368 ON THE MEASURE OF THE FORCES OF BODIES 
centre of gravity. Thus in the example herein given, if A contained 100 times the 
mass of B, the spring would be divided by the point a so as to give 1 part to A and 
100 parts to B; and if the mass of A be made infinite with regard to B, so as to be 
immovable, as in the plane, Fig. 3, the point a coincides with the end of the spring, and 
all the force is communicated to B. 
A very striking example for illustrating the principles of this analysis, and displaying 
the force of elasticity in its highest form, may be imagined under the following order of 
preparation. Divide the charge of powder, intended for a piece of ordnance, by a dia- 
phragm of iron, or any substance that will stand the heat, no matter how light and thin 
it be, into two parts, that shall be to each other as the weight of the gun is to that of 
the ball. Load the piece by placing the end of the cartridge containing the smaller 
portion of the charge at the bottom of the chamber, the ball being placed over the 
larger portion of the charge. Now if the fire be communicated to both parts of the 
charge at the same instant, the diaphragm must, however light, remain perfectly station- 
ary in space, being subjected to equal pressures in opposite directions upon its two sides, 
while the gun and the ball are driven from it in opposite directions, with velocities 
inversely as their weights. Here, as the cannon is often 200 times as heavy as 
the ball, the quantity of powder before the diaphragm, and actually expended in pro- 
ducing the motion of the ball, is 200 times as great as that expended in producing the 
motion or recoil of the gun, though the pressure upon both is the same in intensity and 
in time; but the quantity of the foree communicated to the ball must be, under these 
conditions, directly as the powder expended to produce it; and yet if we take the force 
. of the ball and that of the gun in its recoil, respectively, as the product of the mass 
into its velocity simply, we shall make them equal, one to the other; that is, 1 oz. of 
powder acting from one side of a plane, equal to 200 oz. acting from its opposite side. 
- But, by the measure of the square of the velocity, we have, mass of ball 1, velocity 200, 
and.1 X 200? = 40,000 for the force of the ball; mass of gun 200, velocity 1, and 
200 X  1*— 200 for the force of the gun’s recoil; which corresponds exactly with the 
expenditure of the powder. It may again be observed that these forces correspond, 
inversely, with the masses; for 200: 40,000 :: 1: 200. 
It can hardly be necessary to remark, that in any of the preceding instances we 
may reverse the direction of the motion, and consider the bodies as made to approach 
towards each other, rather than to recede from each other. Thus if A and B, when 
placed asunder as in Fig. 2, are drawn towards each other by a distended spring, 
or by any kind of attraction, or gravitation, inherent in the bodies themselves, the 
force excited in, or transferred to, each will be inversely as the masses of the bodies 
