338 



Mr. A. Mallock. 



The centre of gravity of the rifle is just an inch below the axis of 

 the barrel, and, taking the accelerative pressure on the shot as 

 2250 lbs., the bending couple at the first instant is 187 ft.-lbs. 



2 2 2 



Also Ai = _ , A 2 = — , A 3 = — . 



Thus 



p dA 1 = 118 ft.-lbs., p dA 2 = 59 ft.-lbs., p dA s = 40 ft.-lbs., 



Table I. 



O^dAi = 



133' 



6 2 po(lAi = 



90'-5 



%? dAi 



= 66'-5 



OiPodA-2 = 



66'-5 



OopodAo = 



45' 



3 p dA 2 



= 33'-3 



Bip Q dA z = 



45' 



2 p dAs = 



30' 



6 s p dA s 



= 22'-2 



These are the angular displacements which the muzzle would 

 undergo if in each case it experienced the full statical effect of couple 

 corresponding to the first, second, and third term of the series repre- 

 senting the explosion curve acting so as to deform the system in the 

 first, second, or third mode. 



Owing, however, to the position of the point of application of the 

 couples with reference to the nodes of the various modes (see I, and 

 figs. 2 and 3), it appears that for the first mode the couple will cause 

 0*88 of its full effect, as for this mode the node Ni" coincides nearly 

 with the point of application of the couple. The nodes N 2 ' and N 2 " 

 of the second mode fall at such a distance from P as to reduce the 

 effect of the couples to about 0*35 of the above value. And the reduc- 

 tion is about 0*6 for displacements in the third mode. 



The following table is an approximation to the actual values of — 



Table II. 



, 



n. 



1. 2. 



3. 



1 



2 

 3 



! 



117' j 31' -5 

 59' -5 | 15' -8 

 39' 5 10' -5 



39' 

 20' 

 13' -2 



To determine the periods Ti, T 2 , T 3 , namely the natural periods of 

 the rifle in the first, second, and third modes, experiments were made 

 by tapping the barrel so as to excite the modes in question, and deter- 

 mining the notes emitted by comparison with tuning forks. The 



