the foundation of a fociety for the general encouragement of the arts is now laid, by a fet of patriotic noblemen and gentlemen. May it be as judicioufly conducted as it is nobly conceived, and be inftrumental in raifing Britain to that preeminence in arts, which the has long enjoyed in legiflation, commerce, arms, and fciences.

ART. VI. A Differtation on the Influence of Gravitation, confidered as a Mechanic Power; explaining the Reason why the effective Power of the fame Quantity of Matter, in defcending the fame Height, is twice as great in its uniform Defcent, as in its accelerated Fall: and why twice the Quantity of Refiftance is required to bring a Pendulum to reft, when gradually applied to it, as when applied at once, in its lowest Point, &c. &c. By Alexander Cumming, F. R. S. Edin. &c. Quarto. pp. 83. Price 5s. G. and W. Nicol ;Cadell and Davies; and J. Cumming,

THE laws relative to the defcent of heavy bodies urged

by the force of gravity, have been fuccefsfully difco. vered, examined, explained, and applied, by Galileo, Huygens, Newton, and various other able philofophers; nor have any pains been fpared, by which the limits of their extenfive influence in projectiles, hydraulics, clock making, or mechanics in general, might be ascertained with the ut moft precifion; whence their application in practice might be rendered easy, clear, and determinate. To thofe laudable. exertions we may annex the prefent differtation of Mr. Cumming, in which, though much ingenuity is difplayed, yet the principal part of the new theory is involved in a fort of mift, which, it might be wished, Mr. C. would endeavour to difpel.

The proportions of the times, fpaces, velocities, and momentums, of bodies falling freely in confequence of the gravitating force, have been long known and confirmed by conftant experience; but it has been a matter of much doubt and controverfy to determine what proportion the effective power of bodies, acting by the influence of gravitation, bears to their perpendicular defcent, under the different circumftances of defcending with an uniform motion, and of falling the fame height with an accelerated velocity. The prevalent opinion has been, that in all cafes the effective impreffions of gravity are the fame; viz. that

they

they are as the perpendicular height and the quantity of matter; and totally independent of the time in which the descent is performed. But Mr. C. fhows, that cæteris paribus -the effective power of a defcending body in producing mechanical motion, is increafed by prolonging the time of its defcent; which is analogous to the property of the mecha nical powers. Thus if a heavy body be let fall at once from a given height, its momentum at the end of that fall will be, for inftance, M; it being equal to the product of the quantity of matter multiplied by its laft acquired velocity. And that velocity is (according to the well known laws of defcending bodies) exactly double of the velocity which the defcending body had acquired when it had defcended only a quarter of the given height, at which period the momentum was M. It is alfo well known, that the time of falling through the whole height is the half of that requifite for descending along a quarter only of that height.

Now let that height be divided into four equal parts, and let the fame heavy body, after having defcended through the first quarter, spend all its momentum; so as to begin anew to defcend through the fecond quarter, and fo on through the four parts of the given height.

It is evident, that in this laft cafe, the body must have employed twice as much time in performing the four diftin& falls, as it did in falling the whole height at once. It is also evident that the fum. of the four momentums is M multiplied by 4: viz. 2 M. Thus it appears, that when the heavy body falls at once along the whole height it employs a certain time T, and acquires a momentum M; but when the given height is divided into four parts, the body, in falling fucceffively along thofe diftinct parts, employs twice the time T; and the fum of the momentums is 2 M; which shows that by prolonging the time, the momentum has been increased.

Now, from this inftance Mr. C. deduces fome general propofitions, which, if we rightly understand his meaning, are not conclufive. He fays, that when a body falls at once through a given height, its momentum is as half the height; but that when the height is divided into a number of equal parts, and the body falls fucceffively and diftinctly through thofe parts, the fum of the momentums is as the whole height. This indeed is true in the abovementioned inftance, where the height has been divided into four equal parts; but if the height be divided into a greater number of parts, the fum of the momentums will thereby be increased, and of courfe the ratio cannot be the fame, which ought to

be the cafe if the fum of the momentums were constantly as the whole height.

In page 11, Mr. C fays, "It has already been fhewn, that when bodies' fall with an accelerated motion, the velocity at the end of their fall, is only as half the height. But when the defcent is retarded by any external refiftance, fo as to prevent an acceleration of motion, the impreflions of gravity, and the effective power of the descent, will become as the whole height. But after the time of the defcent is prolonged to twice the time in which the body would fall the fame height; no further increafe of effective power can be gained, by diminishing the velocity, or prolonging the time: the folicitations of gravity after this, become non-effective."

In a note to this paragraph he fays, "Gravity acts inceffantly; but a weight becomes no heavier by remaining longer in the fcale: the impulfe of gravity must be obeyed with a certain degree of alacrity, otherwife it becomes noneffective !!".

