300 ./. W. Gibhs — Equilihrmra of Heterogeneous /Substances. 



ml -r^- ) dt — m\ -^ — ) dp -\- m d}x^ =0. (410) 



XdAti J / i, j3, TO \drn j / 1, |j, m 



By subtracting this equation from (404) we may obtain an equation 

 similar to (406), except that in place of //p and «p we shall have the 

 expressions 



/ di} \<"'^ -, / do \(f) 



\dm J / «, j:>, TO \<:w/i ^/t, 'p,m' 



The discussion of equation (406) will therefore apply mutatis mutan- 

 dis to this case. 



We may also wish to find the variations in the composition of the 

 fluid which will be necessary for equilil)rium wlien the pressure p or 



. . dx dx dy • i ^i x 



the quantities -—„ -y-„ —-, are varied, the temperature remaining 



(too ^^]j ^y 



constant. If we know the value for the fluid of the quantity repre- 

 sented by t, on page 142 in terms of t^^p^ and the quantities of the 

 several components »?,, //ig, wig, etc., the first of which relates to the 

 substance of Avhich the solid is formed, we can easily find the value 

 of //j in terms of the same variables. Now in considering variations 

 in the composition of the solid, it will be sufficient if we make all but 

 one of the components variable. We may therefore give to m^ a 

 constant value, and making t also constant, we shall have 



^ \dp Jt, m \dm^/t, p, m \dm^/t. p, m 



Substituting this value in equation (404), and cancelling the term 

 containing dt, we obtain 



] m -p -v\ dp + m. ( ~r-^ dm^ 



( \dplt,m ) \dm„/t,p.m 



+x.4 + (r. + ,||,).|.. (4u) 



This equation shows the variation in the quantity of any one of the 

 components of the fluid (other than the substance which forms the 



. . . „ dx dx dy . , 



solid) which will b:ilan(*e a variation ot p, or of -^„ -=-„ -v-„ with re- 

 spect to the tendency of the solid to dissolve. 



-|- m 



