AND OTHER WATER WAVES 135 



the interval and fresh sets are formed. The regu- 

 larity of the second is not visibly affected by short- 

 period veering, being too massive. Waves of 

 intermediate size are affected by both kinds of 

 veering and several crossing sets are formed. 



The Observed Profile of Waves at Sea 



Both during a wind and in the case of a swell 

 travelling calmly in deep water, the trochoid repre- 

 sents the apparent form of the wave much more 

 nearly than the curve of sines, for it is easy to 

 observe that the convex part of the wave has a 

 steeper curve than the concave part, the crest being 

 narrower than the trough. But, except in the case 

 of a somewhat flat swell, the greater steepness of 

 the front face of the wave is obvious to the 

 eye, and most markedly so when the wind is 

 blowing. Now, Sir G. G. Stokes found * that 

 waves of permanent type in deep water, what- 

 ever be the order of approximation to which the 

 calculation is pushed, must be symmetrical with 

 respect to vertical planes passing through their 

 ridges. I conclude, therefore, that steep waves at 

 sea are never waves of permanent type. Again, 



1 " Math, and Phys. Papers," vol. i., p. 193, from Trans. 

 Camb. Phil. Soc., vol. viii., p. 441. 



