1753: extract of a letter from count de Bruhi to count de Flem. ming, at Vienna, March 8, 1753: and a number of other extracts and dispatches to and from the Saxon ministers at Dref&n, 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 ministers, and even to suspect the courts of Petersburg, Vienna, and Drejden, we will not venture to deny. Their preparations and negociations were such as might have alarmed any prince of foresight and circumspection : but, whether or not they justify his commencing hostilities, is another question. There is some difference between a prince's putting himself in a posture of defence, and his actually assaulting a suspected neighbour. We apprehend the best justification of his Pruffian majesty is the well known character of that po . Hitic prince, who would hardly have involved himself in a dangerous war against such a powerful confederacy, if he had not thought his own preservation absolutely depended upon his activity and dispatch. We ought to have apprized our readers that these pieces are published in the French tongue, with an English translation, which is but poorly executed : for example, tous les menage. mens, are translated “ all the managements,” instead of all the regard :-on n'a pas touché à tout le reste, is englished,« all the reft has not been touched;" instead of nothing else has been touched : le corps estensible de ce traité, “ the ostensible part of this treaty,” for the public or exterior part; as there is no fuch word as ostensible in the English language : arrangemens, is rendered into arrangements, when the true meaning is regulations or dispositions ; and the author has translated se font toujours expliqués dans le même sens, into " always held the same language,” instead of always explained themfelves to the same effect. There are many other mistakes of the same kind, which we have not leisure to enumerate, ART, Art. IV. An easy 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. 3 s. Innys and Richardson, T HE author, in his preface to this work, informs his rea. conduct cultivation of this necessary science. • The French king (he says) orders that there be professors to teach these sciences publicly in several parts of the king• dom, that the teachers must know designing, and to teach it to their pupils, in order to lay down the appearances of things in their real form and situation; they are to keep • their schools open, and to read four times a week to their scholars, where they must have books and instruments necessary to teach their art, who have handsome salaries from "the government for that service, 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 instruments, explained with a vast variety of experiments, and thereby practice and theory go on hand in hand, and receive mutual aslistance from each other, and that nothing can exceed the order of these schools, the officers 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 so great a number of able and sufficient engiOncers.' The author proceeds to fhew the advantages of a knowledge of the mathematical sciences, especially in military affairs, and to recommend a similar conduct in England, where it is too much neglected. In treating of this important subject, the author supposes his reader to be unacquainted with the doctrine of decimal fractions, but allows him the knowledge of vulgar arith, metic; he las, therefore, given a concise account of the me. thods of performing the several rules of that science, decimally; and concludes it, with the extraction of the square and cube Y 4 cube roots, in the latter of which he follows the method laid down in fir. Isaac Newton's universal arithmetic. He next proceeds to geometry, in which he Thevrs how to construct five of the easiest and most useful problems; but does not define the terms of art used in them. Mensuration is next considered ; and here, he concisely Thews the methods of computing the lengths, surfaces, and solidities, of such figures, as his subject required to be ascertained. Here he has given wooden cuts of the plane, and definitions of the solid 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. Emmerson, à gentleman who has obliged the public, with several 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 requisite charges of powder, are next clearly explained; and a rule given to find the quantity of powder, necessary to fill bombshells; which is illustrated by a table, quoted from a treatise of Mr. Wm. Mountaine's, F.R. S. relating thereto, and to the fufes fixed in those shells. To close this part of the subject, a table is inserted, from Mr. Stone's mathematical dictionary, to thew the requisite weight of powder, for mortars of different dimensions. The following theet contains demonstrations of some of the most useful theorems, in plane geometry, and trigonometry; these, we think, fhould have preceded the mensuration, fome of the rules, there used, being here demonstrated. A few definitions would have assisted the learner, in the reading of those; and (as the method used.nearly relembles algebra) a page or two, concerning the nature and management of equations, might (as we conceive) have been advantageously introduced before them. The disposition and use of a table of logarithms is the next subject handled, by which the reader may learn to shorten 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 dispatched, before the geometrical part is en The tred upon. The solution 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 singular therein; moft of the writers, on that subject, 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 distances by the motion of sound, which is annexed, may, in many cases, be of singular servieę to him. One of the above problems Inews 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 dispatched the requisites necessary to be understood, previous to the young engineer's attempting the art of gunnery, proceeds to define the terms made ure of therein ; he takes it for granted, that if the air did not relift the ball, after its discharge from the cannon, it would describe a curve, called the parabola ; and lays down some of the properties of that curve, in he terms used by engineers : he gives some general rules, for obtaining the necessary data, on which calculations may be grounded, from experiments, as well as for managing the piece in different situations ; he also gives the observations of, and methods practised by, fome eminent engineers; and describes the structure, and properties, of cannons, mortars, petards, hawitzers, bullets, bombshells, and their fuses. 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 shells, will (upon the former suppofition) be projected, and these, in the different situations of level, ascending, and descending ground: these problems, and their folutions, are delivered in words at length, and ilJustrated by examples ; after which follow some farther practical observations. To oblige thofe readers, who would desire to look into the theory of projectiles, he gives an English translation of a theorem and problem, on that subject, given by the celebrated Mr. Mr. Cotes, in his Harmonia Mensurarum; after which, he quotes, from Mr. Emmerson's principles of mechanics, some fcholia resulting 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 necessary, on the subject, supposing the air to be a non-resisting medium ; he quotes Sir Isaac Newton, and the late eminent Mr. Benjamin Robins, F. R. S. as to the resistance of the air and its effects; and gives some account of a latin memoir of D. Bernouilli's, printed in the second volume of the transactions of the Royal Society of Petersburg. From this, he has extracted three tables, containing the result of some curious experiments, made with guns and mortars, exactly placed in the perpendicular, of the times of the ascents and defcents of an iron ball, 23 l 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 : lastly, he concludes with the solution of a difficult problem, concerning the velocity of the ball, at the time of its discharge from the piece; which being more curious than useful, we fall content ourselves with the barç 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 observations and examples annexed to them, are pertinent and familiar. As to the arrangement of his matcrials, which we have ventured in some instances to disapprove ; that might, perhaps, be owing to his great distance from the press, on account of which, he desires the readers excuse for some errors. And, as to the omission of some 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 perusal of learned persons, like themselves, than for the instruction of the unlearned: indeed his aim seems, by the other parts of the work, to have been the instruction of the ignorant; whence these may be supposed to have been omitted, rather by accident than intention: he is farther ex cusable, |