Vibrations of Rifle Barrels. 



329 



vibrations of the system must be supposed to exist as, in combination 

 with the forced vibration, will satisfy these conditions. The subse- 

 quent motion will then be determined by taking the sum of the forced 

 and free vibrations as long as the arbitrary couple acts, and when this 

 has ceased to act, the sum of the free vibrations only. 



If the system could be represented by a uniform rod, the solution 

 might at once be expressed in symbols, since the theory of the trans- 

 verse vibrations of rods and tubes is well known. When we come, 

 however, to a "system" like a rifle, although in many respects its 

 behaviour may be compared with that of a uniform elastic rod of 

 " equivalent length," the ratio between the periods of the vibrations of 

 its various modes are altered, and recourse must be had to experiment 

 to determine both the natural periods and the position of the nodes. 



As far, however, as the rifle can be considered as being represented 

 by an equivalent rod, it must be looked upon as being free at both 

 ends at the moment of firing, because the motion communicated to the 

 rifle is so small at the time the shot leaves the muzzle, that the con- 

 straint which hands and shoulders can impose on it is negligible com- 

 pared to the acceleration forces called into plajr by the explosion. 



This being so, the slowest vibration of which the system is capable 

 is that with two nodes. The next in order of rapidity will have three 

 nodes, and so on, as shown in the figures 1, 2, 3. 



Fig. 1.— Mode I. 



Fig. 2.— Mode II. 



Fig. 3.— Mode III. 



