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• Hume and Voltaire are two remarkable inftances of the facility with which reports respecting the Quakers have been received and propagated. The first of these historians cites (from Echard) an odd compound of affectation and rudeness as the address of the Quakers to James the Second, on his accession to the throne, in which there is not one sentence of the real address. The latter selates (Lettres. jur les Anglois) a story of George Fox's preaching from the pillory to a large auditory, who were so affected with his disccurse, that they seleased him, and put the miniiter who prosecuted him in his place; which is equally dellitute of foundation.

• It is hoped that the learned and respectable Authors of the work alluded to will, in a future edition, do the first Quakers the justice to abate the degree of faith given to Higginson's testimony, and that, in the mean time, the known candour of the Authors of the Monthly Review will admit these exceptions to the truth of it.'

D. J. B.'s first letter (dated March 3) relative to the Author of the Eulogy on the Chancellor De l'Hospital, was transmitted to the Writer of chat Article, abroad; and the answer was not received till the middle of April : which will account, to this very accurate Correspondent, for our not replying to his inquiry, in the concluding page of our last month's Review.-The name of the ingenious advo. cate, to whom the world is obliged for the Historical žalogy abovementioned, is Gibert, not Guib-,'as J. B. rightly supposes.- Our Correspondent is equally right in his corrections of several errors of the press; and the Gentleman is requested to accept our thanks.

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+++ A. B. may be assured that che Two additional Discourses are not overlooked.

HIt. Observator must give us leave to manage and contra& our Correspondence, as best suits our convenience and our limits. We are not conscious of deserving the charge of difingenuity, which he is pleased to prefer against us, without supporting it by any instance.

*** C. C.'s card, from Truro, cannot be inserted, as we fiod, by farther information respecting the fubje&, that, by giving it a place, we might possibly expose ourselves to the trouble of a very unimportant controversy

ERRATA in the Review for March. P. 226, Art. III. in the French title, for la, r. le.

239, I. penult, for two millions in three, r, one million. 242, Art. 38, 1. 7, for Eutelius, r. Entellus, N. B. P. 216, par. 2, the sum of 130 1. Sterling, is, no doubt, an error; the sum paid, we apprehend, must be much greater imod but the passage is printed exactly from the book; and we find ne errata at the end.

THE

MONTHLY REVIEW,

For

M A Y

1778.

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Art. I. The true Principles of Gunnery investigated and explained

Comprehending Tranilations of Professor Euler's Observations
upon the new Principles of Gunnery, published by the late Mr.
BENJAMIN ROBINS, and that celebrated Author's Discourse upon
the Track described by a Body in a resisting Medium, inserted in
the Memoirs of the Royal Academy of Berlin, for the Year 1753.
To which are added, many necessary Explanations and Remarks,
together with Tables calculated for Practice, the Use of which is
illustrated by proper Examples; with the Method of folving that
capital Problem, which requires the Elevation for the greatest Range
with any given initial Velocity. By Hugh Brown. 4to. 159. Boards.
Nourse. 1777

HE treatise of Mr. Robins, intitled, New Principles of
Gunnery, first printed in 174?,

and since (in 1761) published in a collection of his tracts by Dr. Wilson *, contains a great variety of important experiments and observations, which introduced a new theory very different from that which had been taught by his predecessors. Beside many other inquiries concerning the nature and quantity of the force of gunpowder, its increase by heat, the law of its diminution as the vapour let loose in the explosion is dilated, and the velocity generated by a given charge in balls projected from different barrels, this excellent tract contains a particular investigation of the refiltance of the air, and the difference of its effects on swift and Now motions. In the course of this laborious and accurate investigation Mr. Robins discovered that the resistance to swift motions, such as those of bullets and shells Mot from cannon and mortars, is much greater than any preceding writer had apprehended or stated ; and tho'Mr. Huygens, Sir Isaac Newton, Bernouilli, and others had observed, that a curve described by a projectile in the air is very different from a parabola, and had

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P. 28.

also investigated the nature of this curve, yet Mr. Robins was the first mathematician who applied this discovery to useful purposes in practical artillery. His experiments and speculations were very favourably received both at home and abroad; and the treatise already mentioned was translated by M. Euler into the German language: the translation was accompanied with a large commentary, in which he investigated each propofition, corrected what he thought to be defective, extended the subject, and illustrated most of the theorems by examples. Of this commentary Dr. Wilson, the biographer of Mr. Robins, and the editor of his tracts, observes, that it was printed at Berlin in 1745, “ and Mr. Robins (says he) soon after informed me, that M. Euler's principal objections arose from mistakes; the source of which having found out, he intended to publish an answer ; but from that time continual interruptions prevented him.” Editor's Preface to Robins's Tracts,

The remarks of Mr. Euler, together with a paper published in the Memoirs of Berlin, are here translated into English : and accompanied (says the Translator) with explanatory notes, where they were thought necessary. To which are added a set of new tables, calculated from Mr. Euler's theory, for finding the length of the curve described by a projectile in a resisting medium, together with the ordinate and abscissa answering to every point of the curve, and also the time of describing the whole, or any part of it, and the angle which the curve makes with the horizon in any point. The use of these tables is il Justrated with proper examples, in what is necessary for an officer of artillery to be acquainted with. By the common theory, the projectile will return to the horizontal plane with the same velocity as that with which it issues out of the piece, and the angle which the track makes with the horizontal plane, is the same at the exit from the piece as at the fall; but they both differ greatly, unless the initial velocity be very small.'

