2 1 8 Lord Rayleigh on the 



When (19) is multiplied by dp/dz and integrated across the 

 whole layer of transition, we get for the part independent 

 of R, 



2kP P ^dz = K(p^- P ^ 

 Jo) a ~ 



simply, all the other terms in L, M, . . . vanishing. Hence 

 by (16), with integration by parts, 



p 2 -p 1 = K(p 2 2 -p l 2 ) 



The first term upon the right in (21) is the same as when 

 the strata are plane. The second gives the capillary tension 

 (T) , and we conclude that when the transition is continuous 



^mh- m ?M+ m 



From these results w r e see that "the existence of a capillary 

 force is connected with suddenness of transition from one 

 medium to another, and that it may disappear altogether when 

 the transition is sufficiently gradual"*. 



The series (22) would probably suffice for the calculation 

 of surface-tension between liquid and vapour when once the 

 law connecting p and z is known. It is possible, however, 

 that its convergence would be inadequate, and in this respect 

 it must certainly fail to give the result for an abrupt transition. 

 In the latter case, where the whole variation of density occurs 

 at one place, (16) becomes 



p 2 ~ Pl =2K(j,^-p i -')-(p i -p 1 )Y, . . . (23) 

 Y relating to the place in question. And by (17) 



f 00 27T f 30 



Thus 



ft - i , 1 = K(p/-p 1 2 )+2T/R, . . . . (24) 



* " On Laplace's Theory of Capillarity," Phil. Mag. October 1883. 



