136 WAVES OF THE SEA 



both Stokes and von Helmholtz showed that for 

 a single series of waves of permanent type the 

 condition under which greatest steepness could be 

 attained was that the speed of wind and wave should 

 be equal. 



Now, according to observation, the steepest 

 wind-waves in deep water are formed where the 

 speed remains small relatively to that of the wind 

 e.g., in lakes and small seas. Also in the Trades, 

 where the wind is perpetual, there is no sign or 

 symptom of an approach to the " highest wave " 

 of Helmholtz and Stokes. I conclude, therefore, 

 that observation indicates that under natural con- 

 ditions of wind there is no tendency to progressive 

 approximation towards the state of one set of waves 

 of permanent type. 



In this connection, I note that Professor Horace 

 Lamb, who has investigated water-waves as a 

 mathematician, writes ' that " the possible form of 

 waves of permanent type ... is very interesting 

 mathematically . . . but no reason has been 

 given, so far as I know, why free water-waves 

 should tend to assume a form consistent with per- 

 manence." 



1 Presidential Address, Section A, British Association, Cam- 

 bridge Meeting, 1904. 



