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1753: extract of a letter from count de Bruhl to count de Flem ming, at Vienna, March 8, 1753 and a number of other extracts and dispatches to and from the Saxon minifters at Drefden, Berlin, Vienna, Warsaw, and Petersburg. The whole concludes with two letters between the counts of Bruhl and Flemming.

That his Prussian majesty had reason to complain of the Saxon minifters, and even to fufpect the courts of Petersburg, Vienna, and Dresden, we will not venture to deny. Their preparations and negociations were fuch as might have alarmed any prince of forefight and circumfpection: but, whether or not they juftify his commencing hoftilities, is another question. There is fome difference between a prince's putting himfelf in a pofture of defence, and his actually affaulting a fufpected neighbour. We apprehend the best justification of his Pruffian majefty is the well known character of that po- . Hitic prince, who would hardly have involved himself in a dangerous war against fuch a powerful confederacy, if he had not thought his own prefervation abfolutely depended upon his activity and difpatch.

We ought to have apprized our readers that these pieces are published in the French tongue, with an English tranflation, which is but poorly executed: for example, tous les menagemens, are translated "all the managements," instead of all the regard-on n'a pas touché à tout le refte, is englished, "all the reft has not been touched;" instead of nothing else has been touched: le corps aftenfible de ce traité," the oftenfible part of this treaty," for the public or exterior part; as there is no fuch word as oftenfible in the English language: arrangemens, is rendered into arrangements, when the true meaning is regu lations or difpofitions; and the author has tranflated fe font toujours expliqués dans le même fens, into "always held the fame language," instead of always explained themselves to the fame effect. There are many other mistakes of the fame kind, which we have not leifure to enumerate,

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ART. IV. An eafy introduction to practical gunnery, or the art of engineering. By F. Holliday, master of the free grammar School at Haughton Park, near Retford, Nottinghamshire. Pr. 3s. Innys and Richardfon,

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HE author, in his preface to this work, informs his readers of the conduct of the French, with regard to the cultivation of this neceffary fcience.

• The French king (he fays) orders that there be professors to teach these sciences publicly in feveral parts of the kingdom, that the teachers must know defigning, and to teach it to their pupils, in order to lay down the appearances of things in their real form and fituation; they are to keep 'their schools open, and to read four times a week to their fcholars, where they must have books and inftruments neceffary to teach their art, who have handfome falaries from 'the government for that fervice, and to teach gratis. The • directors of hospitals are obliged to send to these academies every year several of their boys, to be taught and furnished with books and inftruments, explained with a vast variety of ‹ experiments, and thereby practice and theory go on hand in hand, and receive mutual affiftance from each other; and ⚫ that nothing can exceed the order of these schools, the offcers placed at the head of them are of the greatest ability < and knowledge in the management of artillery, which they teach with as much method as grammar and accompts are taught in our schools; and hence it is that France is well 'provided with fo great a number of able and fufficient engi

⚫ncers.'

The author proceeds to fhew the advantages of a knowledge of the mathematical sciences, especially in military affairs, and to recommend a fimilar conduct in England, where it is too much neglected.

In treating of this important fubject, the author fupposes his reader to be unacquainted with the doctrine of decimal fractions, but allows him the knowledge of vulgar arith metic; he has, therefore, given a concife account of the methods of performing the feveral rules of that science, decimally; and concludes it, with the extraction of the fquare and

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cube roots, in the latter of which he follows the method laid down in fir. Ifaac Newton's univerfal arithmetic.

He next proceeds to geometry, in which he fhews how to conftruct five of the easiest and most useful problems; but does not define the terms of art used in them.

Menfuration is next confidered; and here, he concisely fhews the methods of computing the lengths, furfaces, and folidities, of fuch figures, as his fubject required to be ascertained. Here he has given wooden cuts of the plane, and definitions of the folid figures, whose contents are required: at the end of this, he has given a rule to find the strength of any piece of timber, which is quoted from Mr. Emmerfon, à gentleman who has obliged the public, with feveral curious and useful mathematical performances.

The proportions of the weights and diameters of bullets, and those of the diameters of guns, with the weight of their requifite charges of powder, are next clearly explained; and a rule given to find the quantity of powder, neceffary to fill bombshells; which is illuftrated by a table, quoted from a treatife of Mr. Wm. Mountaine's, F. R. S. relating thereto, and to the fufes fixed in thofe fhells. To close this part of the fubject, a table is inferted, from Mr. Stone's mathematical dictionary, to fhew the requifite weight of powder, for mortars of different dimenfions.

