214 Lord Rayleigh on the 



his solution appears to me to be vitiated by more than one 

 oversight. By differentiation of (6) he obtains (with A written 

 for K) 



dp = 2 Ap dp, 

 and thence, by (1), 



2Apdp=pdY; 

 so that 



V = 2Ap + constant. 



In the subsequent argument the identity of A with K is 

 overlooked ; and the whole process is vitiated by the illegiti- 

 mate differentiation of (6), wdiich is only applicable at places 

 where p is not varying. The final result, which appears to 

 be arrived at without any assumption as to the physical con- 

 nexion between p and p, is thus devoid of significance. 



Let us integrate (1) from a place in the vapour round 

 which the density has the uniform value p { to a place in the 

 liquid where the uniform density is p 2 . Thus 



f (2) f =Y 2 -Y 1 =2K(p 2 -p 1 ), . ... (9) 



by (3) . The external pressure is uniform throughout, and 

 may be denoted by v/; and by (6), 



^= Pl -Kp^=p 2 -K P / (10) 



At places where p is varying, that is in the transitional layer, 

 -or, as given by (6), does not represent the external pressure ; 

 but we will still regard it as defined analytically by (6). 

 Thus 



By comparison of (9) and (11), 



;?s+- <"» 



or on integration by parts, 



I' 



Jo 



ron (2) r (2) -53- 



'(1) p 



The values of «r at the limits are the same, and have been 

 denoted by tx' . Hence 



—jr-a P =0 . (13) 



J(i) 



