CAFILLABY ACTION. 



velocity is a minimum when 

 and the minimum value is 



For waves whoee length from crest to crest is greater than X, the prin- 

 cipal force concerned in the motion is that of gravitation. For waves whose 

 length is less than X the principal force concerned is that of surface-tension. 

 Sir William Thomson proposes to distinguish the latter kind of waves by the 

 of ripples. 



When a small body is partly immersed in a liquid originally at rest, and 

 horizontally with constant velocity F, waves are propagated through the 

 liquid with various velocities according to their respective wave-lengths. In front 

 of the body the relative velocity of the fluid and the body varies from F 

 where the fluid is at rest, to zero at the cutwater on the front surface of the 

 body. The waves produced by the body will travel forwards faster than the 

 body till they reach a distance from it at which the relative velocity of the 

 body and the fluid is equal to the velocity of propagation corresponding to the 

 wave-length. The waves then travel along with the body at a constant dis- 

 tance in front of it. Hence at a certain distance in front of the body there 

 is a series of waves which are stationary with respect to the body. Of these, 

 the waves of minimum velocity form a stationary wave nearest to the front 

 of the body. Between the body and this first wave the surface is compara- 

 tively smooth. Then comes the stationary wave of minimum velocity, which is 

 the most marked of the series. In front of this is a double series of stationary 

 waves, the gravitation waves forming a series increasing in wave-length with 

 their distance in front of the body, and the surface-tension waves or ripples 

 diminishing in wave-length with their distance from the body, and both sets 

 of waves rapidly diminishing in amplitude with their distance from the body. 



If the current-function of the water referred to the body considered as 

 origin is $, then the equation of the form of the crest of a wave of velocity 

 tr, the crest of which travels along with the body, is 



d\(> = wds 

 where da is an element of the length of the crest. To integrate this equation 



