2 Sir a. Greenhill on 



The square of the wave-velocity is the sum of two terms : 

 the one due to gravity is proportional to the wave-length ; 

 and the other term is inversely proportional, which depends 

 on the tension of the capillary film. 



When the wave-velocity is a minimum these two terms 

 are equal. This should be the velocity of the breeze which 

 begins to ruffle the surface of water, if it were not for 

 the effect of viscosity in the air, which makes a great 

 difference. 



Expressed in a mathematical formula, with skin tension T, 

 dynes/cm, water-density p, g/cm 3 , wave-length X, cm, and 

 wave- velocity U, cm/s, in C.Gr.S. units, 



and U is a minimum U m , by variation of X, when the two 

 terms in (1) of IP are equal, and then 



it X p V p V gp 



Thus, if independent experiment, on the tremble of a 

 dewdrop, makes T=74, and we take # = 981 cm/s 2 , and 

 /> = 1 for water, this makes A,= l*73 cm, and U m = 23*2 cm/s, 

 about half a mile an hour, much less than the breeze which 

 ruffles the water, which would be about ten-fold. 



The discrepancy is accounted for by viscosity in the air. 



2. In the extension to the waves on a sheet of ice of 

 uniform thickness e cm, and modulus of elasticity E g/cm 2 , 

 in gravitation measure, supported on deep water, taken as of 

 the same density p, we find ( 4 American Journal of Mathe- 

 matics,' 1886) 



gX 1 /2?rA 3 </E 

 TT2 _ 27T + 12\ X ) * p m 



^ ■ • • • ; V 



X 



or, putting ^— = V 2 , where V is the velocity of wave-length X 



on the surface of the clear water, and ^— = W 2 , so that W is 



P 

 the velocity of longitudinal waves through ice, 



v ,_ V + T2W 2 J p = + VAV*) W {2) 



1+5! l + ^l 



