294 Lord Rayleigh on the 



In these equations, however, we are to treat K as vanishing, 

 the specification of the forces operative across a plane being 

 supposed to be complete. Hence, as Young finds, we must 

 take 



c 4 C = r 4 R; (23) 



and accordingly 



T= 7rc 4 C(c-r) ^y 



At this point I am not able to follow Young's argument, for 

 he asserts (p. 490) that "the existence of such a cohesive 

 tension proves that the mean sphere of action of the repulsive 

 force is more extended than that of the cohesive : a conclusion 

 which, though contrary to the tendency of some other modes 

 of viewing the subject, shows the absolute insufficiency of all 

 theories built upon the examination of one kind of corpuscular 

 force alone." According to (24) we should infer, on the con- 

 trary, that if superficial tension is to be explained in this way, 

 we must suppose that c > r. 



My own impression is that we do not gain anything by this 

 attempt to advance beyond the position of Laplace. So long 

 as we are content to treat fluids as incompressible there is no 

 objection to the conception of intrinsic pressure. The repul- 

 sive forces which constitute the machinery of this pressure 

 are' probably intimately associated with actual compression, 

 and cannot advantageously be treated without enlarging the 

 foundations of the theory. Indeed it seems that the view of 

 the subject represented by (23), (24), with c greater than r, 

 cannot consistently be maintained. For consider the equili- 

 brium of a layer of liquid at a free surface A of thickness AB 

 equal to r. If the void space beyond A were filled up with 

 liquid, the attractions and repulsions across B would balance 

 one another ; and since the action of the additional liquid 

 upon the parts below B is wholly attractive, it is clear that in 

 the actual state of things there is a finite repulsive action 

 across B, and a consequent failure of equilibrium. 



I now propose to exhibit another method of calculation, 

 which not only leads more directly to the results of Laplace, 

 but allows us to make a not unimportant extension of the 

 formulas to meet the case where the radius of a spherical 

 cavity is neither very large nor very small in comparison with 

 the range of the forces. 



The density of the fluid being taken as unity, let Y be the 

 potential of the attraction, so that 



Y = $S$U(f)dxdydz, .... (25) 



