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adopted; the latter, comparatively, but seldoın. In the department of natural philosophy, generally, we recollect but four books, exclusive of this before us, which give any thing like a fair abstract of the several subjects in a course; these are, Atwood's Analysis of a Course of Lectures on the Principles of Natural Philosophy,' published at Cambridge in 1784; Vince's · Plan of a Course of Lectures, &c.' first published at Cambridge in 1793; Dr. Thomas Young's - Syllabus of a Course of Lectures,' &c. delivered at the Royal Institution, published in 1802; and Dr. Matthew Young's
Analysis of the Principles of Natural Philosophy,' published in 1803. Each of these is an ingenious and useful work; and the latter especially, being extended to nearly double the size of either of the others, contains much that is valuable, and not a little which a mere English student could scarcely be shewn in any other performance.
Professor Playfair, though travelling over tlie same regions with the authors just mentioned, and, of course, compelled to behold many things in nearly the same points of view, yet by no means confines himself to the paths of his precursors. The road which he takes is, correctly speaking, of his own striking out, and, in the main, it is direct and smooth. He examines nearly all that comes in his way with the eye of a keen observer, and, in giving us the result of his inquiries, it is not often that he can be fairly accused of either pedantry or affectation.
The subjects of which the Professor treats in the present volume, after an introduction on the properties of matter, are dynamics, mechanics, hydrostatics, hydraulics, aerostatics, and pneumatics. In discussing these, though an entire and thorough deviation from the usual route is neither to be expected nor wished, yet the plan here pursued is sufficiently original and characteristic of its author to be worth detailing. Thus, under the head dynamics, the measures of motion are first explained; the succeeding propositions relate to the first law of motion, the communication of motion by impulse, equably accelerated or retarded motion, the motion of projectiles, and motion accelerated or retarded by variable forces. The part devoted to mechanics relates to the centre of gravity, the mechanical powers, including the funicular machine, friction, mechanical agents, the motion of machines, descent of heavy bodies on plave and curved surfaces, the centre of oscillation, descents along cycloidal surfaces, and the rotation of bodies both about fixed and movable axes. An appendix to this part contains the principles of the construction of arches, and those by which the comparative strength of different beams of timber is ascertained. Under hydrostatics the author treats of the pressure of fluids, the equilibrium of solid bodies floating on fluids, and the phenomena
of capillary tubes. The portion appropriated to hydraulics, treats of the motion of fluids issuing through apertures in the bottoms or sides of vessels, of conduit pipes aud open canals, of the percussion and resistance of fluids, of the undulations of fluids, and of hydraulic engines, comprizing those moved by the impulse of water, those moved by the weight, and those by the reaction of water. The part on aerostatics contains propositions and observations on heat and on the equilibrium of elastic fluids. And under the head of pneumatics, the last treated in this volume, air is contemplated, first, as accelerating or retarding motion ; 2dly, as the vehicle of sound; 3dly, as the vehicle of heat and moisture. And in one or other of these sections the author treats of machines for raising water, of the steam engine, of motion produced by the explosion of gunpowder, of the resistance of the air to projectiles, of the vibrations of sonorous bodies and the propagation of those vibrations through the air, of wind and rain.
Such is the distribution of subjects: and it is but just to add, that the Professor has discussed them generally ably, and almost always perspicuously, as far as he goes. We say as far as he gues, because, in giving an abstract of a course of lectures, a writer can but seldom enter into the detail of demonstrations and experiments; and must therefore feel considerable difficulty in determining what may be safely omitted, and what it is absolutely necessary to retain. We have seen some syllabuses of lectures which were perfectly grotesque in their representations, though the lectures themselves were highly interesting and valuable. Indeed in all the works of this kind which we have seen, with the exception of the Syllabus of Dr. Thomas Young, the authors demonstrate only by fits; and the reason is obvious. Where they have a demonstration to present which is new, or striking, or more concise, or more perspicuous, than usual, it is of course inserted; while the other theorems or results are merely enunciated; the auditors of the lectures being expected to call the proofs to mind, while the general reader is left to imagine that however they may be omitted in the abstract, they were duly given in the lecture room.
This, however, is a defect which was not likely to escape the penetration of such a writer as Professor Playfair. He endeavours to supply it by referring to those places, in the works of other authors, where the requisite information is to be found; and this is the principal novelty in his · Outlines,' though we shall have to offer a few remarks on it, presently. But before we enter upon any observations tending to the improvement of this work, we shall select two or three passages in which we think the author has been successful, either in demonstrating de novo, or in presenting the results of the inquiries of former investigators.
4 A a
Of the former kind, is Mr. Playfair's demonstration of the second of the two subsequent properties relative to the collision of elastic bodies; the first is due to Bernoulli.
* 76. In perfectly elastic bodies, the sum of the products made by multiplying each of the bodies into the square of its velocity, is the same after collision that it was before it.
Let A and B be the masses of the bodies, a and b their velocities before collision, a' and their velocities after it. Then, as the quantities of motion before and after collision are the same (68)
A a + Bb= A d + BV,
or A a2 + B 62 = A a'? + B 62. • See another demonstration, Maclaurin's Account of Newton's Discoveries, Book 11. chap. iv. § 12.
*77. If between two unequal elastic bodies A and C, a third B be interposed; and if the least A, be made to strike with any given velo, city on B, the motion communicated to C will be the greatest possible, when B is a mean proportional between A and C. It is easily shewn from $ 74 that the velocity communicated to C is = 4 A Ba
4 A a
A + B +
AC • This fraction is a maximum, when the denominator A + B +
B is a minimum, that is, since A and C are given, when B’ = AC, or when B is a mean proportional between A and C.
