in the fourth chapter. Here, however, Mr. G. only relates the opinions of various philofophers, without attempting to propofe any new theory, capable of explaining thofe phenomena. In fhort, he leaves this enquiry, as he found it, in a very imperfect state.

In the fourth book, which treats of the motion of nonelaftic fluids, and the forces with which they act upon bodies, this author, fenfible of the difficulty of reconciling the refult of experiments, with the theory of this fubject, which is denominated hydrodynamics, gives in the first chapter the theory in a regular feries of propofitions, and then collects in the fecond chapter the accounts of experiments instituted by Boffut, Venturi, Dr. M. Young, and others.

The reafon why the theory of this fubject does not agree with the experiments, is, that all the circumftances, which affect the motion of fluids, fuch as the attraction among their particles, the attraction of the fluids to folids, the refiftance of the air, &c. cannot be accurately determined. With refpect to the effect of water upon the motion of waterwheels, the fame caufes of difagreement between the theory and the refult of actual experiments, induced this author to give the theory in the third chapter, and the account of Mr. Smeaton's experiments in the fourth chapter.

The mechanical properties of elaftic fluid, under the title of pneumatics, form the fubject of the fifth book. In this, conformably to the plan of the other books, feveral necessary remarks, defcribing the mechanical properties of air, and other elaftic fluids, are prefixed to the theory. The first chapter contains the propofitions which relate to the equilibrium of elaftic fluids; and as a confequence of thofe propofitions, the various methods of measuring altitudes by means of the barometer are described in the fecond chapter. The third chapter contains a feries of propofitions regularly arranged, and perfpicuously demonftrated, relative to the motion of the air, when the equilibrium of preffure is removed.

In the fifth chapter this author treats of the refiflance of fluids to bodies moving in them, in which he thus expreffes himself.

"The force with which bodies moving in fluid mediums, as water, air, &c. are impeded and retarded in their motions, is ufually termed the refiftance of fluids; and as all our machines move either in water or in air, or both, it becomes a matter of importance in the theory of mechanics to enquire into the nature of this kind of force.

"We

"We know by experience that force must be applied to a body in order that it may move through a fluid, fuch as air or water, and that a body projected with any velocity, is gradually retarded in its motion, and generally brought to reft. The analogy of nature makes us imagine, that there is a force acting in the oppofite direction, or oppofing the motion; and that this force refides in, or is exerted by the fluid. And the phenomena refemble those which accompany the known refiftance of active beings, fuch as animals. Therefore we give to this fuppofed force the metaphorical name of Refiftance. We also know that a fluid in motion will hurry a folid body along with the ftream, and that it requires a force to maintain it in its place. A fimilar analogy makes us fuppofe that a fluid exerts force, in the fame manner as when an active being impels the body before him; therefore we call this the Impulsion of a Fluid. And as our knowledge of nature informs us, that the mutual actions of bodies are in every cafe equal and oppofite, and that the obferved change of motion is the only indication, characteristic, and measure of the changing force, the forces are the fame (whether we call them impulfions or refiftances) when the relative motions are the fame, and therefore depend entirely on these relative motions. The force, therefore, which is neceffary for keeping a body immoveable in a stream of water, flowing with a certain velocity, is the fame with what is required for moving this body with this velocity through stagnant water.

"A body in motion appears to be refifted by a stagnant fluid, because it is a law of mechanical nature that force must be employed in order to put any body in motion. Now, the body cannot move forward without putting the contiguous fluid in motion, and force must be employed for producing this motion. In like manner, a quiefcent body is impelled by a stream of fluid, because the motion of the contiguous fluid is diminished by this folid obftacle; the refiftance, therefore, or impulfe, no way differs from the ordinary communications of motion among folid bodies, at least in its nature; although it may be far more dif ficult to reduce the various circumftances to accurate computation, or to obtain all the requifite data on which to found the calculus.

"The refiftance which a body fuffers from the fluid medium through which it is impelled, depends on the velocity, form, and magnitude of the body, and on the inertia and tenacity of the fluid. For fluids refift the motion of bodies through them; 1, by the inertia of their particles; 2, by their tenacity, i. e. the adhefion of thofe particles; 3, by the friction of the body against the particles of the fluid. In perfect fluids the latter cafes of refiftance are very inconfiderable, and therefore are not taken into the account; but the former is always very confiderable, and obtains equally in the most perfect as in the most imperfect

fluids. And that the refiftance varies with the velocity, fhape, and magnitude of the moving body is fufficiently obvious.

"We must carefully diftinguifh between refiftance and retardation: refiftance is the quantity of motion, retardation the quantity of velocity, which is loft; therefore, the retardations are as the refiftances applied to the quantities of matter; and in the fame body the refiftance and retardation are propor

tional."

A fimilar difagreement between the theory, and the experiments, to that which has been remarked with respect to fome of the above mentioned subjects, induced this author to treat of the former in this chapter; viz. to determine theoretically the force of fluids in motion, or the refiftance of fluid against bodies moving in them; and to give an account of the principal experiments that have been inftituted on this account, in the fixth chapter, which is the laft of the fifth book.

This fift volume concludes with an index of the most remarkable pa ticulars in it.