We cannot understand why the folicitations of gravity fhould become non-effective after the abovementioned limit. If Mr. C. means, that when the given height is divided into a number of parts, fo that the fun of the times, which a body must employ in falling feparately through all those parts, is greater than twice the time which a body would employ in falling the whole height at once; then the fum of the momentums will no longer be increafed; we may confidently deny the propofition, and the following calcu lation will, we truft, corroborate our allertion.

It has been fhown above, that when a given height is divided into four parts, a heavy body in falling diftinctly along.thofe four parts, will employ twice as much time, and the fum of the four momentums will be twice as great, as when the body falls the whole height at once. Therefore according to Mr. C. by a farther prolongation of the time, the fum of the momentums ought not to receive any farther increase.

Let the given height be 64 feet; then a body, for inftance of one pound weight, will fall through it in two feconds. At the end of the fall, its velocity will be fuch as would carry it on uniformly at the rate of 64 feet per fecond; therefore its momentuin is 64 pounds.

When the given height is divided into four equal parts of 16 feet each, the body will employ one fecond to perform each of thofe falls, and will thereby acquire a momentum of

32lb.; therefore the fum of the times employed in the four falls is 4", and the fum of the momentums is 128lb.

Let the fame height be divided into fixteen equal parts of four feet each. Then the fame body will employ half a fecond in falling through each of thofe spaces diftinctly, and at the end of each its momentum will be 161b. Therefore the fum of the times is 8", and the fum of the momentums is 256lb.

Thus the fame height may be divided into a greater number of parts, &c. and the fum of the momentums, as well as the fum of the times, will be found to increase continually.

The greatest part of Mr. Cumming's differtation confifts of the application of the abovementioned theory to the doctrine of pendulums, and to various other parts of mechanics; but as the whole depends upon the theory, we need not extend our obfervations any farther; for the flability of the fabric naturally depends on the nature of its foundation.

ART. VII. The Authenticity, Uncorrupted Prefervation, and Credibility of the New Teftament. By Godfrey Lefs, late Profeffor in the University of Gottingen, &c. Tranflated from the laft Edition of the German. By Roger Kingdon, A. M. of St. John's College, Cambridge. 8vo. Rivingtons, &c. 180.

396 PP.

78.

THAT most found, useful, and judicious book, Lardner's Credibility of the Gofpel Hiflory, has greatly improved: the fubfequent defences of Chriftianity. It has feemed as an ample fource, from which the writers on the evidences have drawn fuch materials as were beft adapted to their purpofes, or moft approved by their reafon. A great part of it is moft ably abridged by our acute, countryman Paley, in his book on the Evidences; and Profeffor Lefs, in another form of argument, has made a more extenfive use of that work. To obviate the remark of Bolingbroke, "that the defenders of Chriftianity have been accustomed merely to tranfcribe each other, and thus to perpetuate errors and fallacies," Dr. Lefs has been laudably fcrupulous to confine himfelf to fuch proofs as are removed from the poffibility of cavil. For this reafon, in recounting the writers of the first christian centuries, who by their quotations prove the exist ence of the books of the New Teftament in their times, he brings forward only the inftances in which particular books

and writers are exprefsly mentioned by name: and, for an ampler view of the fame teftimonies, he every where refers to the work of Lardner. But, according to the teftimony of his countryman, Michaelis, Lefs has occafionally gone be yond Lardner.

"Various teftimonies which Lardner had quoted, are omittted by Lefs, because they were not fufficiently convincing, and he has jupplied what Lardner bad omitted. Every reader will re. mark, in perufing this treatife, what I have learnt in frequenț converfation with the author, that it is the refult of a confcientious, even anxiously confcientious inquiry, which he had inftituted for his own private conviction. Doubts on which Lardner never thought, he has felt, and proved."

This important teftimony to the merit of his author, is properly cited by the tranflator, as well as that of Mr. Marth, is the preface to this book, p. vi. He further informs us

that

"The whole work of Dr. Lefs, which is called by the gene. ral name of Gefchichte der Religion, or Hiftory of Religion, is comprif d in three volumes. The first is employed on the history of both natural and revealed Religion. In the fecond, the divine origin of Chriftianity is proved at large. And the third is Occupied with the examination and refutation of objections to the Christian Religion." P. vii,

The care of the tranflator in extracting this part, as a diftinct treatise, from the body of that work, is thus further explained,

"As the following treatise is taken from the body of a work of fuch magnitude, which is only divided according to the grand divifions of the fubject, I conceived it neceffary to alter its form by breaking it into the fubdivifions of books, chapters, &c. in order that the connection of one part with another might be more readily perceived, and the whole more eafily comprehended. From the fame caufe I have fometimes omitted a word, a fentence, or even a whole paragraph, which appeared unnecessary in the prefent inquiry, and had an evident reference to parts of the work unconnected with the subject of these sheets." P. viii,

This treatife, as here given, is divided into two parts. I. On the Authenticity of the New Teftament, II. On the Credibility of the New Teftament. The former of these parts is fubdivided into three books, 1. On the internal evi

Removed, or folved, feems to be the word required in this place, rather than proved.-Rev,

dence,