each other are greatest, both because their motions are floweft, and because the action of the fun is leaft, they are made to move in various directions, many of them contrary to the order of the figns, and to the course of the planets; fo that afcending towards different parts of the heavens, they recede to great distances from each other. That the comets are folid compact bodies fir Ifaac Newton concludes from their near approach to the fun, where vapours and all rarer fubftances would foon be diffipated and confumed by the heat. The remarkable comet of the year 1680 approached fo near the body of the fun in its perihelion, that dry earth, placed at the fame diftance, might acquire a heat 2000 times greater than that of red hot iron. And though the communication of heat, especially to large bodies, is gradual; and the comet receded with an immenfe velocity from the fun; yet as it is computed, that the heat at that distance was about 28000 times greater than that of the fummer fun in England, it must have conceived, and be fo conftituted as to bear, a very great degree of heat, fuch as would diffipate the most folid bodies in this earth. We muft alfo fuppofe, that the denfities of all the comets are adapted to the feveral degrees of heat, to which they are refpectively exposed in their different orbits.

From all the phenomena relating to thefe bodies, as well as the other parts of the fyftem, fir Ifaac Newton concludes, that their motions could not have their origin from mechanical caufes. And that the revolutions of the comets, paffing freely through the orbits of the planets, in all directions, in very ec centric ellipfes, and in very different planes; and the motions of the planets, performed in the fame direction, in ellipses approaching nearly to circles, and in planes inclined to each other in very small angles, must be the effects of the most wife and excellent contrivance for the beft ends. Six primary planets, projected at different diftances, revolve round the fun in periods, which bear a regular and invariable proportion to their diftances. One fatellite revolves round the earth: but Jupiter and Saturn, the two planets most remote from the light of the fun, are illuminated, the former by four, the latter by five fa tellites, revolving in the fame direction, and nearly in the fame plane; and, the periods and diftances of fuch as tend to the fame centre being compared together, the fame harmony takes place between them, as was obferved in the cafe of the planets. One uniform principle of gravity is diffufed over all the bodies in the fyftem; which extending itfelf to their centres, and to every particle which they contain, is the power by which they are united together, and preferved entire; and varying according to the inverfe proportion of the fquares of their distances, regulates their revolutions, and retains them in their proper or bits. No other law of gravity could have been established fo proper, either for uniting the parts of the feveral globes, or for preferving their regular courfes. If the gravities of particles are fuppofed to vary inverfely as the cubes of their diftances, the at tractions of fpheres, compofed of fuch particles, will be indefinitely greater in contact than at the leaft finite diftance (441 and 442.) If the gravities of the planets had been made to vary inverfely as the cubes of their diftances from the fun, or in any greater proportion, the confequence would have been, that whenever their motions became oblique to the directions of their forces, they would from that time either afcend for ever from the fun, or defcend continually till they fell upon his body (218.) But the alternate approach and recefs of the planets in every revolution; and the motions of the comets, defcending very near to the furface of the fun, and then afcending to immense distances in very eccentric orbits, evidently follow from the established law of gravity (213. and 218.),

From every thing that can be discovered with any certainty relating to the conftitutions and denfities of the planets it appears, that they are nicely adapted to their different fituations, and to the different degrees of heat and cold, which they must bear at their respective distances from the fun. The proportions of the quantities of matter and denfities of three of the planets are pretty accurately determined: and the mean density of the

earth

earth appears to be almoft fix times greater than that of Saturn, and above four times greater than that of Jupiter. And it is probable that the densities of all the planets increase, the lefs their distance is from the fun. If a body of the fame density as the earth was placed in the orbit of Venus or Mercury, the fuid parts would foon be diffipated with the heat: if it was removed to the distance of Jupiter or Saturn, they would be congealed with the cold: but the greater density of the inferior planets, and rarity of the fuperior, are exactly fuited to the feveral distances affigned them in the fyftem. From fome obferv. ations upon the figure of Jupiter, the diameter at the equator of that planet is found to exceed its axis, fo much more than it ought to do, upon the fuppofition of an uniform denfity, that there is great reafon to fuppofe the denfity at the centre much greater than at the furface and that the proportion of the denfity, at the furface of that planet, to the denfity of the earth, approaches much nearer to the proportions of the densities of the folar rays, at their respective distances, than the proportions of their mean denfities above mentioned. And it does not seem improbable, that the denfities at the furfaces of all the planets are nearly proportional to the heat of the fun at their respective distances.

