244 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



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

 mass, the values of fa which will make the equilibrium stable or 

 unstable. 



If the component to which y/ and T l relate is found only at the 

 surface of discontinuity, the condition of stability reduces to 



- (530) 



cr -n 



bmce 1 1 = 



we may also write 



I\ da- 1 dloga- 1 



~^W< ~2' ' dlogT^ ~2' 



dT 

 Again, if I\ = and -j- 1 = 0, the condition of stability reduces to 



(532) 

 P -P 



. / 



Since y, = 



we may also write 



' or - (533) 



' 3" 



When r is large, this will be a close approximation for any values of 

 I\, unless y/ is very small. The two special conditions (531) and 

 (533) might be derived from very elementary considerations. 



Similar conditions of stability may be found when there are more 

 substances than one in the inner mass or the surface of discontinuity, 

 which are not components of the enveloping mass. In this case, we 

 have instead of (526) a condition of the form 



Jl+(r y2 ' + 2r 2 )^+etc.<^"-p', (534) 



from which -^P, -&, etc. may be eliminated by means of equations 

 derived from the conditions that 



yiV+I^s, y 2 V+r 2 s, etc. 

 must be constant. 



Nearly the same method may be applied to the following problem. 

 Two different homogeneous fluids are separated by a diaphragm 

 having a circular orifice, their volumes being invariable except by 

 the motion of the surface of discontinuity, which adheres to the edge 

 of the orifice ; to determine the stability or instability of this surface 

 when in equilibrium. 





