Theory of Surface Tension. 657 



where pi is the density of an electrically neutral constituent 

 at P', and p and p the densities at P and P' respectively. 

 In (23), 0/ stands for 



Opi 



so that d contains a term of the form M0 + N, where M and 

 N are arbitrary constants. F contains a term equal to 

 (M.0 + l$)p. so that the right-hand member of (25) is 

 independent of the arbitrary constants M and N. If it 

 were possible to choose the constants M and N so that 



p' j dx — 2Ci j" pidx 



could be neglected, with respect to T for all the possible 

 values of the temperature and densities at P', then (25) 

 would simplify into 



T=$Fda:, (27) 



which, I consider, is not a proper expression of T. Equation 

 (27) has apparently the same form as commonly given, but 

 it is different in these respects : F contains Bo"/<^ and is 

 made up of two terms, the first being equal to 



f D EdD 



Jo 



and the second being independent of D but a function of 

 tt-f3 variables a, ^-, 0, pi, /o 2 . . . . pa, where during the 



integration these w + 3 variables are to be kept constant. 



Next let us find the relation between the temperature 

 coefficient of surface tension and the entropy per unit area 



H=- fU«k, (28) 



the integral being extended from P' to P". 



In the case of one independent constituent, so called, the 

 temperature coefficient of T is definite ; but when there are 

 more independent constituents, there is an infinite number 

 of the temperature coefficients according to the different 

 modes of change. Let us take any definite mode of change 

 and denote the corresponding variations by using the symbol d. 



By (23), (24), (25), and (28) we have at once 



dT 

 dO 



PMl. Mag. S. 6. Vol. 43. No. 256. April 1922. 2 U 



