Chap. XI:

MECHANICS.

919

The metre is 3-28 feet, the kilogramme 2*2 pounds, the kilogrammetre 7*216 dynains,and the horse power is 525 dynams, which nearly coincides with Bolton and Watt’sdynamical unit.

Mechanical power is the term used by Smeaton ; momentum of activity by Carnot; dynamiceffect by Monge, Hachctte, Coulomb, and others, all signifying the quantity of action ormechanical labour.

It is evident that labour is judged of by its quantity, or rather that of the work per-formed, which must be proportioned to the # mechanical labour required. Labour, then, isthe quantity of action, which pays itself in force.

Labouring force is measured by the product of the resistance overcome, and the spacethrough which it is overcome.

Parallelogram of Forces. Independently of the action of simultaneous forces, the actionof force on a body, whether at rest or in motion, is always the same, and impresses on itthe same degree of velocity in both circumstances. A body left to itself is moved bygravity with the same degree of velocity at each instant of time : when it leaves thestate of rest by having motion imposed upon it by force of any kind, as a shell, in itspassage through the air, it describes a parabola; the velocity of the projectile at each in-stant is always the resultant of the velocity which it received at the instant immediatelypreceding that which we have considered; and the very slight velocity which gravityimpresses on it during the interval of time, also very small, separates these two suc-ceeding instants: thus where two forces are applied to the same body, they will impressupon it at each instant, and simultaneously, the degrees of velocity common to each, andthese degrees, according to the general laws of nature, are proportionate to the intensity ofthe forces.

A single force which is equivalent to two or more forces is called the resultant, andrelatively to it, they are called the components.

A force acting on a body at A, in the directionof A B, as well as in that of A C , when theseforces are equal, and act together, the body willin the same time be moved through the distanceA D, or the diagonal of the parallelogram. Theforces in the direction A B, AC , AD are re-spectively proportional to the lines which representthem. The two oblique forces A B, AC , arc equivalent to the single direct force A D,which may be compounded of these two, by drawing the diagonal of the parallelogramA D.

A body acted upon by two forces at the same time will pass through the same point, asit would do if these forces were to act separately and successively : and if any new motionbe impressed, this does not alter its motion in lines parallel to its former direction.

Suppose three forces A, B, C, acting against oneanother at the point D, and whose direction is on thesame plane ; if they are all in equilibrio their forceswill be to each other respectively as the three sidesof a triangle, drawn parallel to their lines of direction,

DI, Cl, CD. The three forces A, B, C, are to eachother as the sines of the angles through which theirrespective lines of direction pass when produced.

DI : Cl : : CDB : CDAand C I : C D : : C D A : A D B.

It must be evident that if the force C alters itsdirection from that applied in either direction, itsdiagonal and corresponding sides are affected, theparallelogram DHCI is changed in form, and thewhole proportions vary. The united effects of two Fig. 1226.forces moving in the direction of the sides of aparallelogram are expressed by a diagonal drawn in that figure.

If a body acts against another by any force whatever, that «_

force is exerted in the direction of a line perpendicular to thesurface on which it acts. Suppose the ball B strike the body C in *—an oblique direction, so as to form the angle A B D : the magni- Dtude of the stroke will be directly as the velocity, and the sine ofthe angle of incidence A B D, and the body C receives the strokein the direction E B, perpendicular to the surface D B.

The magnitude of the stroke is represented by BE, and themotion impressed on the body that receives it is equal to the a

magnitude of the stroke, and to the motion lost in the strikingbody.

Fig. 1227.

Fig. 1225.

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