the rate of two miles, or two miles and an half an hour, (that is, 2.9 or 3.6 feet per second) may be taken as the average work of a strong draught horse in good condition. A different view of the manner of estimating animal force, has been taken by COULOMB, Mém. de l'Instit. Nat. tom. 11. p. 380, &c. 179. It appears to be a certain fact that when a man carries only his own weight, the quantity of his action, that is, the height he is able to ascend in a given time, multiplied into his weight is greater than when he carries any additional load; and COULOMB thinks it probable that this diminution of action, is in proportion to the additional load carried. Now it appeared from his experiments, that when a man carried a load equal to his own weight, his action was reduced nearly one half; and, therefore supposing the reduction always proportional to the load, if w be the weight of the man's body, I an additional load which he is made to carry, H the height to which he ascends in a given time, when walking freely, and h the height to which he ascends in the same time, with the load 7; then his action in the latter case or (w + 1) け w H (1 is loaded with one-fourth of his own weight; ) 1+ 1 = H (.699). 'The value of H is deduced from the ascent of the Peak of Teneriffe. BORDA, accompanied by eight men on foot, ascended in the first day (7h 45m), to the height of 2923 metres, or 9593 feet. This was at the rate of 1225 feet in an hour. Had each of the men carried a load equal to the fourth part of his weight, they would only have ascended at the rate of 857 feet an hour. • When 1 2 w = 0, or 72w, the height h=0. With a load equal to twice a man's weight, he could not ascend. 180. The strength of a man being supposed to follow the law now laid down, its greatest effect in raising a weight will be when the weight of the man is to that of his load, as 1 to - 1+3, or nearly as 4 to 3. H w (1 'Because h = 270) w+ 1 Hwl (1-. .) ; now h, or the weight multiplied into the height into which it is to be raised, is the measure of the effect, or of the work done, which, therefore, will be a maximum when the last formula is so, that is, when l = w( + √ 3.) If in the equation h = riable, the other quantities being constant, the locus of the equation is a hyperbola, which may be easily constructed. The theorems just given only differ from CoULOMB's, by being somewhat simpler, and free from all reference to any particular mea sure sure of length or of weight. On this subject, however, many more experiments are wanting.' The preceding is an interesting quotation, to which we have only one objection to offer. It might be imagined from the language of the learned professor, that the formula WP (1- 3)* for the estimation of animal energy, had little besides its simplicity to recommend it; and that scarcely any thing was known from experience as to the safety with which "we may suppose the strength of animals to follow the law expressed by that formula.” But the truth is, that it is extremely easy to ascertain by experiment the correctness of any assumed formula, and that the requisite experiments have long ago been made. M. Schulze has recorded in the Memoirs of the Berlin Academy of Sciences for 1783, a tolerably extensive series of experiments; from which he has shown, that the above formula is a sufficiently correct expression for human mechanical energy under the supposed circumstances, and that Euler's other theorem, W= P(1), leads to extreme anomalies in many of its applications. Indeed, the results offered by the two theorems for the case of a maximum effect, are enough to determine the point: according to the first formula, we should have vc, according to the latter v ✔c, when the maximum occurs; and this last result is well known to be completely at variance with experiment. With respect to the action of horses, Mr. Playfair's predecessor, Professor Robison, made many experiments, and found that when drawing a lighter in a canal, and loaded so as not to be able to trot, that action varied nearly as (1 − 2)1 or as (c v); which corresponds much better with the first than with the second of the theorems just given. So that there can be no occasion for the doubtful language employed by Professor Playfair on this subject. After what we have said of the general merits of the work before us; we trust the author will not impute it to any unfriendly motive, if we devote the remainder of this article to the less grateful, but more useful task of suggesting alterations and improvements. And first, we will point to a few places where the professor may be inclined to supply omissions. We cannot but express some surprize that at page 139, there is no mention of Dr. Abram Robertson's theorems respecting rotatory motion, in the Philosophical Transactions for 1807; that at p. 160, Mr. Playfair should have forgotten Girard's valuable work on the resistance of solids; that at p. 270, he should neglect to mention Dr. T. Young's interesting inquiries respecting the motion of musical cords, cords, as well as omit the curious subject of temperament entirely; and that at p. 150, he should make no reference to Berard's Treatise on the Theory of Arches and Domes, though it is doubtless the best which has been published out of England. This is the more remarkable, as the professor has referred to Bossut, whose Essay on Arches exhibits three or four very gross blunders; and as he has noticed in terms of high commendation, Mr. Atwood's Dissertations on Arches, though they are well known to have been written after the mind of that excellent mathematician had been greatly impaired by long sickness, and to be so tedious, prolix, inelegant, and sometimes erroneous, that the friends to his reputation sincerely wish he had never published them. If it were not that an attention to the sublimer sciences is generally acknowledged to check the indulgence of prejudice and partiality, we should really be apt to suspect that Professor Playfair had more than once felt their influence. But we proceed to a few omissions of another kind. Thus, at p. 9, the author has neglected to distinguish between adhesion and cohesion, though such distinction is perfectly conformable to the precision of modern philosophical writers. So again, p. 43, the student is not told where it is that a heavy body falls from quiescence 16 feet and 1 inch, in the first second of time; though it would be very wrong for him to conclude that the space would be the same in all places. At p. 61, where Mr. Playfair treats of the motion of the centre of gravity, he forgets to introduce the leading theorems of the centrobaric method,' as it is technically called; although it is one of the most useful