GRAVITY WAVES OF FINITE AMPLITUDE 
'T, V. Davies of King's College, University of London, 
has discovered a new method for treating tne classical 
problem of steady gravity waves in an irrotational, incom- 
pressible fluid. He has been able to solve the problems 
of (a) periodic waves in a channel of infinite depth, (b) 
the solitary wave, (c) periodic waves in a channel of 
finite depth, and (ad) periodic waves at the interface 
of two streams of finite depth. 
"The method used by Davies is a development of that of 
Levi-Civita in his paper of 1925. The first approximate 
solution contains a variable parameter yp which satisfies 
Oppo, ( p. being known in each case); the lower 
range of #» corresponds to the classical waves of small 
amplitude, the upper limit corresponds to the case in which 
breaking occurs at the crest. The Stokes result, that the 
angle of breaking at the crest is 120°, is verified in each 
case and the problems of wave velocity, energy, form of 
the free surface, and the drift at the base of the fluid, 
have in the main been solved. The first approximation is 
in error by 137 at the extreme case of breaking at the crest, 
but the error decreases when the crest is horizontal and 
when the ratio of wave height to wave length is smaller. 
The higher approximations have been derived in cases (a) 
and (b).'™ 
*The / in this quotation has a meaning here which is different 
from its meaning in the rest of the text. 
