the number of revolutions of the wheel performed in a given time may be thus found. Another rectangular index m np shows the parts of a revolution. At the commencement of the motion, the point o is directed to 0 on the graduated rim of the wheel.

Having found by this instrument the number of revolutions and fractional parts of a revolution which have been performed in a given time; multiply the circumference of the wheel by that aumber, and we shall then find the velocity with which the circumference of the wheel moves.

(52.) The third property, in virtue of which water becomes a mechanical agent, is that power which, in common with all fluids, it possesses of transmitting pressure equally in every direction. If water be confined in any vessel, and a pressure to any amount be exerted on a square inch of that water, a pressure to an equal amount will be transmitted to every square inch of the surface of the vessel in which the water is confined.

One of the most remarkable instances of the employment of this property as a mechanical agent, is in Bramah's hydrostatic press, the theory of which is extremely simple. A large solid plug or piston AB (fig. 25.) is constructed so as to move water-tight in a cylinder C D. The space beneath the piston is filled ⚫ with water, and communicates by a pipe EF with a small forcing-pump, worked by the piston G, and by which the water is forced into the chamber of the cylinder

CD below the great piston. Let us now suppose the entire space between the two pistons to be filled with water, and a pressure of one pound exerted on the water by means of the piston G of the forcing-pump. Let us also suppose that the diameter of the piston G is a quarter of an inch, and that the diameter of the piston B is one foot. In that case, the

base of the piston B, which is pressed by the water, is 2304 times the base of the piston G, which presses the water, and in virtue of the power of transmitting pressure to which we have already alluded, a pressure of one pound will be transmitted to every part of the base of the greater piston which is equal to the base of the less. Thus an urging pressure of one pound on the base of the lesser piston G will produce a pressure of 2304lbs. against the base of the greater piston B. This property of fluids, therefore, seems to invest us with a power of increasing the intensity of a pressure exerted by a comparatively small force, without any other limit than that of the strength of the materials of which the engine itself is constructed.

This property of liquids also enables us with great facility to transmit the motion and force of one machine to another, in cases where local circumstances preclude the possibility of instituting any ordinary mechanical connexion between the two machines. Thus merely by means of water-pipes the force of a machine may be transmitted to any distance, and over inequalities of ground, or through any other obstructions.

CHAPTER VI.-Air considered as a
Mechanical Agent.

(53.) AIR may become a mechanical agent by means of its four properties, weight, inertia, fluidity, or power of transmitting pressure, and its elasticity. In our treatise on PNEUMATICS, Chapter III., it was proved, that a column of air, whose base is one square inch, and whose height is that of the atmosphere, weighs about fifteen pounds. Consequently, it follows, that an horizontal surface sustains a weight or pressure amounting to fifteen times as many pounds as there are square inches in its extent. If then we have a solid substance with an horizontal surface, for example, a piston placed in a vertical cylinder, and that we are able by any means to remove all resistance from below it, it will be forced down by a mechanical pressure of fifteen times as many pounds as there are square inches in its upper surface, and in this way a mechanical agent of a power limited only by the magnitude of the piston will be obtained.

But peculiar difficulties in giving efficacy to this power arise from two

other properties of air, its fluidity and its elasticity. By the former it transmits the pressure arising from the weight of the incumbent atmosphere equally in every direction, so that it is not only an horizontal surface which sustains the pressure of 15lbs. per inch, but surfaces in all possible directions and positions suffer the same pressure. Also, by reason of air being an elastic fluid, it expands itself, so as to fill every open space not actually occupied by other bodies, whether solid or fluid. Consequently in the case we have supposed, air must occupy the space in the cylinder below the piston as well as above it, and if so, the fluidity of the air will transmit the pressure arising from the weight of the atmosphere to the lower surface of the piston with undiminished force, and thus we shall have the piston pressed upwards and downwards with equal forces, and consequently no mechanical advantage will be obtained.

(54.) It appears, therefore, that before the weight of the atmosphere, whether acting immediately downwards, or transmitted laterally, obliquely, or upwards, by means of its fluidity, can be used as a mechanical agent, it is indispensably necessary that the air be removed from the other side of the body on which this weight or pressure is designed to act. Recurring to the example of a piston in a cylinder, it is necessary to remove the air from one side of the piston before its weight or pressure can take effect upon the other side. Now if this removal, as is often the case, be effected by mechanical means, it must, on the slightest consideration, be quite apparent that it will require exactly as much force to remove the air from one side of the piston, as will be subsequently gained by the pressure of the atmosphere on the other side. Suppose, for example, that from two feet in length of the cylinder below the piston, the air which it originally contained be withdrawn by mechanical force. To effect this will require a force of at least 15lbs. for every square inch in the section of the cylinder, acting through the space of two feet, and after it has been effected the piston will be forced into the vacuum with exactly the same force.

