height assumption so that the property that the sum of two 
solutions is also a solution will be obtained. 
If the non-linearity of the problem is of the greatest 
interest, the work of Stokes [1847] as summarized by Lamb [1932] 
illustrates the type of results which are obtained. In Chapter 
IX, Section 250 of Lamb, for example, the problem of waves of 
finite amplitude in water of infinite depth is treated "as a case 
of steady motion" under the assumption that the wave is periodic 
in time. The notation is somewhat different from that which is 
used here, but equation 4 in Lamb shows that the non-linearity 
of the free surface and of Bernoulli's equation is considered in 
the derivation to find the speed of the wave. The solution is 
approximate because it is in series form. The wave profile is 
approximated for the first three terms by a trochoid, and the 
whole wave profile moves forward with the speed 
c= (2 (1+ ee)? , x = ‘ 
Davies' Results 
A recent monograph by Lowell [1950] on gravity waves of finite 
amplitude describes some results which have been obtained by T.V. 
Davies [1951] of King's College, University of London. jtorvenlll De 
summary of his monograph is quoted in full below. Davies' work 
has unified the previous theories of waves of finite height and 
has yielded some improved theoretical relationships about the 
ratio of wave height to wave length. . 
