meanor, there is not the fame reafon for extending the limits of the officer's commiffion, becaufe fociety is not fo ftrongly interested in the purfuit. It is of great ufe to diffinguifh where the law is governed by philofophical, and where by political principles. In the flagrant crimes, which either immediately, or remotely affect the public, the latter rule invariably in flight offences of a more private nature, the law is fometimes governed by the former.

Thus, we have endeavoured to give our readers a general view of the nature and merits of the work before us, which we have perused with great fatisfaction, and to which we freely own ourselves indebted for no fmall fhare of information, In fine, we moft earnestly recommend it to the perufal of the studious in general, who defire to be acquainted with the principles of jurifprudence, particularly in equity, which is one of the most enlarged and liberal purfuits that can engage a rational mind. They will find thefe principles explained with great order, fagacity, and perfpicuity: and the parts which may feem liable to objection, will be moft amply counterballanced by the fingular merit of the performance upon the whole. R-d

Elements of plane Trigonometry, in which is introduced a Differ tation on the Nature and Ufe of Logarithms. By Francis Maferes, M. A. of Clare-Hall, Cambridge. 8vo. 7 S. T. Payne, &c.

HIS work, fays our Author, was written with an inT tention to make the attainment of the useful fcience of Trigonometry, as easy to young beginners, as the nature of it will permit; the common treatifes on this fubject being, as he conceives, from their too great brevity, and other circumstances, not entirely fit to anfwer that purpose. He divides his work into three parts; the firft, containing the doctrine of Trigonometry, properly fo called; or an explanation of the method of computing a table of fines and tangents, by common Geometry, without the help of infinite feries; and of folving the feveral cafes of plane triangles, by the means of a table fo computed. This part is no more than a copious paraphrafe, as he himfelf confefles, on Dr. Keill's Elements of Trigonometry.

The fecond part, is a collection of fome of the most remarkable properties of fines and tangents, and the other lines REV. April 1760. belonging

U

belonging to a circle: many of which are of frequent use in the feveral branches of mixt mathematics.

The third part treats of the fluxions of fines and tangents, and the other lines belonging to a circle; together with the relations of thofe feveral lines to a circular arc, to which they belong.

The first part begins with the ufual definitions, proceeding to the more familiar and eafy theorems and problems, relating to the fines of angles, and their fides; of which numerical examples are given. Then the fine of one minute. is found by a continual bifection of an arc of 30 degrees; from whence, and a known property of the circle, the fines of every minute in a degree are eafily obtained, as the Author fhews by examples. The fine of one degree being known; thofe of the feveral degrees from one to fixty, are obtained from another property of the circle: whereby, all the reft are alfo eafily found.

But, notwithstanding the great fimplicity of these propofitions, and method of proceeding, the calculations are very tedious; for which reafon, the Author has given, in Art. XII. by way of a fcholium, Sir Ifaac Newton's infinite feries, expreffing the fines and co-fines of arcs by parts of that are: as likewife, Dr. Keill's improvement on these feries. By the help of which, and the known ratio of the diameter to its circumference, the fines and co-fines are moft expeditiously computed: but, as the demonftrations depend on the method of fluxions, the reader must be acquainted therewith, in order to understand them.

Thus two different methods of computing fines are here exhibited, each having its peculiar advantage and defect. The first depends, indeed, upon the moft fimple principles, but the computations are very tedious; again, the fecond is deduced from much higher principles, while the calculations are as eafy as could be wifhed. This part concludes, with the ufual theorems neceffary in the folution of all the cafes, in plane triangles, together with thofe folutions.

The fecond part begins, with the combination and relations between the fecants, tangents, fines and co-fines, which are applied to moft cafes that can happen.

In this part, our Author endeavours to give, as he premifes in his preface, a clear account of the doctrine of the fines of multiple arcs, and to explain what is meant by fuch a fine's becoming negative, or, as the algebraifts express it,

paffing

paffing from affirmation through nothing into negation, which, being an obfcure and myfterious kind of expreffion, he thinks, required a copious explanation. For this reafon he expatiates at large on his twenty-fixth Propofition; viz. The radius of a circle, and the fine of any arc being given, to This profind the fine of any given multiple of that arc.

pofition, and it's fubfequent corollaries, take up eighty pages for which he apologises, by faying, they could not, without omitting fomething material to the purpose, be reduced into a narrower compafs. That the great quantity of calculation, and the number of algebraic expreffions used in them, give them at first sight an air of difficulty: but it will be found upon examination, that they are in reality a great deal easier for this unfavourable appearance; for this is owing to the fetting down the reafonings and operations all at length, which the reader must have supplied by his own industry, if they had been omitted for making the demonftrations appear more fuccinct and elegant. And for the fame reason it is true in general, of all books of Algebra, that (if the subject and method of demonftration are the fame) the more calculation appears in them, the cafier they will be underftood.

