482 Dr. J. Robinson on Konig's Theory of the 



we have 



V L 2"D6 7rC l 7rC 2 T 



Z^giritfB cos _cos^-^ 



-Io = - 4 (3cos0-5cos 3 0), 



where 6 is the angle between the Z axis and the direction 

 of r. 



Therefore 



jj ^irW'WxW^ cos 6 (3 — 5 cos 2 #) 

 Z/j— ^ 



The same expression is got for Z 2 . 



This only differs from the expression when the velocities 

 are the same in the terms w 1 and w 2 , i. e. we have io x w 2 in 

 place of w 2 . We can thus apply the treatment given by 

 the author*, if we make this substitution of Wi w 2 for w 2 . 

 Then we find that the force exerted by one whole ripple A 1 

 on the next one A 2 is 



-p _ 2n 1 iro-T( 6 ?v 1 w 2 



*i ^~z » 



o- being the density of the gas in the tube and a 12 the distance 

 apart of the ripples A x and A 2 . If the distance apart of the 



A » \ ** 



-7c 



ita,,,-* 



c 23 



ripples A 2 and A 3 is « 23 , the force exerted by the ripple A c 

 on Ao is 



^ _ 2n S 7To-Ji G w 2 iv o 



*2—~ ;n 9 



o*8 



if ni is the number of small spheres per unit lenoth of 

 A 1? &c. 



* Zoc. «Y. p. 182. 



