MancJicstcr Memoirs, Vol. xliv. (1900), ^^o. 1>. 5 



We thus obtain 



j; - /3 = .^ sin 2W/J - y^sm 2;;//^ cos 2w/p 



-^sin«2;///3 . . (7), 

 and 



r/'{(l> + ixP)/' ((/. - ^4/) = I + J) cos 2W/> 



4/;/" (Xj 4- 3\.j)- + 4///\, sin'-^ 2W/5 + 1 2//As(3 - 5 cos^ 2/;//3) 

 + y^i^ 



m%^ (\i + 3\s) cos 2W/5 + 2^X3 sin^ 2w/3 cos 2W/3 

 j/rX-i (Xi sin- 2-'/'//3 4 X-j cos- 2///)^) - //'/X:^ sin* 2w/5 , 



+ 48 2>i ^^^ ^^" 



Taking, in the first place, only the first term in the series 

 we find that putting 



r =^4,'/3 tan 2w/3 / 2;///) , 

 fn/h _ I - cos 2W/J 

 sin 2W/3 4C0S- 2////3 - I ' 

 the defect of pressure over the service at the crest is 



i6gp/ii siii*2w/3 cos-2w/3/(4 cos-2W/3 - 2 cos 2w/3 + i)-, 

 and this defect decreases rapidly along the slope of the 

 wave. 



If jnp is small, //i : /3 is small and the defect may be 

 negligible, but here I propose to examine the magnitude 

 of the next term in the approximation necessary to satisfy 

 the conditions without stipulating for a small value of the 

 ratio /ii : /3. 



Another problem suggests itself to the mind, which 

 appears to be quite consistent with the results of Scott 

 Russell's experiments, namely that the motion is not one 

 capable of being reduced to steady motion, but that the 

 gradual reduction of the altitude of the wave is a necessary 

 part of the phenomenon. This view has had the support 

 of Sir George Stokes, but the method now adopted is not 

 suitable to the investigation of it. 