as well as curious applications of the centre of gravity, and although the relation between that centre and the figure generated by the revolution of a line or plane, which is the foundation of the method, is distinctly stated by Pappus in his Mathematical Collections, a work to which our author has referred at the page just specified. At p. 125, art. 203, it should, we think, have been shown that when ar, or the cone is right angled, the centre of oscillation is in the centre of the base; and that in oblique angled ones the centre of oscillation falls entirely below the solid; this would, at least, have led Mr. Playfair to correct the definition given in the preceding page, where he says of a compound pendulum, that the centre of oscillation is a point in it'; which very frequently is not the case. Again, at p. 127, where it is affirmed that the vibrations of a cycloidal pendulum whether great or small are isochronal; it ought to have been added, that this is merely true on the supposition that the whole mass of the pendulum is concentrated into a point; and that cycloids, when used to regulate the motions of pendulums, produce errors of another kind much greater than those which they are are intended to obviate. This, we think, has been remarked both by Atwood and Gregory. So again, at p. 148, when treating on the theory of arches, the author acknowledges that what he has advanced, rests on a defective hypothesis; it is therefore extraordinary, that he did not introduce at least one other hypothesis, and exhibit the equation of equilibrium between the arch and the piers, supposing the latter not susceptible of a motion of rotation, but one of translation; that is, not likely to turn, but to slide. Once more, when treating of the resistance of fluids, pp. 201, 202, Mr. Playfair speaks both of the experiments of Bossut and those of Mr. Vince; yet he does not seem to have instituted any comparison of their results, as M. Lacroix has done in the Bulletin de la Société Philomathique. Such a comparison developes some singular irregularities in those results, which Dr. T. Young has endeavoured to explain, (Journal Royal Institution, vol. ii. and more fully Nat. Phil. ii. 229.), and which should not have escaped the professor's notice in this place. We are aware that the various particulars which we regard as omissions, may be brought forward in their proper order and connection in the lecture room; and therefore, that the specifying them here may be represented as a kind of hyper-criticism. But we wish it to be recollected that the book will be seen by many who never belonged to Professor Playfair's class, that to such the information, of which we here regret the omission, is in most cases essential, and that the Synopses of Atwood, Vince, and Young, though not half the size of Mr. Playfair's, are not chargeable with a fourth of the number of similar defects. We shall next glance at a few points which we consider as at least doubtful. Such, for example, is our author's definition of a hypothesis. A fact (says he) assumed in order to explain appearances, and having no other evidence of its reality, but the explanation it is supposed to afford, is called a hypothesis.' The professor has probably a right notion of what he here intends to define; but we suspect that those who know no more of an hypothesis than can be learnt from this definition, will be far to seek. It may serve to designate the Ptolemaic or Tychonic hypothesis, but will not be very appropriate if applied to the Newtonian hypothesis in astronomy. Bodies differ in their capacity for receiving and maintaining different figures. Some receive new figures with difficulty, but maintain them easily. Such are the bodies usually called solid. 'Others receive any figure easily, but cannot maintain it without the assistance of other bodies. Fluid bodies are of this kind.' These are more like enigmatical than philosophical representa tions of the things intended. Give them to a person who did not previously know how to distinguish between solidity and fluidity, and he might certainly be led to doubt whether an oak tree was a solid, or whether sand, dough, and sponge, were not fluids. 6 The motion of a body falling freely to the ground, belongs to Dynamics: the motion of the same body descending on an inclined plane, belongs to Mechanics.' According to the principle on which this distinction is founded, the curve of quickest descent, and the precession of the equinoxes, belong to mechanics, rather than to dynamics. This is passing strange.' In reasoning upon the first law of motion, Mr. Playfair first shows that a moving body left to itself will not change its direction; and then proceeds thus: Lastly, it cannot change its velocity; for if its velocity change, that change must be according to some function of the time; so that if C be the velocity which the body has at any instant, and t the time counted from that instant, V the velocity at the end of the time t, the relation between V, C, and t, must be expressed thus, V = C + A + B t + &c. Now there is no condition involved in the nature of the case, by which the coefficients A, B, &c. can be determined to be of any one magnitude rather than of any other; each of them is therefore equal to O, and the equation is V = C, so that the velocity remains constant.' We object to this, 1st, because it is unnecessary; 2d, because it is unsatisfactory. Unnecessary, because both change of direction and change of velocity being changes of state, cannot be even imagined to take place without a cause; and therefore the proposition is admissible independent of the Professor's refined reasoning. Unsatisfactory, because many other things, whether doubtful or not, may be proved by the same process, without the alteration of a single word. Let it be affirmed, for instance, that the suns of this and of all other systems, move round our moon, or any other satellite, as a centre of force; and let it be farther asserted that in such case, the motion of Sirius (or any other fixed star) is uniform; the assertor, in order to establish his proposition, has only to say, it cannot change its velocity,' and, following the Professor verbatim through the above quotation, he will accomplish his object; though the thing thus proved is one of the most improbable things in nature. Our author treats of Archimedes' screw, under the head of mechanics; yet we cannot help doubting whether it would not have fallen better among the discussions respecting Hydraulics; especially as it is a machine for raising water. Mr. Playfair too, like some other philosophers of the present day, seems fond of a reference to ideal laws, such as the law of continuity, |