﻿356 Dr. J. McCowan on the Highest 



across the axis of z. This condition may be written, by (1) 



h= y (l-fk 2 sec 2 \mz) s/l-tf^(?\mz . dz, . (28) 



which gives, remembering that k = cos fync, 



mh = 7r{l — cos J mc — \f sin ^mc .sin mc}. . (29) 



We may now proceed to evaluate the constants in (1) in 

 terms of h the mean depth of the liquid in the channel. 

 Eliminating IP between (22) and (13) we get 



mc = mh-\- JtanmA, (30) 



while (13) and (26) give 



(1— f) 2 =cot mh cot ^mc (31) 



If now we solve equations (29), (30), and (31) for m, c, and 

 /, we shall find mh= 1*0025 approximately: hence, remembering 

 that at best the surface-pressure is only to be approximately 

 constant, it will be sufficient to take for our present purpose 



mh=l, (32) 



and it is just possible that this may be the exact value. 

 Substituting this value in (30) we get 



c==l-78A (33) 



This gives for the maximum wave-height 



c-h= Vo =-78h, (34) 



which differs by less than the experimental error from the 

 value '75 h which I have already {S. § 10} given as a fair 

 average of some experiments I made in connexion with my 

 former paper. 



Again, from (13) and (32), or (22) and (34), we obtain for 

 the velocity 



JJ 2 =l'56 9 h, (35) 



which shows that the maximum wave travels about 25 per 

 cent, faster than low waves in the same depth of channel. 

 Finally, substituting from (32) and (33) in (31) we get 



/='28 (36) 



We have now only to substitute the values of the constants 

 just determined in our general equations. 



