Discontinuous Wave-Motion, 51 



related that at the two points x = and ,v = l, -~ has always 



zero value, the velocity at any point on the finite string in 

 the actual case can be found for any instant during the 

 vibration by summation of the values of the two functions. 

 At time t = 0, in the experiment described, the initial dis- 

 placements of the string from the position of equilibrium 

 are everywhere zero, and we may therefore take half the 

 initial velocity at each point for the positive velocity- wave 

 and the other half for the negative velocity-wave, and the 

 two wav.^s miy be constructed in the manner shown in the 

 .figure below. 



<- 



By superposing the waves after shifting them through 

 equal distances in opposite directions, the character of the 

 motion at every point on the string can be found by inspec- 

 tion, and the configuration of the string can be found from 

 the known velocities and the times during which they subsist. 

 The geometrical construction shown in the figure emphasizes 

 the fact that the case is essentially one of the propagation of 

 a discontinuous wave. 



The experiments described in this note were first made at 

 the Presidency College, Madras. 



The Indian Association for the Cultivation of Science, 

 Calcutta, 27 th August, 1915. 



E 2 