It appears, therefore, that in order to render the atmospheric pressure an available mechanical agent, a vacuum, or a partial vacuum, must always be produced; and further, that if this

vacuum, or rarefaction, be produced by mechanical means, no power will be gained, since it will always require as much force to accomplish this, as will be exerted by the atmospheric pressure when it has been accomplished. In the use of mechanism, however, the gaining of power is not always the end to be attained. It is frequently a matter of great convenience, and, in a certain sense, of great mechanical advantage, to be able, by a power which acts in some particular manner, to obtain another equal power, whose mode of action may be different, and better suited to the purpose to which mechanical agency is to be applied. This is, in fact, the case in every instance in which the atmospheric pressure is obtained by mechanical rarefaction, and in every such case the atmospheric pressure should not be looked upon as the prime mover, but rather as an intermediate agent deriving its entire efficacy from that power, whatever it may be, which is used to produce the rarefaction. A most obvious instance of this may be observed in the common suction-pump, described in our Treatise on Pneumatics, Art. 40. This machine is introduced into that treatise, not because it owes its original mechanical efficacy to the pneumatical principle of atmospheric pressure, but because this principle is involved in the detail of its operation. In this machine, the first mover is the power, whatever it be, which works the piston. This power, at the commencement of the operation, produces a rarefaction in the space between the piston and the surface of the water in the well. The weight of the atmosphere acting upon the external surface of the water in the well forces into the pump-barrel just so much water as the power applied to the pump-rod would have been capable of lifting, were it immediately applied to that purpose. This appears very evident from the investigation contained in Art. 42. PNEUMATICS.

What we have observed of the suction-pump may be applied in general to all cases where the atmospheric pressure receives its efficacy from mechanical rarefaction. Strictly speaking, we cannot consider the atmospheric pressure as a first mover at all; the first mover is the cause, whatever it be, whether mechanical or otherwise, which produces the rarefaction.

(55.) By that quality called inertia, air, when in motion, exerts a force upon

any solid body, which obstructs its course. (PNEUMATICS, Art. 9.) This force is used as a first mover, by means analogous to water-wheels, viz. by flat surfaces exposed to the impact of the wind, by that impact made to revolve on a centre. When this rotatory motion is once produced, it may be easily transmitted, and modified by machinery, and applied to any required purpose.

If the sails of a windmill be constructed in a manner analogous to the float-boards of an undershot-waterwheel, the plane of the wheel must be in the direction of the wind; and it is evident that one half of the wheel must be sheltered from the action of the wind, for otherwise equal forces would tend to turn the wheel in opposite directions, and no motion would ensue. Besides this, the wind would act with very little advantage on those sails whose planes are nearly in its own direction. For this reason windmills of this construction are not generally used. On the other hand, the arms which carry the sails revolve in a plane facing the wind. In this arrangement, if the sails were in the same plane with the arms, the wind would fall perpendicularly upon them, and merely press the arms against the building perpendicular to the plane in which they are designed to move. on the other hand, the sails were perpendicular to the plane in which the arms move, their edges would be presented to the wind, and would, therefore, offer no resistance, and there would be no motion. In order to make the arms revolve, the sails must, therefore, be placed in some direction intermediate between those of the wind and the plane in which the arms revolve.

If,

The most accurate experimentalists and the most profound mathematicians have instituted inquiries, practical and theoretical, to determine that position which should be given to sails of windmills, in order to produce the best effect. Most of the theoretical calculations on this difficult subject have been vitiated by conditions and hypotheses, which are inadmissible in practice. The angle which Parent and others deduced from mathematical calculation to be the best at which the planes of the sails could be inclined to the axis of motion or the direction of the wind, was found to be one of the worst in Mr. Smeaton's experiments. The position determined by Parent, was the best

at the beginning of motion, but his calculation proceeded on the supposition, that the wind struck the sail at rest, and was, therefore, inapplicable to the continuance of its action.

