Vibrations of Rifle Barrels. 



331 



Approximately, the equation to the curve between the nodes C and D 

 for the mode of vibration which has these nodes may be taken as a 

 simple harmonic function of x 



or y = Cqq sin 2tt _ ; 



(i 



hence the displacement at P due to F acting at Q, and the displacement 

 at Q due to F acting at P, are each equal to 



CF sin 2tt - , 



a 



' pd a-2x ■ x /1N 



or y QV = x S]n 27r - 



2 x (a -x) a 



In a rifle the point of application of the couple is settled by the 

 nature of the connection between the stock and the barrel, and it is a 

 matter of great difficulty to make certain how the strains are dis- 

 tributed. The actual maximum pressure in the barrel which is spoken 

 of as " chamber pressure " is known for various small arms and various 

 explosives with considerable accuracy; but the curve of pressure in 

 terms of the travel of the shot along the barrel is much more difficult 

 to ascertain. In this paper, therefore, I shall consider several types of 

 such curves in order to show what effects are to be looked for as the 

 pressure curve changes its character. 



The condition fulfilled in each of the pressure curves considered is 

 that each must give the same muzzle velocity to the shot by acting on 

 it through the length of the barrel, and in the numerical results given 

 the velocity and weight of the projectile are taken as 2000 feet per 

 second and 215 grains respectively, with an effective length of barrel of 

 2-3 feet, these being nearly the velocity, weight, and length of barrel 

 used in the Lee-Enfield rifle. 



The simplest case of all (and the furthest removed from truth) is 

 that of a uniform pressure acting on the base of the shot throughout 

 the length of the barrel. 



Here we have, if po is the acceleration, v m the muzzle velocity, % the 

 time taken*by the shot in reaching the muzzle, and / the length of the 

 barrel, 



Vm = Po® (2), 



fir 2 



« = 2 - (5), 



VOL. LXVIII. 2 A 



