1. Under the action of the powder pressure the gun and its top-carriage acquire a velocity opposite in direction to that of the projectile, and there results a recoil the extent of which depends upon the resistance opposed to it. We will first consider the case of free recoil, since upon its solution depends that of the case of resisted recoil.
2. FREE RECOIL.—Let — be the entire mass which moves in recoil, and let v' and s' be the velocity acquired and the space passed over in the time t from the beginning of motion; also let P be the total effective pressure (gas pressure diminished by the resistance of friction and forcing) on the bottom of the bore at the same time t.
These equations, of course, are only true up to the time when the pressure P becomes zero. At that time, which we denote by the maximum velocity of free recoil (v'.,) has been attained, and thereafter the velocity remains constant.