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with an air of difdain, look down on a novel-writer, and strive to perfuade the world, that he is fit for nothing elfe.

Eyter. There may be a good reason for it; the more folid sciences are often neglected for thefe trifling purfuits.

Blum. We well know what the gentlemen of the bar call folid fcience-barbarous constructions and phrafes, which nobody under

Bands..

Eyter. And do people understand your prefcriptions?

Blum. Alas! no, Sir: and I give you leave to turn our quackish cant as much into ridicule as you please.

Eyter. You are caught, Doctor. Every profeffion has, and, by rights, ought to have, its quackery, to command refpect. You have your recipe, and I have my claufula rati, grati, et indemnificationis. Serviteur."

[Exit. The fcene of "the Reconciliation," is extremely natural and affecting.--

"" ACT. V. SCENE X.

(4 garden with a bower on each fide.)

Charlotte. (with her apron full of flowers.)

Frank. Ho! ho! Charlotte, are you, too, here?

Charl. frawing flowers from one arbour to the other.)

Frank. What are you about?

Phil. Charlotte, what are you doing?

Charl. I am frewing flowers on the road, which, for fo many years, has been covered with thorns.

Frank. What does the mean?

Phil. (nodding to Blum.) Pray, Doctor, tell me, who is that Arange gentleman ?

Blum. I have invited him, becaufe to-day is his Birth-day.
Phil. (noved.) His Birth-day?

Frank. (unealy.) Come hither, Charlotte. Do you know him?
Charl. Ch, yes; very well.

Frank. Who is he?

Charl. Fifteen years ago you would not have asked that question. Frank. Zounds !-who is he?

Charl. (running swiftly to the other arbour, and clinging round her father's neck.) It is my father!

(A paufe. The two brothers look at each other furtively, but with great emotion: the Doctor examines them with attention and pleasure.)

Frank. (apart.) How poorly he looks!

Phil. (apart.) How old he is grown!

Frank. (apart.) How fhabby his drefs! he has, perhaps, been in diftrefs, whilft Mrs. Grim was robbing me.

Phil. (apart.) Fie upon that proud fhame that would prevent me from flying into his arms!

Charl. (kneeling down between the two arbours, ftretching out

her

her arms, and looking with earnest looks, alternately, at her father and her uncle.)

Phil. (rifes, and goes one step out of the arbour.)

Frank. (very uneasy.) Zounds! I believe he is coming.

Charl. Hither, my dear uncle!

Frank. (rifes.) To thee! what must I do, then?

Charl. To me, my father!

Phil. With pleasure, my child! (He goes to her, and takes her

band.)

Charl. (in afweet careffing tone.) To my dear uncle!

Frank. Well, I am coming. (goes nearer to her.)

Charl. Your hand

Frank. (looking the other way.) Here

Charl. Nearer, nearer! (drawing the hands of the two brothers fo near that they meet.)

Phil. (deeply affected.) Brother!

Frank. (looking at him, throws away his flick, and opens his arms.)

Phil. (finks on his breaft.)

Charl. (prings up of a fudden, and throws herself round Blum's neck.) My thanks, good men!

Frank. Look at me, brother-eye fixed on eye! let me fee, if there be the leaft fpark of refentment left!

Phil. Doftn't thou fee a tear that will quench it?

Frank. (fill in the greatest emotion, takes him by both hands.) Brother, thou look like the image of diftrefs! thou hast been in want! thy whole perfon upbraids me with it.

Phil. I have been ill.

Frank. Well, then, get better now, or I won't set my foot over the threshold of the door.

Phil. My good brother! thou haft, in fpite of our mutual fituation, generously fupported me.

Frank. What! is that a farcafm?

Phil. Haft thou not paid my bills?

Blum. Dear Sir, pardon me this pious fraud: I was thinking of the means to reconcile you, and I acted in the name of your brother. Frank. You are hard upon me, Sir! but I thank you for that leffon.

Phil. Oh! my daughter! what a fon thou haft given me !
Frank. Son! what's that?

Phil. This generous man, to whom innocence and goodness of heart are equivalent to wealth and riches.

Frank. I understand.-Well done! but poor the girl is not. Isn't the my fole heir is it not fo, Charlotte -Oh, we know each other, by this time! (pointing at Ann.) What's the crying for,

now?

Phil. She is pleafed, poor old woman!
Frank. Isn't that our good old Ann ?
Phil. It is fhe.

Frank.

Frank. Ann, is it you? Reach me that hand that has given me fo many flices of bread and butter. Well, you have continued an honeft girl; and you fhall never want any thing to chew while "you have a tooth in your head.

Ann. (Jobbing.) I cannot talk-now.

Frank. Well, then, hold your tongue. We all fee your tears come from the heart.-But what the deuce is become of my gout, · Doctor? I think my flick has got it all."

It is almoft unneceffary to add, that, in point of morality, the Reconciliation" is unexceptionable.---And, though the tranflator hath but indifferently performed his part, we have read it with a high degree of pleasure and fatisfaction.

ART. XI. A Courfe of Mathematics, in two Volumes, compofed, and more efpecially defigned, for the Ufe of the Gentlemen Cadets, in the Royal Military Academy, at Woolwich. By Charles Hutton, LL. D. F. R. S. and Profeffor of Mathematics in the faid Academy. 8vo. Price 15s. Robinfons, London: 1798.