Mr. Robins inferred, from an experiment on ignited gunpowder, that its elaitic force is 1000 times greater than that of common air, but M. Euler adopts the opinion of M. Daniel Bernouilli, in his Hydrodynamie, printed at Strasburgh in 1738, who makes it 10,000 times greater. Mr. R. had also observed, that air confined in any space, and heated to the degree of redhot iron, will be four times more elastic than air in its naturalftate; upon which M. Euler remarks, that, though this may be the case with natural air, “ yet there is great reason to question whether the same thing will hold in air fome hundred times denfer, such as that which is confined in the powder, namely, whether its elasticity will, by the heat, become four times greater. It fill appears uncertain whether air some hun.

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dred times denser than natural air, and possessing the same de. gree of warmth, will be just as many times more elastic; and, it is still more uncertain whether, if air so many times denser than the common air, and heated to the degree of red-hot iron, will, by being so heated, have its elastic force increased so as to be just four times greater, notwithstanding this is found to be the case with air in its natural state of density.'

In estimating the velocity with which a ball quits the piece, Mr. Robins lays down two principles; one of which is, that all the powder of the charge is fired and converted into an elastic Auid, before the bullet is sensibly moved from its place. M. Euler, after fuggesting several circumstances which are omitted, and which ought to have been taken into the account in forming this estimate, expresies his entire diffatisfaction with the fore-mentioned principle; and his objections against it have unquestionably great weight. After endeavouring to evince that the Author's reasoning, from his own experiments, is not sufficient to establish this principle, and accounting for the agreement of this theorem with the conclusions drawn from his experiments, he appeals to other experiments, whence it appears that the total explosion is not instantaneous. These were made by General Gunther at St. Petersburgh in 1728. Amongst others, there was one made with a piece whose cylinder was 71. English feet long: it was fired vertically with different charges. The time from the explosion till the ball's return to the ground was exactly observed by means of a pendulum ; from which Mr. Bernoulli computed the velocity with which the ball issued out of the piece : notwithstanding that he calculated upon the Newtonian principle of the resistance, that makes not againft our present enquiry; he found that the piece being loaded with 1, 4, and 8 ounces of powder, the ball must have ascended in vacuo 541, 13694, 58750 feet. Then 1:16 foot was fawed off the piece, so that the cylinder was exactly 6 feet long; the picce was then fired vertically with the same charges of 1, 4, 8 ounces, and he found that, in vacuo, the ball must have ascended only 274, 2404, and 6604 feet; so that the 8 ounces carried the ball near 9 times higher before than after the shortening the piece: therefore the velocity with which the ball issued out of the piece must have been about three times greater in the first case than in the last. But according to Mr. Robins's theory, the difference must have been scarcely perceptible : hence it appears that, before the cannon was shortened, a good part, indeed the greatest part of the powder fired whilst the ball moved through the latt foot and a half of the cylinder. The fame conclulion follows in the lefler charges, although the difference is not so great; and hence it appears likewile, that the greater the charge is, the more time

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will be employed before it all fires ; which, of itself is almost self-evident.

· The riffled barrel, which is known to carry much farther than a barrel not riffled, is another proof that the powder does not fire all at once ; for, if it did, the riffled barrel would not carry near so far as the other. For considering

For considering the great resistance the ball has to overcome in a riffled barrel, even if we neglect the motion of the ball round an axis, which requires a force to effeet it, there cannot be the least doubt entertained about it: yet, notwithstanding this great resistance, a ball acquires a greater velocity when fired out of a riffled than when fired out of a common barrel, when every thing else is the fame. There must therefore be a much greater force exerted in a riffled than in a common barrel, to overcome the resistance, and also to communicate a greater velocity to the ball. This force is generated by the powder only, which is in both cases the same. There can be no cause assigned why the force fhould be greater in one than the other, except that in the riffled barrel all the powder, or at least the greatest part, fires before the ball quits the piece; and a fmaller quantity fires in a common barrel. The last argument seems to give the greatest light into the matter in hand, as it proves not only that the powder does not fire all at once, but that only a small portion of it commonly fires before the ball is out of the piece. For which reafon the afore-mentioned opinion of Mr. Bernoulli's becomes the more probable, namely, that the elastic fluid generated by the explosion of the powder, has an elastic force near 10000 timesgreater than the pressure of the atmosphere, notwithstanding that our author makes it only 1000 times greater.'

On the fupposition, the truth of which he had already conrested, Mr. Euler allows with Mr. Robins that no particular form of chambers in guns or mortars can be of any advantage with respect to the increase of the impelling force. But on the contrary supposition, that the powder does not fire all at once, • the question (he says) comes to this, whether the figure of the space which contains the powder may not contribute to a quicker or lower explosion ? For if this question be answered in the affirmative, there can be no doubt but the figure which causes the quickest explosion is the best. For the quicker all the powder fires, the greater and of the longer continuance will. the force which acts upon the ball be, and the quicker will its motion be. That the figure of the chamber contributes not a little to the quickness of firing is easy to be proved. Consider a very long and narrow tube filled with powder, and fired at one end. In this case the fire will not extend so soon to the other end as if the tube were shorter. It is easy to conceive, that if the chamber of a piece consist of such a long and nar

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