When the wind acts upon the sail in motion, it is necessary to take into account the velocities both of the sail and the wind. For if the sail moved before the wind with a speed equal to that of the wind itself, no effect would be produced. The effect will depend on the difference of the velocities, that being the velocity with which the wind strikes the sail. Now as the obliquity of the sail to the wind should depend on the force with which the wind acts upon it, and as those parts of the sail which are nearer to the centre of motion move more slowly than those which are more remote, it follows that the position of the sail should vary at different distances from the centre of rotation. From several experiments executed on a large scale, Mr. Smeaton concluded the following positions to be among the best. Let the radius be conceived to be divided into six equal parts, and let the first part, beginning from the centre, be called 1; the second 2, and so on; the extreme part being 6.

(56.) The last property, in virtue of which we have stated that air becomes a mechanical agent, is its elasticity. The nature of this property, and the laws by which it acts, have already been explained in our treatise on PNEUMATICS, Chap. IV. When this property is considered as a mechanical agent, it is subject to nearly the same observations as we have already applied to the weight and pressure of the atmosphere. To give effect to the elastic force of air, it is necessary that it should predominate over the weight of the atmosphere, a pressure to which, as we have before stated, all bodies in their ordinary state

The general resemblance which the best form of windmill sails bears to the arrangement of the feathers in the wings of birds is very striking, and one of those beautiful instances of the truly mathe matical principles on which the works of the creation are constructed.

are subject. If increased elasticity be communicated to air by mechanical means, it must be by compression or condensation. It is evident, that in this case, no power whatever will be gained, in as much as it will require exactly as much power to produce a given degree of condensation in a given quantity of air, as is equal to the increased elasticity with which that condensed air will be endued. However, in this case, as in that of the ordinary use of atmospheric pressure, although no power be gained by mechanical condensation, yet considerable advantage may be derived from this as a method of transmuting one power into another, and as means of accumulating the effects of a small intermitting power, so as to convert it into a severe or continued pressure.

We have already seen an instance of this in the air-gun. (PNEUMATICS, Art. 52.) If we attempted, by mere manual force, to project a bullet, we should find our efforts attended with but a small effect; but if it were possible to unite in one impulse the combined force of a vast number of separate impulses, we should produce the desired effect. The air-gun, then, is nothing more than a contrivance, by which a great number of separate exertions of our strength are accumulated and combined, and made to act simultaneously. The process of condensing the air is conducted by a number of successive muscular exertions; and the elastic force which the condensed air thus receives, is exactly equal to the sum of these several exertions of human strength, and may, therefore, be considered as a magazine in which these separate exertions are contained in such a manner, that their combined intensity may be, at any moment, applied to the ball or other missile to be projected.

In this instance, the object to be attained is the production of a severe but instantaneous effect. The elastic property of air is also sometimes used to convert an intermitting or reciprocating action into a continued and uniform one. The fire-engine, described in our treatise on PNEUMATICS, Art. 48, is an instance of this. The force which works the pistons is intermitting or reciprocating, while the pressure of the condensed air in the air-vessel, produced by that intermitting force, is continuous in its action. Its total action, however, must be precisely equal to the sum of the forces which depress the pistons.

The force of condensed air may be applied to produce a severe and continued pressure, on a principle similar to that of Bramah's hydrostatic press, already described. Let B (fig. 26.) be a

fig. 26.

D

large cylinder, in which a solid piston or plunger moves air-tight. Let DE be a small tube, having a stop-cock at G, and terminated in a screw at E. Let C be a strong metal ball, capable of bearing an intense bursting pressure, having a small tube, terminated by a screw at E, by which it may be connected occasionally with the tube DE, or with a condenser, (PNEUMATICS, Art. 38,) and also furnished with a stopcock at F.

By means of a condenser screwed upon E, the stopcock F being opened, let air be forced into the ball Č, until it presses against the cock F, when closed, with a force of more than one ton. The condenser being then removed from E, the air cannot escape, the cock F being closed. Let the ball and tube CFE be then screwed upon the tube DE, and the cocks F and G both opened. The condensed air will expand through the tube D, and fill the part of the cylinder below the piston. If, after this expansion, the elastic force of the compressed air is such that it would press on the stopcocks with a force exceeding that of the atmosphere by one ton, there will be an effective pressure against the piston A, of as many tons as the number of times that the section of the tube D is contained in that of the piston. Suppose the section of the tube to be a quarter of an inch in diameter, and the piston to be one foot, the pressure on the piston will then be equal to 2304 tons.

In this case, like all the former, air is only used as a convenient means of accumulating mechanical force; and ought not, properly speaking, to be looked upon as the prime mover. As in using the weight or pressure of the atmosphere, we consider that cause, whatever it be, that produces the vacuum, or the rarefaction, to be properly the prime