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of analytical chemistry. As such the description well deserves attention; otherwise we must confess we do not think the examination of a mineral spring of so much geological importance, as to justify so detailed an account in a volume like this.

In the eleventh paper Mr. Smithson Tennant mentions the occurrence of native concrete boracic acid as a volcanic production of the Lipari Islands, and recommends the examination of other volcanic districts with a view to this object. And in the eighteenth, Mr. Pepys relates the melancholy catastrophe of a company of mice, who, prying more curiously than cautiously into a solution of sulphate of iron, lost their lives in it, but were rewarded for their scientific death, by a deoxygenisation of the metallic salt, which produced grains of pyrites, sulphur and black oxyd of iron.

We have only to add that the volume is well and correctly printed, and that the plates, which are done up separately, are very neatly engraved.

Art. XIV. Traité Elémentaire des Machines: Par M. Hachette. Instituteur de l'Ecole Impériale Polytechinque. (An Elementary Treatise on Machines, &c.) 4to. pp. xx. 304. with 28 folio plates. Price 21. Paris, J. Klostermann fils. London, Dulau and Co. 1811.

ALTHOUGH treatises on the nature, construction, and power of machines, are very interesting, and, when ably executed, extremely useful; yet we meet with them less frequently, than with works on most other subjects connected with the arts and sciences. The Germans have, in the course of three centuries, the extensive collections of Besson, Boiteler, and Leupold; the Italians have Ramelli, and two or three of a more modern date; the French have the collection of machines approved by their Academy of Sciences, and those by Belidor, Berthollet, Perrouet, and Prony; and the English possess the collections given by Emerson and Gregory in their respective treatises of mechanics, Bailey's account of the machines approved by the Society of Arts, the machines described in the transactions of that useful Society, descriptions dispersed through the several volumes of the Repertory of Arts and Manufactures, and others given in some of our general Dictionaries of Arts and Sciences, especially in the Pantalogia, and in Rees's New Cyclopædia. Each of the works here specified may be consulted with advantage, by those who are tracing either the theory or the construction of machinery. But there still remains much to be done; and we therefore always turn with considerable avidity to any new work which embraces, either entirely or in part, the same objects.

A complete treatise on machines would comprehend, in some measure, the description of all arts and trades: for there is not any mechanical art which has not its tools; and the majority of machines are no other than instruments or tools so perfected, that by their means men entirely uninstructed, may accomplish what could otherwise be effected only by the most skilful and able workmen. In this sense, however, a complete treatise on machines is not to be expected: and hence every writer who devotes his attention to the subject must adopt some principle of selection. M. Hachette, in the work before us, confines his attention to a particular class of machines, namely, those which are intended to transmit motion, and more especially those which receive the action of the respective movers directly. The sole movers applicable to machines, are animals, water, wind, and combustibles: the nature of these movers determines the form of the machines which may directly receive their action. Thus combustibles can only become movers in three ways. 1st. By passing from the solid to the gaseous state. 2dly. By converting water or some other liquid into gas. 3dly. By elevating the temperature of a permanent gas: this may obviously give rise to three species of machines moved by combustibles. With regard to the wind, if we exclude sailing vessels, there will only be one class of machines receiving its action directly, which is the wind-mill, having its arbor of rotation horizontal or vertical, according to the form of the vanes or sails attached to that arbor. The machines which receive directly the action of water are more numerous.

To describe and explain the principal machines which directly receive the action of one of these movers, is M. Hachette's object in the more considerable part of his first chapter. He has, moreover, paid attention in this chapter to some hydraulic machines of the second class, viz. those which serve to raise water, but which are not necessarily put in motion by that liquid, such as pumps, Archimedes's screw, &c. The first chapter, in fact, relates to the following distinct topics, and occupies one hundred and sixty pages :-Elementary machines, the force of animals, water considered as a moving force-Hydraulic machines of the first class, viz. water wheels, hydraulic pendulums, chain pumps, syphons, Venturi's syphon, Hero's fountain, hydraulic ram, hydraulic ram upon the principle of the sucking pump, machines moved by columns of water, machines moved by the ascent and descent of a hollow floating prism-Hydraulic machines of the second class; viz. machine of Verra, hydraulic tube, centifrugal machine, Archimedes's screw, pumps of various kinds, air pump, machine at Marly, Bramah's hydraulic press, and

windmills. At the end of this chapter is a treatise on steam engines, and Berthollet and Carnot's description of the new machine called the pyreolophorus. There is likewise an appendix to this chapter, in part by M. Monge, relating to vertical and inclined chain pumps, pumps of continued aspiration, suckers and pistons, bellows, ventilators, and hat-making. How it happens that this latter article, any more than mousetrap-making, or fiddle-making, should find its way into such a treatise, we cannot conjecture.

The second chapter relates to the elementary machines known among the French by the name of engrenages, and among our workmen hy the terms tooth and pinion work, and bevel geer. The theory of this branch of machinery constitutes one of the most important applications of "Descriptive Geometry:" but it has not, previously to the treatise of M. Hachette, been completely developed in any book; and the methods followed by workmen, are in general very imperfect. The present author, after explaining the geometrical principles which serve for the basis of the theory, applies it to the determination of the forms of teeth, pinions, wipers, endless screws, wheels and lanterns, cylindrical, conical, &c.

The third chapter, occupying about sixty pages, comprehends the description of the principal machines employed in constructions, such as pulleys, rollers, capstans, cranes, pileengines, machines to cleanse roads and harbours, machines for sawing piles, and machines for spinning cotton. The author explains by a number of plates carefully and correctly executed, principally by M. Girard (designer to the Polytechnick School) the construction of each machine: he then explains the method of estimating the effects of the machine, and in many cases points out the advantages and defects.