The following fheet contains demonftrations of fome of the moft ufeful theorems, in plane geometry, and trigonometry; thefe, we think, fhould have preceded the menfuration, fome of the rules, there ufed, being here demonftrated.

A few definitions would have affifted the learner, in the reading of thofe; and (as the method used nearly resembles algebra) a page or two, concerning the nature and management of equations, might (as we conceive) have been advantageously introduced before them.

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The difpofition and use of a table of logarithms is the next fubject handled, by which the reader may learn to fhorten most kinds of arithmetical operations; and therefore we recommend the reading thereof, immediately after the extraction of the cube root; by which means the arithmetical part of the work will be difpatched, before the geometrical part is entred upon. The

The folution of plane triangles follows, and here the author has been more prolix, than in the former parts of the work; tho' it must be granted that he is not fingular therein, moft of the writers, on that fubject, having proceded nearly in the fame manner.

The application of plane trigonometry, to the taking of heights and distances, which is next introduced, is of great importance to the engineer, and therefore copiously treated of; and the estimation of diftances by the motion of found," which is annexed, may, in many cases, be of fingular servieę to him.

One of the above problems fhews how to plant two batteries, to play on the faces of two bastions of a fortification, which gives the author occafion to define some of the terms, used in that art, but he proceeds no farther therein.

The author, having thus difpatched the requifites neceffary to be understood, previous to the young engineer's attempting the art of gunnery, proceeds to define the terms made use of therein; he takes it for granted, that if the air did not refift the ball, after its discharge from the cannon, it would describe a curve, called the parabola; and lays down fome of the properties of that curve, in he terms used by engineers: he gives fome general rules, for obtaining the neceffary data, on which calculations may be grounded, from experiments, as well as for managing the piece in different fituations; he also gives the observations of, and methods practifed by, fome eminent engineers; and defcribes the ftructure, and properties, of cannons, mortars, petards, hawitzers, bullets, bombshells, and their fufes.

After these, he gives a variety of problems, concerning the forces and elevations of pieces of artillery, and the distances to which the balls, or fhells, will (upon the former fuppofition) be projected, and thefe, in the different fituations of level, afcending, and defcending ground: thefe problems, and their folutions, are delivered in words at length, and illuftrated by examples: after which follow fome farther practical obfervations.

To oblige thofe readers, who would defire to look into the theory of projectiles, he gives an English tranflation of a theorem and problem, on that subject, given by the celebrated

Mr.

Mr. Cotes, in his Harmonia Menfurarum; after which, he quotes, from Mr. Emmerfon's principles of mechanics, some fcholia refulting from his computations; with which, the author fays, the answers, to all the foregoing problems, have been found, exactly, to agree.

Having thus given, as much as feems neceffary, on the fubject, fuppofing the air to be a non-refifting medium; he quotes Sir Ifaac Newton, and the late eminent Mr. Benjamin Robins, F. R. S. as to the refiftance of the air and its effects; and gives fome account of a latin memoir of D. Bernouilli's, printed in the second volume of the tranfactions of the Royal Society of Petersburg. From this, he has extracted three tables, containing the refult of fome curious experiments, made with guns and mortars, exactly placed in the perpendicular, of the times of the afcents and defcents of an iron ball, 23 hundredth parts of an English foot in diameter, and of the heights, to which it was carried in air, and would have been carried in vacuo, when discharged with different quantities of powder: laftly, he concludes with the folution of a difficult problem, concerning the velocity of the ball, at the time of its difcharge from the piece; which being more curious than useful, we fhall content ourselves with the bare mention thereof.

Upon the whole, we think, that the authors, quoted in this work, are well chofen; the practical rules inserted, are clearly delivered, and the obfervations and examples annexed to them, are pertinent and familiar.

As to the arrangement of his materials, which we have ventured in fome inftances to difapprove; that might, perhaps, be owing to his great diftance from the prefs, on account of which, he defires the readers excufe for fome errors. And, as to the omiffion of fome definitions, &c. that might have been of service to the more ignorant of his readers; it is an error too frequent with the learned, who are more apt to write for the perufal of learned perfons, like themselves, than for the instruction of the unlearned: indeed his aim seems, by the other parts of the work, to have been the inftruction of the ignorant; whence thefe may be fuppofed to have been omitted, rather by accident than intention: he is farther ex

cufable,

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