The fecond volume of this work contains in the firft place the practical part of mechanics, which occupy about eighty pages; and after this the reft confifts of defcriptions of a great variety of machines, and mechanical contrivances, which are very neatly delineated in the plates which form the third volume. The contents of the practical me. chanics are:

"On the construction and fimplification of machinery. On rotatory, rectilinear, and reciprocating motions. On bevel. geer, and proportioning the number of teeth. On uniformity and fmoothness of motion. On the operation and ufe of a fly. On friction and the fiffness of cords, with the experiments of Vince, Coulumb, &c. An example of the power of the capftan, allowing for friction and the rigidity of cords. On water as à mover of machinery. . On wind, as a mover of machinery, with Smeaton's rules relative to wind-mills. On the ftrength of fired gun-powder. On fteam, as a mover of machinery, with the refults of Bettancourt and Dalton. On animal ftrength, men and horfes."

As it would protract the prefent account to too great a length, if we attempted to notice all the particulars that are contained in this practical part of the work, we fhall only endeavour to give an idea of the whole, by means of fome general remarks, after a concife defcription of its materials.

This author commences by an enumeration of the general ules of machines, and by recommending to the young engineer

engineer a ftrict attention to the fimplicity of machines juftly obferving, that part of the power is loft by the interpofition even of the fimpleft machines; but in more com plicated machines, that lofs of power, which arifes from friction, ftiffness of materials, &c. is indeed very great. He then proceeds to fhow how a rotatory motion may be produced by means of a reciprocating one, how to communicate motion in any direction by wheels, and to conftruct the wheels proper for the purpofe; how to regulate any motion fo as to render it uniform, and fo forth.

As most of the propofitions laid down in the first volume take no notice of friction and the fliffness of ropes; and as the effect of machines is in great measure obftructed by those causes, this author has given a very good account of the experiments made by various ingenious perfons, for afcertaining the influence of thofe obftructions under different circum ftances; fuch as the difference of materials, difference of weight or preffure, &c.

The greateft, and by no means the least useful, part of thefe practical mechanics, relates to the moving power; and in this Mr. G. gives a concife, but clear and comprehensive view of all the particulars, which have, by long continued experience, been afcertained, or that appear worthy of attention concerning the force of human beings, and of horfes, of water, of wind, of fteam, &c. The refults of experiments are stated in tables or otherwife, fome contradictory affertions are in a great measure reconciled, and the opinions of the most accurate and experienced philofophers, and engineers are introduced. The following fpecimen is extracted from page 75, where this author fpeaks of the power of the horfe.

"It has been stated by Defaguliers (vol. I. page 251) and fome others, that a horse employed daily in drawing nearly ho rizontally can move, during eight hours in the day, about 200lb. at the rate 2 miles per hour, or 33 feet per fecond. If the weight be augmented to about 240 or 250lbs. the horse cannot work more than fix hours a day, and that with lefs velocity. And in both cafes, if he carry fome weight, he will draw better than if he carried none. Mr. Sauveur eftimates the mean effort of a horfe at 175 French, or 189 averd. pounds, with a velocity of rather more than three feet per fecond: and this agrees very nearly with our deduction in art. 378, vol. I. But all thefe are probably too high to be continued for eight hours, day after day; for in our investigation just referred to, we affumed ten feet per fecond, as the utmost walking velocity of a horfe; a velocity which we conceive no horfe would be able to continue

long.

long. In another place Defaguliers ftates the mean work of a horfe as equivalent to the raifing a hogfhead full of water (or 550lbs) fifty feet high in a minute. But Mr. Smeaton, to whose authority much is due, afferts, from a number of experiments, that the greateft effect is the raifing 550lb. forty feet high in a minute. And, from fome experiments made by the Society for the Encouragement of Arts, under the direction of their late able Secretary, Mr. S. Moore, it was concluded that a horse, moving at the rate of three miles an hour, can exert a force of eighty pounds."

The description of machines occupies about five-fixths of the fecond volume, and they are arranged in alphabetical order; fo that air pump comes first, then follows Anemometer, Atwood's machine, balance, &c. Among those defcriptions we find moft of the latest discoveries and improvements, not barely defcribed with refpect to the mechanifm, but likewife examined concerning their advantage or disadvantage over machines, their real power, and other particulars; to a great many of those descriptive articles, a fhort hiftory of the original difcovery, together with the fubfequent improvements, is prefixed; fo that all together it contains a reasonably good hiftory of mechanical contrivances. The number of machines or mechanical contrivances, which are defcribed in this volume, exceeds 150.

Having now given as concife an account of this rather extenfive publication as feemed practicable; we fhall, with the like brevity, exprefs our opinion with refpect to the whole.

In a fubject fo intricate, fo various, and fo interefting, as that of mechanics, where much mathematical reafoning, theory and experience, hiftorical information and modern practice, opinions and hypothefes, demand the ftrictest attention on the part of the author, it is hardly to be expected that the careful examination of a difcerning reader hould not find fome defects, irregularities, or errors, especially in a first edition. And fuch in fact is the cafe with the prefent work; yet it must be confeffed that those defects, &c. are, upon the whole, not very material. As an elementary work, this treatife on mechanics is by far preferable to any other work extant, at leaft in the English language. The ftyle is perfpicuous, the arrangement of materials is, in very few places, fufceptible of improvement; the information it contains is extenfive, and the plates are elegant; we do not, therefore, hesitate to recommend it to the attention of the fcientific world; and, with refpect to any defects, we are perfuaded that the author will endeavour to remove

them