Every one knows that the word force is susceptible of a variety of acceptations, all indicated by some qualifying expression attached to the word; as force of inertia, dead force, living force, motive force, accelerative force, &c. He, therefore, who endeavours to measure the force of machines in motion, must first determine what kind of force he will assume for his measure. M. Hachette assumes that which is denominated living force (vis viva), which he carefully distinguishes from simple force. Let M and m be two masses moving with the uniform velocities V and v, the products MV, mv, measure the simple forces: denoting by H and h the heights from which these masses must fall to acquire the velocities V and v, the products MH, mh, would measure the living forces: but, according to the established theory of the fall of heavy bodies, if s be the space described by a heavy body falling in the first

MV 2 46

second from quiescence, we should have 4 s H=V2, and 4 sh =2; therefore, the products MH and mh which measure the living forces, are equal to the quantities and so that these forces are in the ratio of MV2 to. mv, while the simple forces are as MV to my; that is, the former are as the squares of the velocities, while the latter are as the velocities simply all which is sufficiently obvious to those who have but slightly attended to the theory of mechanics. Living force, says M. Hachette, after Montgolfier, is that which is paid: thus, a man receives a certain sum to elevate a determinate quantity of water to a given height; and if he raises it to a double height, he will receive a double sum. Movers applied to machines ought in this way to be contemplated as living forces, and estimated in the same manner with them.

Conformably with these notions, our author proceeds when estimating the forces of machines. His introductory developement of principles, furnishes a fair specimen of the perspicuity with which he treats his subjects; though we cannot afford space for more than one section of it.

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• Machines are moved by animals, by water, by air, or finally by the action of caloric; each of these bodies is capable of producing motion, and, for that reason, they are called movers. To compare movers one with another, we measure the dynamic effect which they produce in a determinate time of all dynamic effects, the most simple is the elevation of a weight to a certain height taken for unit; for example, of a kilogramme to a metre in height; this effect being expressed by the number 1, when we say that a force is equal to 2, or 3, or 4, &c. we mean that in given time assumed for unit, that force is capable of elevating 2, 3, or 4 kilogrammes to the height of a metre. When the forces are very great, it is commodious, in order to estimate them, to employ units that are more considerable, calling them, minor unit the force capable of elevating a kilogramme to the height of a metre, we assume for the major unit the force capable of elevating a thousand kilogrammes, or a cubic metre of water, to the height of a metre. Admitting, thus, two kinds of units, it becomes necessary in each particular case to denote that which is employed.

• Whatever be the mover, it is equivalent in a given time T to a certain number n of forces taken for units, acting during the same time T; but, if the force taken for unit is capable of raising a weight W to the height H, W H will be the expression of that force during the unit of time, therefore n WHT will be the measure of the force which the mover may develope in the time T, the quantities n, W, H, T, employed in expressing this value being denominated factors of the force; a force which acts according to a certain direction may be destined to communicate motion to a body in another direction; the instruments employed to change either the directions or the factors of forces, are named machines. From this defininition of machines it may be seen that they can never

augment the value of forces which are employed to move them; nor can the direction of a force be changed otherwise than by decomposing it into two, the one in the new direction given, and the other in the direction of a fixed point which destroys it; nor, again, can the change of factors obtain, but through the intervention of other bodies, the friction of which necessarily destroys a portion of the primitive force; whence it follows, that the force transmitted by a machine, cannot in any case be equivalent to the force employed to move it; and experience shews that, in the best hydraulic machines, for example, the force transmitted is at most the half of the moving force.

To know the true object of machines, it must be remarked that the factors of the expression n W HT, have limits which depend on the nature of the mover, capable of producing the force of which the quantity n WHT is the measure if the mover be, for example, a given weight of gunpowder, the time T, of its action, is necessarily very short; if it were the action of a man, or of an animal, as of a horse, which we would retain the longest time possible, the duration of a continued labour will be about 12 hours, and it will be interrupted by a rest of about 12 hours; we cannot, therefore, obtain directly from this mover a dynamic effect n WHT in which T exceeds 12 hours: the same man who is capable of a dynamic effect ʼn WHT in his day's labour, cannot in a very short time t develope a force measured by a quantity n'wht which we suppose equal to n WHT; for this would be to suppose that he could exert in an instant t, an effort equivalent to the labour of an entire day, which is impossible.

n

The real and useful object of machines is to render any mover whatever capable of a given dynamic effect; a man may, by means of a machine, raise alone a weight which could not otherwise have been raised, but by the combined action of several other men; he might propel a cannon ball with a velocity equal to that which it would receive from gunpowder; and reciprocally one might obtain, by means of gunpowder, dynamic effects equal to those which result from human force.

Thus, supposing that the dynamic effect to be produced in a given time is expressed by E, and that the force capable of producing that effect is transmitted by a machine which consumes upon itself a force measured by an effect equal to E, it is necessary that the mover should develope 2 E of force; but, whatever be the mover, it will produce in the time T the dynamic effect n WHT; therefore in another time T' it will be capable of developing the force measured by 2 E, and, by means of the machine, this latter force would produce the effect E in the determinate time proposed.

Machines contemplated under this point of view, are means of accumulating or preserving the forces which one or more movers have furnished during a certain time, and of employing them in another time, whether larger or shorter, to produce a determinate effect: the forces thus yielded by the movers have for measure this latter effect augmented by the forces lost on frictions and pressures on the machine itself.

The usual movers do not always act with the same uniformity: the action of water and of caloric is exerted with more regularity than those of animals and of wind; machines have here again, this advantage of combining together movers of different natures, and of causing to