are to be expected from the exertions, and the affiftance of theoretical men. "For fome years, he fays, I have seen, (or thought I have feen), and often regretted, that a forbidding diftance and awkward jealoufy feem to fubfift between the theorists and the practical men engaged in the cultivation of mechanics in this country: and it is a defire to shorten this distance, and to eradicate this jealousy, that has been a principal ftimulant in the execution of the following performance."

After this, he gives a sketch of his work, and affigns his reafons for the plan he has adopted.

The firft volume of this work is devoted to the theory; the fecond, to the practical and defcriptive branches. Though thofe volumes are of the octavo fize; yet as the type is fmall, and the page full, they contain a vast quantity of materials. The contents of the first volume, which is divided into five books, and each book into chapters, are as follows.

"Book 1. Statics. Introductory definitions and remarks. i. Axioms or laws of motion and reft. 11. On ftatical equilibrium, and the compofition and refolution of forces. 111. Of the centre of gravity. IV. On the mechanical powers or fimple machines. v. On the ftrength and ftrefs of materials.

chords, arches, and domes.

"Book 11. Dynamics.

VI. On

Introductory definitions and re

the vibraIV. On the with the

marks. 1. On motion, uniform and variable. 11. On the descent and ascent of heavy bodies in vertical lines, the motion of projectiles, defcents along inclined planes and curves, tions of pendulums, &c. III. On central forces. rotation of bodies about fixed axes, and in free space orems relative to the centres of ofcillation, gyration, percuffion, fpontaneous rotation, &c. v. Phyfico-mathematical theory of percuffion. vi. On the motion of machines, and their maxi mum effects.

"Book 111. Hydroftatics. Introductory definitions and remarks. 1. On the preffure of non-elaftic fluids. 11. On the determination of the specific gravities of folid and fluid bodies. Extenfive table of fpecific gravities. III. On the equilibrium, ftability, and ofcillations of floating bodies. IV. On the phe. nomena of attraction in capillary tubes.

I.

"Book Iv, Hydrodinamics. Introductory obfervations. On the discharge of fluids through apertures in the bottoms and fides of veffels, and on fpouting fluids. 11. Account of experi ments made by different philofophers on the discharge of water through apertures and tubes, and the practical deductions from thofe experiments. 111. On the effect of water upon the motion

BRIT. CRIT, VOL, XXVIII. AUG. 1806.

of water wheels. IV. Account of Mr. Smeaton's experiments on water wheels.

"Eook v. Pneumatics. Preliminary remarks on the mechanical properties of atmospheric air. 1. Equilibrium of elastic fluids. II. On the admeafurement of altitudes with the barometer and thermometer. III. On the motion of air when the equilibrium of preffure is removed. IV. On the theory of air pumps, and pumps for raifing water. v. On the refiftance of fluids to bodies moving in them. v1. Experiments on the re

fiftance of fluids.

The preliminary definitions, with which the first book commences, are clearly ftated, and are accompanied with very proper obfervations. The following is a fpecimen.

"Among other forces it has been cuftomary to fpeak of the vis inertia, or inert force of matter; applying the term to that property of bodies by which they tend to retain their prefent ftate, or are indifferent to motion or rest. But while we admit that much of the language relating to powers, forces, actions, &c. is metaphorical, we muft object to fuch use of it in the prefent cafe; this property being improperly called a force: ft. Because were it actually fuch, it must be of fome definite quan tity in a given body, and therefore an impreffed force lefs than that would not move the body; whereas any impreffed force, however fmall, will move any body however great. 2dly. Because it seems to indicate an active power refident in matter; or rather, it implies an abfolute contradiction, namely, that a body fhould be both active and inactive at the fame time. It is de firable, therefore, that only the term inertia, or inertnefs, fhould be retained for this term will imply, as it ought to do, that matter is a merely paffive thing."

The first chapter contains the three well known Newtonian laws of motion and reft, which are briefly illuftrated. These are with propriety placed immediately after the definitions; fince they are the axioms, or the fundamental principles, upon which the fubfequent enquiries are almost entirely dependent.

The fubje&t of the fecond chapter is, (after the fatement of a few neceffary propofitions relative to the equilibrium, compofition and refolution of forces) fubdivided into four parts under the titles, 1. Of forces difpofed in one plane, and concurring in the fame point. 2. Of forces directed to one point, but not confined to one plane. 3. Of forces fituated in one plane, but applied to different points of a body. And 4. Of forces not confined to one plane, directed to various points of a body.

Each

Each of thofe fubdivifions contains a feries of propofitions concerning its peculiar title. Thofe propofitions are illuf trated and demonftrated by references to the diagrams in the plates of the 3d volume.

In the third chapter, (on the centre of gravity) this author inveftigates fome general theorems, which may be useful in finding the centre of gravity of any propofed body; and after this he proceeds to demonftrate other propofitions belonging to the fame fubject; fuch as to find the centres of gravity of different figures, of different folids, and fo forth. In the fame chapter he alfo treats of what is called the Centrobarye method. His words are as follows.

Among the feveral ufes to which the doctrine of the centre of gravity may be appropriated, one, which for its elegance and fimplicity deferves being mentioned here, is that which is called the Centrobaryc method, and by which the magnitudes of furfaces and folids may often be determined with great facility. The relation between the centre of gravity and the figure gene. rated by the revolution of any line or plane, which is the foundation of this method, was firft diftinctly stated by Pappus in the preface to his feventh book: but it was not completely difcuffed till the time of father Guldin; who in the fecond and third books of his treatife on the centre of gravity, treated this method very fully, and exhibited its utility in a variety of examples. The doctrine is comprised in the following propofition, and the corollaries which naturally flow from it.

