The foregoing calculation however involves an assumption not in exact conformity with actual conditions, by taking for granted that the _centre of gravity_ of the rifle is in the line of the axis of the barrel, while in fact this centre is almost always lower, and therefore the kick of the recoil acts in part as a turning-over push, tending to tilt up the muzzle of the gun, and for that reason the firer must hold the weapon very firmly or he will miss his aim. When such a rifle as we have supposed is fired, say from the shoulder, it would follow from the above calculation that the backward kick of the recoil is equivalent to a blow from a 10–lb. weight moving at the speed of 7½ ft. per second. This would certainly be a very uncomfortable experience, but the backward momentum must be met somehow. We have supposed that the gun is free to move, but we know the firer presses it firmly against the muscles of his shoulder, and the stock of the gun is spread out and provided with a smooth hollow heel plate, so that any pressure from it is felt as little as possible, especially as the muscle against which it is applied acts as an elastic pad. With the rifle thus firmly held we may regard the marksman and his rifle as forming only _one mass_, and the centre of gravity of this being now much below the axis of the barrel, the effect of the recoil tends to overthrow the man backwards; but he learns to resist this by standing firmly, so that the elasticity of his whole frame comes into play; and besides this, the mass factor of the momentum being now so large, the velocity factor becomes comparatively insignificant. Although the momenta of gun and projectile are, according to Newton’s law, _equal_ and opposite, the case is very different with regard to their _energies_, or powers of doing work, for the measure of these is jointly mass and _the square of the velocity_. The _energy_ (_vis viva_) of a body of weight in pounds = W, moving with the velocity of v feet per second is always Wv^2/64·4, that is, it will do this number of foot-lbs. units of work before it comes to rest. It would require too much space to demonstrate and fully explain here what this means, but the reader may refer to our index under the entries “Energy” and “Work,” or to any modern elementary treatise on dynamics. If the calculation be made of the energies of the ball and of the rifle due to our calculated velocities of recoil, it will be found that that of the ball is 160 times greater than that of the other, and the ball possesses this energy in a much smaller compass. [Illustration: FIG. 80.—_Trajectory of a Projectile._ ]