Ripple Formation in Kundt's Tube. 483 



Equating F 1 and F 3 for the equilibrium o£ the ripple A 2 

 we get 



niWiW 2 _ n 3 w 2 w 3 



To a first approximation, putting n 1 = n 3 we get 



/«23\ 3 = W 2 W 3 



\a 12 ) Wiw 2 



For the forces between the other ripples we get similar 

 equations : — 



( au t — WzW * 



\a 2 J w 2 io 3 





Forming the product of the terms on the left, and of those 

 on the right-hand side of these equations, we get 



/ a r .r+i\ 3 _ W r W r +i 

 \ a 12 ) " W\ it'* 



-©' 



approximately. 



If a l2 is the distance apart of two ripples at an antinode, 

 and a r .r+i this distance at a distance k from an antinode, 

 we have 



V a V2 J V Wa ' 2 I 



IT l\ 2 



and , 



a r.r+l 2 7T IC 



= COS3 — = . 

 «12 2 / 



This is a more rigid investigation than thai in the Phil. 

 Mag. for July 1909, where it was found that 



a r.r + l + IT k 



2- = COS* - ; . 



012 2 / 



There the investigation was based on the following assump- 

 tion : — 



Konig's theory was limited to the case where both spheres 



2 12 



