372 Dr. N. Ernest Dorsey on the Surface- Tension of 



mentioned Lord Rayleigh's appeared to be the most promising, 

 and is the one finally adopted. 



Method of Ripples. 



This method is based on the relation between the surface- 

 tension of a liquid and the velocity of propagation on its 

 surface of a train of small waves of given period. This was 

 deduced by Lord Kelvin * for the case of infinitely small 

 waves on the surface of a perfect liquid of given depth. His 

 formula is 



N -12tt + P \ r X ' 



Here V is the velocity of propagation ; X is the wave-length ; 

 T is the surface-tension ; p is the density ; h is the depth of 

 the liquid ; and g is the acceleration of gravity. If n is the 

 frequency of the waves, we can write this equation thus : 



I = p< -^ — cotn — -. — § i - 



^ I 2tT X 47T 2 j 



NOW 4 ^ 



cotn -=-— = -^- h = 1 + 2e a approximately 



X l-e~T 



if h is large. In this work It is never less than 1*1 cm., and 



4zirh 

 X is never as great as 0*5 cm. Hence —— <fc 25 ; 



A. 



.'. COth^ > 14 26-25. 

 A, 



This shows that we may consider 



coth -r— = 1, 

 and may write the equation 



Lambf gives the more exact formula for the case of a liquid 

 of infinite depth, 



y- \P-P' ffa | 2ttT 1 



or 



p + p' 2tt (p-p')\/' 



* Phil. Mag. [4] xlii. p. 375 (1871) 

 t Hydrodynamics, p. 446. 