The latter part of our Author's reafon for extending this propofition to fuch an immoderate length, appears to us infufficient. None, indeed, will difpute, that the demonftration, of which all the fteps are fet down, is more clear than another, of which the greatest part are omitted. He is not accounted tedious, therefore, merely for having thus made his demonftration clear; but for his not having demonftrated that proposition, a fhorter way; which might have been done without fluxions, by the help of the binomial theorem, It is true, the negative fign must be admitted, which the Author looks upon to be very ambiguous. But, whether his averfion to the use of this fign, be owing to his not rightly confidering its definition and confequential reasoning, or to what, is a query to be refolved only by our Author himfelf: for befides, that in the ufe of the negative fign, nothing is admitted but what immediately flows from its definition; the changing of the figns in the circle, from pofitive to negative, and from negative to pofitive, appears by infpection and confequently, his diflike of this fign, especially in the circle, is the more extraordinary.

The third part begins with fome confiderations, on the generation of the fines, co-fines, verfed fines, tangents and fecants, by motion, whence the fluxions, or their ratios, are

U 2

deduced.

deduced. All this, however, rather belongs to a treatise upon fluxions, than to the prefent: we fhall proceed therefore, to the differtation on the nature and ufe of logarithms, which is ufhered in with a definition, and a long differtation upon proportion in general; then all the different co-fines, whofe lines, or areas, can be expreffed by logarithms, are? confidered amongst which, the principal are the hyperbola, the logarithmic curve, and the logarithmic fpiral. After this: the Author proceeds to the definition of the word modulus, introduced by Mr. Cotes; giving us his conjectures, concerning the reafons that probably induced that gentleman to pitch upon particular quantities for a modulus: to the etymology of the word logarithm; and other equally important confiderations. The whole confifting of no less than two hundred and eighteen pages.

The conclufion of this work contains an account of the moft remarkable feries, relating to circular arcs and logarithms: but as they are to be found in other writers, and are inferted by our Author, without any new improvements, we fhall here conclude our brief sketch of the out-lines of this performance.

Socrates, a Tragedy of three Acts. of Monfieur de Voltaire.

H

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Tranflated from the French 12mo. Is. Dodsley.

AVING confined our former animadverfions* on this piece, chiefly to the circumstances of its publication and fuppofed author, our readers, whofe curiofity is probably excited by its being thus openly attributed to Mr. Voltaire, will be defirous, perhaps, to learn fomething farther concerning the work itself.

The death of Socrates being one of the moft ftriking pasfages in ancient hiftory, the fitnefs of the fubject for theatrical representation, has been long a matter of critical controverfy. In England, it has been generally given up by the beft judges, as an improper one, and incapable of being wrought up with fuccefs for the ftage. Some of the beft French writers, however, think it not inconfiftent with the genius of their theatre.

Among thefe, Mr. Diderot recommends it as one of the moft interefting and pathetic of antient or modern history; and draws a sketch of the plan on which he conceives it might be fuccefsfully executed. There is a fpecies of the

Vid. Review for Feb. 1760.

drama,

drama, fays he, wherein leffons of morality may be delivered, even directly, to the audience with fuccefs: an example of which might be given in the death of Socrates. Hear what the critics fay of the following defign.--If they condemn it as dull and inanimate, depend on it they have no idea of true eloquence, no paffions, no fenfibility. For my part, I cannot help thinking that, if it were executed by a man of real genius, it would afford a representation the moft affecting, and at the fame time a leflon of morality, equally delightful and instructive.

Let the fcene open with the cell of a prifon.--Socrates, loaden with irons, lying on a bed of ftraw.—His friends, having bribed the guards to confent to his escape, enter, before break of day, to tell him of his deliverance.— They wonder at the foundnefs and ferenity of his fleep. All Athens is in an uproar, while the innocent cause of their difturbance, confcious of his integrity, enjoys his ordinary repofe! They moralize on the fatisfaction which the reflection of having lived a virtuous life, gives the good man in the hour of death.

Scene II. Socrates awakes; fees his friends, and expresses some surprize at their fo early vifit.-He tells them his dream. They inform him of the fteps they have taken for his enlargement: on which, he enters into the merits of their defign; expatiating on the refpect he owes to his own character, and the impropriety of his evading the laws of his country; which fhould ever be held facred."

In the next scene, the guards enter, and take off his irons : on which occafion, is introduced the fable of pain and pleafure. Then enter his judges, and his accufers, with the populace. He is accused and defends himself, his apology' ending the third scene.

The fourth scene opens with the trial, in form. The accufations against him are read: Socrates challenges his judges and the evidence, and appeals to the people.-Nothing can be conceived more ftriking and beautiful than fuch a scene, if reprefented only as it really happened. The judges retire, to confult about their fentence; the friends of Socrates staying behind, who, forcfeeing his certain condemnation, are greatly diftreffed.-Socrates difcourfes with, and confoles, them, by his reflections on the immortality of the foul.

In an excellent treatife on Dra natic Poefy, published fome

time fince.