Manchester Memoirs^ Vol. I. (1906), No. 8. 23 



If we introduce X, in place of Ji in the equations (27) 

 to the wave profile, and omit terms in which the coefficient 

 is less than 00 1, we get 



x=-\ct'^a) 



27r A„ 



- — (-0054:* --on l") sin ^{ct + a), 

 27r Ag 



\ -> ''TT 



}= - —(■35141'+ "0424^+ •oi84'^)cos-^^(^/ + a) 

 2 7r A„ 



- A(-oo34'* - -006^) COS 4!'(r/ + a), 

 27r \ 



where —"= i + •1234"+ •0454;*+ •0284''' . . (36). 



\ 



From these it will be seen that although it is needless 

 to obtain further terms in the trigonometrical series, the 

 continuation of the coefficients of the first two trigono- 

 metrical terms would be necessary in order to draw 

 diagrams, except for moderate values of X,. 



The Connection with Mr. Mitchell's Highest 

 Wave in Water. 



The results of the last section suggest a change in the 

 method of treating the equation of surface condition in 

 order to determine the coefficients in the expansion of 

 the velocity more conveniently, and also to justify more 

 fully the convergency of the expressions obtained. It is 



