624 RICE ART. L 



and so equation [547] takes on the special form [540] in this 

 case. 



The reader will now find no difficulty in following the matter 

 on pages 242-244. The special corollary concerning the system 

 in which "the interior mass and surface of discontinuity are 

 formed entirely of substances which are components of the 

 external mass" (of which a drop of water in an indefinitely large 

 mass of vapor is a good illustration) offers a good example for 

 applying the sufficient test which is given on page 252, and on 

 which we have already commented. Thus, the interior volume 

 being v' and the radius r, let the radius increase to r + 8r. Now it 

 is a feature of the method, which must not be overlooked, that 

 As and Av' are not to be taken as SirrSr and iirr^Sr respectively; 

 that overlooks the higher powers of dr which are vital for the 

 purpose of the test. Actually, if we merely retain first powers 

 of 8r, 8s = SttSt, 8v' = ^ivr'^br and 8v" = -^irr'^br', therefore 



S(a5s) - S(p5?;) = {<T.87rr - (p' - p")47rr2}5r, 

 which is zero (as it should be for equilibrium). But 



As = 87rr5r + 47r(5r)2, 

 and 



Av' = ^TcrHr + 47rr(5r)2 + y {brY = -Av". 



Hence 



2(0- As) - 'LivAv) 



= 47r«T(5r)2 - 47rr(p' - v") i^rY - J ip' - v") (5r)' 



f . 2{8rY\ 



= ^ivaU8ry - 2{8rY - ^] 



= - 47r(T(5r)2 



(provided 8r is small compared to r). This is negative for any 

 sign of 8r. Hence the sufficient test of stabihty is not satisfied. 



