650 Mr. Shizuwo Sano on the T hermodynamical 



constant, for every point in the fluid for all values of 

 #■> pi? P2? • • • Pn, Da?, D#, D z > For every point of the second 

 fluid, is assigned another constant value of <r, say <r f/ . 1 

 consider every point in the transition layer on a line normal 

 to the layer to have different values of a varying from a' to <r" . 



It was hinted in my former paper on the equilibrium of 

 fluids in an electromagnetic field * that a theory explaining 

 the existence of surface tension can be formed by assuming 

 that F contains a x , cry, a z . According to my theory, every 

 point along the orthogonal line in the transition layer is in a 

 different state of aggregation and is in stable equilibrium, 

 both mechanically and chemically, although I shall not enter 

 into any investigation of the conditions of stability. Though 

 I assume that the fluids vary continuously from one phase to 

 the other, the conception differs entirely from that contained 

 in van der Waals's equation of condition. 



In the paper referred to, I proved that the conditions of 

 chemical equilibrium are 



|? + qm + % = C h [»<=i, 2, 3, . . . n], . . (1) 



OPi 



where M?e and ^ g are electric and gravitational potentials 

 respectively, and qi the quantity of electricity associated with 

 the unit mass of the z-th constituent, and d is independent of 

 £c, y, z. In obtaining (1) it was assumed that the gravitational 

 field was uniform, but it can be easily seen that the proof is 

 more general. In (1) the effect of mutual gravitational 

 attraction of different portions of the fluids under consider- 

 ation is neglected. 



It was also proved that if there is a reaction equation of 

 the form 



%S*=0, ....... (2) 



where S; represents a molecule of the z'-th constituent and 

 v's are integers, then the equation of chemical equilibrium 

 corresponding to the reaction (2) is 



Xvtmi^- =0, . . . . . . (3) 



Opi 



mi being the molecular weight of the z-th constituent. 



Proceeding in a similar way as in my paper above men- 

 tioned, the equations of mechanical equilibrium are easily 



* Proc. Math.-Phys. Soc. Tokyo, ii. p. 365 (1905) ; Physih Zeitschr. vi. 

 p. 566 (1905). 