THE

HE object and plan of this useful work are thus fet forth in the preface:

A fhort and eafy courfe of mathematical fciences has long been confidered as a defideratum for the use of students, in the different schools of education, one that should hold a middle rank between the more voluminous and bulky collections of this kind, and the mere abstract and brief common place forms of principles and memorandums.

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"For long experience in all feminaries of learning, and particu larly in the Royal Military Academy of Woolwich, has thewn that fuch a work was very much wanted, and would prove a very great and general benefit, as, for want of it, recourfe has always been obliged to be had to a number of other books, of different authors, felecting a part from one, and a part from another, as feemed moft fuitable to the purpofe in hand, and rejecting the other parts, a practice which occafions much expence and trouble, in procuring and keeping fuch a number of odd volumes, of various modes of compofition and form, befides wanting the benefit of uniformity and reference, which are found in a regular feries of compofitions. To remove these inconveniencies, the author of the prefent work has been induced, from time to time, to compofe various parts of this Course of Mathe matics, which the experience of many years ufe in the Academy has enabled him to adopt and improve to the most useful form and quantity for the benefit of inftruction, and, to render the benefit more eminent and lafting, the Mafter-General of the Ordnance has been NO XII, VOL. III.

M

pleafed

pleased to give it its present form, by ordering it to be enlarged and printed."...

The first volume contains the three important branchesArithmetic, Algebra, and Geometry.

In Arithmetic the rules are fet forth with perfpicuity and precifion, and the examples, both in number and arrangement, feem well adapted to the practice of fchools. At the bottom of the pages explanations are given, with fcientific demonftrations, where fuch are neceffary; Fractions, both Vulgar and Decimal, are treated in a clear and comprehenfive manner, and a new and eafy method is given for extracting the Cube Roots, and the Roots of all higher powers.

Algebra contains rules and examples likewife well adapted to fcholaftic ufe. We think this tract would be ftill clearer, had the author introduced more numerical illuftrations than he has; this want, however, may be fupplied by the teacher. The rules and questions will be found arranged in judicious gradations; an advantage too rarely attended to by writers on this fubject.

The rules here given for eftimating and computing all algebraic expreffions of quantities are plain and practical, and all the higher equations are folved by the rule of double pofìtion.

The Geometry is here digefted in a new, neat, and methodical manner. The author expreffes a hope, in his preface

"That he will not be too feverely criticized, if, through a defign of rendering this branch more easy and fimple, he has, in fome inftances, deviated from the tedious and rigid ftrictness of Euclid, particularly in the doctrines of ratios and proportions."

The problems of Geometry, with the demonftrations, follow the theorems and the cuts, which are well executed, and placed on their proper pages. The volume concludes with the application of Algebra to Geometry.

The fecond volume begins with Plane Trigonometry, which includes rules and examples for calculating fines, tangents, and fecants. These are followed by Menfuration of fuperficies and folids, of timber and artificers work, with Land Surveying, in which a new form of a field book is introduced, with an appropriate plan. Next follow conic fections, a tract which deferves particular notice. Here each of the three fections has its leading property deduced or demonftrated, from the folid or cone itfelf, and all the other properties are drawn from that one alone, without any farther reference to the cone, and without any of the arbitrary and

mechanical

mechanical descriptions or definitions of curves in Plano, Here the analogy of the feveral fections to one another is clearly fet forth, and all the propofitions and demonftrations. in the Ellipfe are the very fame as the like number of the Hyperbola; we alfo find here other new and curious proper

ties of the conic fections.

So far this work may be confidered as treating of the elementary part of the mathematical fciences. Next follows the application of those branches to philofophical and mechanical fubjects, fuch as the general laws of motion and forces, fimple and compound, momentary and continual, uniform and accelerated or retarded. Next are given the compofition and refolution of forces; the laws of gravity; motion of projectiles; practical gunnery; defcent of heavy bodies; defcent of bodies on inclined planes and curves; motion and vibration of the pendulum; the mechanical powers; centre of gravity; preffure of banks of earth, with thickness of walls to fupport the fame; preffure of arches, with the proper piers for them; centres of percuffion, ofcillation, and gyration; the balliftic pendulum, for finding the actual and real velocity of cannon balls; hydroftatics; hydraulics; pneumatics; fiphons; water-pumps; air-pumps; diving-bells; condenfing machines; barometer and thermometer. After which, practical exercises and questions are given, in fpecific gravity; weight and dimenfions of balls and fhells; with many other useful and curious problems in mechanics and natural philofophy.

The doctrine of Fluxions is next explained, and illustrated in as plain a way as the nature of the fubject would allow. The inventor, Sir Ifaac Newton, defines Fluxions the Velocities, by which quantities are generated, and Dr. Hutton fimplifies this definition by calling a fluxion a rate or proportion, according to which any flowing quantity increases, and he has exemplified this fublime fcience with a great variety of useful problems, fuch as the maxima and minima, rectifications, quadratures, contrary flexure, radius of curvature, involutes, evolutes, &c. The practical application of this fcience is contained in a great number of curious and interefting examples concerning forces, with the relation between them and the time, velocity, and space defcribed. Thefe conclude with a new problem, which calculates the velocity with which a cannon ball is discharged from a piece of ordnance of given dimensions, and charged with a given weight of gunpowder. The refult of this calculation is compared with that of many of the author's former experiments, by which the real strength of fired gunpowder is here accurately determined, and proved

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