"Prop. If any line, right or curved, or any plane figure,' whether it be bounded by right lines or curves, revolve about an axis in the plane of the figure, the furface or folid generated will be refpectively equal to the furface or folid whose base is the given line or agure, and its height equal to the one described by the centre of gravity of the faid generating line or figure.”

On account of its reference to a diagram, it is not in our power to add the demonftration of this curious propofition. The fimple machines, or the mechanical powers, are defcribed in the fourth chapter, which contains the propofitions relative to the powers, the actions, and the different forms of thofe machines; namely, of the lever, of the wheel and axle, of the pulley, of the inclined plane, of the screw, and of the wedge.

The fifth chapter treats of the ftrength and ftrefs of mate. rials. This fubject, which is of the utmoft confequence to the practical branch of mechanics, is far from being easily inveftigated; nor have the efforts of the greateft philofophers and mathematicians been able to form it into a theory fufficiently accurate and fatisfactory. Indeed, whoever, for a

moment reflects on the heterogeneous and variable nature of wood, metals, ropes, and other materials that enter in the conftruction of machines, will eafily conceive, that the best approximation to the true ftate of the matter in any particular cafe, must be obtained from actual experiments inftituted upon the materials themfelves. Agreeably to this obvious remark, Mr. Gregory prefers Galileo's fimple theory originally laid down in his dialogue "On the cause of the coherence of folids," when aflifted by proper experiments.

That the refiftance of folids might be fubjected to calcu lation, Galileo fuppofed firft, that bodies were compofed of folid fibres, parallel to one another; he then enquired what was the force with which they refift the action of a power ftretching them in a direction parallel to their length, and found that it was proportional to the number of integral fibres: next, confidering the fibres as fubjected to an effort perpendicular to their length, he found that the refiftance of the integral fibres, was proportional to their fum multiplied by an arm of a lever, which is always at a certain part of the vertical dimenfions of a folid in the plane of its rupture. The length of this arm of lever was regulated, according to Galileo, by the pofition of the centre of gravity of the plane of rupture, according to others, by the centre of percuffion, &c. But the distinctive character of Galileo's hypothefis confifts in this, that the refiftance of each of the fibres is independent of their quantity of extenfion at the inftant of their rupture.”

A general maxim deduced from the examination of this fubject is, that

"When feveral pieces of timber, iron, or any other materials are introduced into a machine or ftructure of any kind, the parts not only of the fame piece, but of the different pieces in the fabric, ought to be fo adjusted with respect to magnitude, that the ftrength may be in every part as near as poffible in a constant proportion to the train to which they will be subjected.”

This chapter alfo contains the refults of experiments made relative to the firength of various forts of wood, and of other bodies; which have been extracted from the works of different authors.

The fixth chapter of this firft book treats of chords, arches, and domes; but in the demonftration of the propofitions which relate to them a good deal of the fluxional calculus is employed. They are otherwife too complicated to admit of & very fhort, and, at the fame time, intelligible abftract.

The fecond book, the fubject of which is Dynamics; namely, that branch of mechanics which has for its object the action of forces on folid bodies, when the refult of that action is motion, commences with a few definitions and remarks.

The fubjects of the fix chapters into which this book is divided have been mentioned in the table of contents.

The first chapter contains the propofitions which determine the proportion of the times, velocities, fpaces, and quantity of matter, of bodies in motion whether uniform or accelerated.

The fecond fubdivifion of the fecond chapter treats of the motion of projectiles; but this intricate fubject is not examined in its full extent by Mr. G. He only confiders the motion of projectiles under the fimpleft fuppofition, viz. as if they moved in vacuo, and then adds a few words on the great difference which exifts between this theory, and the refult of actual experiments; referring the reader for further information to the works of other authors, fuch as Robins, Euler, and Hutton.

Of the other parts of this and the remaining chapters of this fecond book, we may only obferve in general, that their various fubjects are examined with fufficient minutenefs, the propofitions are demonftrated with perfpicuity, and are arranged with judicious regularity. Several remarks are like wife introduced among thofe propofitions which greatly tend to illuftrate the theory.

Fluids are commonly divided into elaftic and non-elaftic; viz., thofe which may be compreffed into a smaller space, and those which are either incapable of any fuch comprellion, or are, at most, comprellible only in an exceedingly flight degree. The doctrine of the preffure and the equilibrium of the latter, under the general title of Hydroftatics, forms the fubject of the third book of the prefent work. This book is divided into four chapters, to which feveral inftructive remarks are prefixed.

In the first chapter the preffure of fluids is examined, and the propofitions refpecting it are demonftrated, both by the algebraical and the geometrical mode of reasoning.

The fecond chapter, which fhows how to determine the fpecific gravities of bodies both folid and fluid, defcribes the ufe of the hydrostatical balance, and of the hydrometer; it gives the rules neceffary for determining the fpecific gravities of bodies, and contains a rather extenfive table of fpecific gravities.

In chapter the third, the equilibrium, stability, and ofcil. lation of floating bodies, are naturally deduced from that which has been explained in the preceding part of the work. The phenomena of the attraction of fluids between the contiguous furfaces of folids, which is generally known under the title of attraction in capillary tubes, are examined