Manchester Mcvwtrs, Vul. I. (1906), No. 8- 27 



would seem not unlikely that the solutions in the case 

 of other irrotational waves are susceptible of similar 

 simplification. 



The Tractical Limit of the Height of Waves. 



In this paper I have not considered either the origin- 

 ation of the wave, nor its propagation into still water, but 

 only the circumstances under which uniform propagation 

 is possible ; and a differential motion of drift is one 

 such circumstance. The magnitude of this drift of the 

 fluid which diminishes from the surface downward is 

 worth a closer consideration, for it appears probable that 

 the practical limit of the height of deep water waves is 

 effectively determined by this magnitude and not by the 

 theoretical limit to the extreme shape of the wave. 



When the steady motion with which we have started 

 is reduced to a progressive wave motion, the measure of 

 the rate of this drift at the water surface is, by (27). 



or, on simplification, 



[/e+^h'+r^-hy . . . (44). 



If we give to // the extreme value "323 which we have 

 approximately assigned to it, this will turn out to be 

 about 'iSc, or nearly one-sixth of the velocity of the 

 wave. If we give h the value -25, the rate of drift falls to 

 •07^ about, that is to less than one-half of its value in the 

 theoretically extreme case. 



After allowing for the fact that the series used in (44) 



