﻿690 



Dr. J. R. Wilton on Ripples. 



The following table will show that surface tension is 

 always of considerably greater effect than viscosity *. 



Wave length, 

 X. 



Suface Tension 

 Correction, 



K. 



Viscosity 

 Correction, 



T. 



Eatio, 



k/t. 



9*4 cm, 



033 



•075 

 •30 



1-2 



4-8 

 19 



•0004 

 •0011 



•006 

 •03 

 •11 

 •36 



80 

 68 

 50 

 40 

 44 

 53 



6-3 „ 



31 ., 



1-6 „ 



•8 „ 



•4 „ 





Thus k/t is never less than 40, so that we may neglect 

 viscosity even for small ripples without risk of serious error, 

 provided always that the condition that X/'004z8 is to be 

 " large " is not forgotten")". But for longer waves the correc- 

 tion due to the formation of air waves is of the same order 

 of magnitude as k : thus, when \ = 35 cm., 



k= 1/400, 



nearly. Hence, if we include T but omit the other two 

 corrections, we must apply our results only to ripples and 

 waves of from, say, 1 mm. to 20 cm. in length, so that the 

 form of waves which ordinarily occur in the open sea 

 will not be affected by any of these considerations. We 

 shall, actually, apply our formulae only to ripples of from 

 5 mm. to 25 mm. in length. With this understanding we 

 proceed to determine the form of a wave when surface 

 tension is taken into account. 



Let R be the radius of curvature of the wave : R will be 

 reckoned positive when the concavity is upwards. Then, if 

 II is the atmospheric pressure, the pressure along the free 

 surface, within the water, is 



j9=n-T/R, 



* It will be observed that for ripples, down to half a centimetre in 

 length, we may still speak of the correction due to viscosity, but it is 

 absurd to speak of the " correction " due to surface tension, for the latter 

 is the predominating influence in determining the form of ripples of 

 2 cm. lengthy or less. 



f The viscous time factor is, however, far from being negligible for 

 short ripples. 



