the Conservation of Force. 117 



viva, which depends on the squares of the velocities, will be 

 quadruple that of either wave taken singly, and the vis viva of 

 the system of two waves at the moment of complete occulta- 

 tion will be double that of the system of two waves before 

 interference. 



If, from the case of oppositely moving waves in a tube 

 filled with air, we turn to that of opposing waves propagated 

 along a stretched cord, we shall arrive at analogous results. 



Suppose, for instance, that we have, moving in opposite 

 directions, two waves, each of which till the moment of inter- 

 ference is propagated unalterably, the displacement in each of 

 which is in the same plane, and on the same side of the 

 position of rest of the cord. Suppose that the waves are of 

 the same length, that each has a single position of maximum 

 elevation (viz. at the middle point), and that at equal distances 

 from the centre the elevation above the position of rest is in 

 each the same. 



Thus, before interference, the particle-velocity in the front 

 half (reckoned in the direction of propagation of either wave) 

 will be in a direction from the position of rest of the cord, 

 while in the hinder half of each the velocity will be towards 

 the position of rest of the cord. 



Whence it follows, on the principle of the superposition of 

 small motions, that, when the waves are in a state of complete 

 occultation (that is, when the centre of the one is coincident with 

 the centre of the other), the particle-velocity throughout the 

 whole of the portion of the cord over which the disturbance 

 extends will be zero, at the same time that the distance of 

 each point from its position of rest will be double what it 

 would be at the same distance from the centre of either wave 

 taken singly. In this position of the two waves, therefore, 

 the vis viva will entirely disappear. 



If, the waves being in other respects as described in the 

 last paragraph, the displacement in the one lies wholly on the 

 one side of the position of rest of the cord, while in the other 

 the displacement lies wholly on the opposite side of the same 

 line, the result of the interference will be different. In this 

 case the portion of the cord occupied by the interfering waves 

 at the period of complete occultation will be in the position of 

 rest, at the same time that the particle-velocity at each point 

 will be double of that at the corresponding point in either 

 wave taken separately. Thus the " sum of the tensions " will 

 be zero, while the sum of the vires vivo3 in the system of two 

 waves will be double of what it was before interference. 



It is difficult to conceive of any case of the point-blank 

 interference of two waves where the results would not be 

 similar to those which have been above pointed out. 