4 A a
4 A a The velocity of C is
and the A + 27 AC +C (A + C)'
4 A Ca motion of C =
WA+02 "If the number of the bodies in geometrical progression be increased without limit, the quantity of motion communicated to the last, from a given quantity of motion in the first, however small, may also be increased without limit. Notwithstanding this, as all the bodies move backward after collision, but the last, if they form an increasing series the sum of ail the motions in the direction of the first mover conti
Also the sum of the products of each body, into the square of its velocity, aiter collision, remains as it was before, equal to Aa?.'
Altogether, we think the section on the communication of motion by impulse, whence the above is quoted, very neat; there are, however, two omissions which the author will do well to supply when he has opportunity. The first is that of a proposition explainįng the circumstances of the collision of bodies imperfectly elastic
in any degree. The second is of a remark tending to prevent any misinterpretation or misapplication of Bernoulli's celebrated proposition respecting the conservation of motion : they are only perfectly elastic bodies, (that is, in other words they are no bodies at all,) in which the sum of the products formed by multiplying each body by the square of its velocity is not changed by the impact.
We should have liked to quote freely from those parts of the Professor's work in which he gives a summary of the results deduced by Du Buat and Robison, concerning the motion of water in conduit pipes, canals, and rivers, and those of Robins and Hutton, on the motion of projectiles, and to have compared the former with the calculations of a late writer in the Philosophical Transactions, who has newly modelled the whole of Du Buat's doctrine: but, as we have many remarks to offer on different parts of the book, we can only venture upon one extract of any length, which relates to a subject rather more important in practice, that is, the estimation of the mechanical agency of animals.
* 176. The strength of men, and of all animals, is most powerful when directed against a resistance that is at rest; when the resistance is overcome, and when the animal is in motion, its force is diminished; lastly, with a certain velocity, the animal can do no work, and can only keep up the motion of its own body.
• A forinula having the three properties just mentioned, will afford an approximation to the law of animal force. Let P be the weight which the animal exerting itself to the utmost, or at a dead pull, is just able to overcome; W any other weight with which it is actually loaded; and v the velocity with which it moves when so loaded; C the velocity at which the power of drawing or carrying a load entirely ceases; then W=
is an equation that has all the three conditions mentioned above.
· Not only, however, has the formula P (1) these conditions, but the square of it has the same, or, indeed, any function of it which vanishes when I vanishes, that is, when v = c. We are left, then, at liberty to choose any of these functions, and would assume the formula above as the simplest, if another condition did not seem necessary to be included. It is certain, that in all cases, when v approaches to č, or when the speed becomes great, a small variation in the weight is accompanied with a great variation in the velocity. The simplest formula that corresponds to this condition is, when I is raised to the
* 177. Therefore, till experience has led to a more accurate result, we may suppose the strength of animals to follow the law expressed by the formula W = P(1 – 3
This equation, supposing W and wv variable, is an equation to a parabola, the construction of which will serve to represent this law more clearly to the imagination.
"A formula for expressing the law of animal action was first proposed by EULER, in a Dissertation on the Force of Oars, Mém. Acad. de Berlin, 1747. That which he employed was W = P(1-2), different from both those we have mentioned, but a function of the first, and one that becomes 0 when v = c. EULER, however, changed this to another, Mém. Acad. de Berlin, 1752, and Nov. Com. Petrop, viii. p. 244, the same that we have adopted. He appears to have done so merely on account of the analogy thus preserved between the action of animals and of Auids. The physical fact mentioned above, is a better reason for the preference.
' 178. The effect of animal force then, or the quantity of work done
in a given time, will be proportional to W v, or to P v (1),
4P will be a maximum when y= and W=
that is, when the ani3'
9 mal moves with one third of the speed with which it is able only to move itself, and is loaded with four-ninths of the greatest load it is able to put in motion.
The quantities P and c can only be determined by experience, and as they must differ for different individuals, an average estimation of them is all that can be obtained. Even that average is but imperfectly known; Euler supposes, that for the work of men P may be taken = 60lb. and c = 6 feet per second, or a little more than four miles an hour.
A man, according to this estimate, when working to the greatest advantage, should carry a load of 27lb. and walk at the rate of two feet in a second, or a mile and one-third an hour.
• A horse, according to Desaguliers, drawing a weight out of a well, over a pulley, can raise 2001b. for eight hours together, at the rate of two miles and a quarter an hour. Supposing the horse in this case, to
200 x 9 work to the greatest advantage, P= = 450, and c= 2.25 x 3 = 64 miles per hour.
"This estimate seems to give too high a value to P. It will suit better with general experience to make P = 420, and c = 7.
• When a horse's work is estimated by the load he draws in a cart or waggon, a great reduction must be made, in order to compare the force he exerts with that which is necessary for raising a weight, by drawing it over a pulley. Though accurate experiments on the friction of wheel carriages are wanting, we probably shall not err much in supposing the friction on a road, and with a carriage of the ordinary construction, to amount to a twelfth part of the load. If then, a horse draws a ton in a cart, which a strong horse will continue to do for several hours together, we must suppose his action the same as if he raised up the twelfth part of a ton, (2240lb.), or 1861b. perpendicularly against the force of gravity. To raise a weight of 1861b, therefore, at