Ripple Formation in Kundt's Tithe. 

 The kinetic energy of the system = 



T=K.E. of the spheres + ^(V + V^O 



477 



wnere 



32 f y k 



3*- B 2 - I. 



Wi? ? J ij w*i are the components of the velocity of the 1st sphere. 

 m 2 , u 2 , it' 2 „ „ ,. 2nd 



a 1? /> b c'i are the coordinates of the centre of the 1st 

 a 3 , b 2 , c 2 „ „ „ 2nd 



X 1? Y 1? Z x are the components of the force on the 1st 

 X 2 , Y 2 , Z 2 „ „ ,, 2nd 



B-x and R 2 are the radii of the spheres. 

 r is the distance between the centres of the two spheres. 



Now Kirchhoff did not integrate these equations generally 

 for special values given to the forces, but he calculated the 

 forces necessary to produce uniform motion. He assumed 

 u u V],w u ?/ 2 , v 2 , w 2 constants, and so obtained the potential 

 of the forces X 1? Yj, Z x to be 



^2 1. ~cs 2 - 7s 2 - 



-ttR.'Rs 3 (< ^ + »i 2 5 , ? + "V ~" 

 L 0«" Olr Oc- 



V± yl y* \ 



Konig * makes this the starting-point for his theory of 

 the formation of the ripples in the Kundt tube experiment. 



* Wied. Ann. xlii. p. 549 (1891). 



