Theory of Surface Tension. 655 



point. But (19) contains only two arbitrary constants, so 

 that it cannot satisfy all these three conditions. Therefore 

 in this case the transition layer cannot exist. 



It will be remarked that in this case the transition layer 

 is just like a fluid in which there are two independent con- 

 stituents, since n kinds of molecules are connected with each 

 other by only n — 2 independent reaction equations. 



In the casein which there are more independent constitu- 

 ents, the reasoning quite similar to the above holds good, and 

 we see that the neglecting of terms containing cr x in the 

 expression of F leads to impossible conclusions. 



Hence, it seems to me that when we are considering the 

 equilibrium of fluids in the transition layer we must suppose 



that F depends upon ^- , so that the existence of surface 



tension is itself closely connected to the fact that the 

 system can exist in two phases in contact. 



Now suppose that F depends upon a x . At first let there 

 be neither cation nor anion in the fluids. In this case our 

 equations are 



P=Oi,[J=l, 2, ...«], .... (20) 

 -F+«r„|2 +2 Pi |f =C„ +1) . . (21) 



0&X Opt 



D = 0, (22) 



where the n + 1 constants are to be considered as deter- 

 minate. A glance at equations (20), (21), (22) shows that 

 the equation determining a as a function of x is a differential 

 equation of the first order, the constant of integration being 

 determined by the fact that a = a' at P . 



BF 

 It is more general to suppose that ^=r does not vanish at 



P when D = 0, and that 



does not vanish. When M/V — ty e " does not vanish, the layer 

 of transition may be looked upon as a doable sheet of free 

 electricity, but not or! real electricity. 



Finally, let us suppose that F contains g x and that there are 

 electrolytic ions in the fluids. In this case our equations are 

 (15), (17 j, (18), and (21), and the equation for determining cr 

 as a function of x is a differential equation of the third order, 



