70 Mr Larmor, On the Influence [April 28, 



Thus when the depth is so great that the ripples do not disturb 

 the bottom 



1 dC .. 



<b = =- e cos mx, 



T m at 



as this leads to zero velocity at a great depth. 



dV 



The electric charge diminishes the surface pressure by — a -^— , 



— ( o— ) > or approximately j— ( -=- j , which is equal to 

 (1 + 26m cos mx). 



or 



4"7r V On J 



A 



4tir 

 The surface tension T diminishes the surface pressure by 



d 2 u 

 T ■—-, , or — TCm* cos mx. 



dx 2 



Now the equation of fluid pressure is 



£= const. +gy-^ -h v ; 



so that we must have at the surface, approximately, 

 — - — (1 + 26m cos ??z#) H cos ma? 



47Tp p 



1 cf 6 

 = const. + qu cos m« ^ cos ma?, 



which requires 



d 2 „m 2 /_. go A\ 

 ctr p V ^ 2777 



This gives the periodic time 



m ' / V m 27r 



A,p 27T p 



where A, is the wave length ; and the velocity of propagation is 

 277-T g\_87ra 2 Y 



\p 2tt p 



The result is in fact the same as would be produced by a decrease 

 in surface tension of amount 



8TT(i 2 /m, or 4o- 2 X,. 



