J. TF. Glhhs — Equilih'ium. of Heterogeneous Substances. 407 



which roprcsoiits the total quantity of the component specified hy the 

 suffix, must be constant. It is evidently equal to 



Dividing by 4;r and differentiating, we obtain 



(,.2 y^' j^2rl\)dr-^i^ r3 dy^' + r^ dT ^ = 0, 

 or, since y^' and r^ are functions of /<j, 



(,-,./ + 2 r.) * + (^^ 'h'^ + r ;i£') a, , = 0. (527) 



By means of this equation, the condition of stability is brought to 

 the form 



{ry,' + 2r,r- 



If we eliminate r by equation (522), we have 



3 ( jo' -p") dfu^ "'" 2 o- diJ. 1 



If p' and o' are known in temis of t, /ij , //g, etc., we may express the first 

 member of this condition in terms of the same variables and ^j)". This 

 will enable us to determine, for any given state of the external mass, 

 the values of /<j which will make the equilibrium stable or unstable. 

 If the component to which ;/,' and F^ relate is found only at the 

 surface of discontinuity, the condition of stability reduces to 



r^^ du. . 1 



IT IT, > 2- (^8°) 



bmce ^ I ^ n — i 



we may also write 



r. da ^ 1 d\o^G ^ 1 



Again, if Fi = and -j-^ = 0, the condition of stability reduces to 



--^>f -J—, > 1- (532) 



Smce ^^=^,' 



we may also write 



y' dp' . 1 Jlog (»'-»") ^ 1 



p'-p"dy^'^^' d\ogy^' ^3* ^^'^'^> 



Trans. Conn. Aoad., Vol. III. 52 Nov., 1877, 