The light of the fixed ftars being of the fame nature with the light of the fun; and their magnitudes being at least as great; fir Ifaac Newton conjectures, from the conformity obfervable in all the appearances of nature, that they are allo funs enlightening other fyftems of planets. From the fmallness of the angles, under which they appear through telescopes, magnifying to a very great degree; from the immenfe distances, to which fome of the comets recede from the fun, without coming within the attraction of the nearest fixed ftar; from their apparent aberrations, compared with the immenfe velocity of light; and from the fmallness of their annual parallax; it appears, that their diftances are fo great, that the whole orbit which the earth defcribes round the fun, if viewed from fuch distances, would subtend an angle hardly obfervable; the fun would appear as a point; and the reflected light of the planets would become invisible. A body then of the fame nature and magnitude as the fun, attended with a fyftem of planets, and removed to the dif tance of a fixed ftar, would appear to us as a fixed ftar is really feen, diminished to a fmall lucid point, and divefted of thofe planets. But it is not agreeable to that excellent contrivance and difpofition of things, evidently adapted with the moft perfect wisdom to the belt ends, to fuppofe that bodies of fuch magnitudes fhould be removed to immenfe diftances from the folar fyftem, and from each other, without defign, and without any objects near enough to receive their beneficial influences. Nor can it be imagined, that bodies, fuited in their nature to fupport and enlighten as many fyftems of planets, fhould be intended only for the use of this fmall globe, where the far greater

T 4

num

number of them is invifible to the naked eye. By the help of glaffes three thoufand fixed ftars have been obferved and their places determined. And as every improvement of the telescope has conftantly been followed by the difcovery of multitudes, unfeen, before; we have reafon to conclude, that as their dif ftances are beyond our conception, fo their number is unlimited.

Whether we have any relation to the more distant bodies of the universe, either of the folar fyftem, or any other, is entirely unknown. And as, for wife reafons, the Author of Nature has rendered it impoffible for us to have access to any of them, this part of our knowledge, in our prefent ftate, must be imperfect. But as we immediately perceive, from the nearest and most obvious effects, the influences of that Supreme Being, who by ftated and established laws regulates and fuftains the whole fyftem of nature; though the more immediate caufes, the inftruments of his action, are partially and obfcurely known to us; fo we difcover enough in the diftant parts of the univerfe to enlarge our conceptions of the Almighty Power, which fashions and fupports fo many immenfe bodies; which gave motion to the greatest and the leaft; which produced all degrees of velocity, fome too fwift, fome too flow for our perceptions; and which regulates by certain laws, and with equal facility, the motions of the largest planets, and of the fmalleft portions of matter, And from our partial knowledge of the scheme of nature, and the intimations which we perceive of greater and more furprising operations beyond the reach of our faculties, we may be led to confider our prefent ftate as incomplete without relation to a future exiflence: and to reflect on the more extenfive and perfect views which will be difclofed to us of the defigns of Providence, if endowed with enlarged faculties, we fhall then be enabled to behold the various effects of nature, as they are derived from the firft caufe, and to comprehend more fully the whole scheme of the divine operations, extended as it really is, beyond all imaginable limits of space, or periods of time.'

Illuftrium Virorum Elogia Sepulchralia. Edidit Edvardus Popham. Col. Oriel Oxon. nuper Socio. 8vo. 55. Dodfley.

THIS is a felect collection of monumental infcriptions, ex

hibiting the names, employments, and perfonal qualities of fome of the moft eminent poets, hiftorians, philofophers, divines, lawyers, warriors, and princes, which England, France, Italy, and other nations of Europe, have produced, in the courfe of about four preceding centuries. They are ranged in alphabetical order, for the convenience of turning to any one of them immediately, as occafion may require; but the chronological order, with an index, would have been

prefer