[ 649 ] 



LXXVII. Thermo dynamical Theory of Surface Tension. By 

 Shizuwo Sano, Physical Institute, Imperial University of 

 Tokyo *. 



IN this paper I am going to present to the reader a 

 thermodynamical theory of surface tension in the 

 transition layer between fluids, based on several assumptions, 

 some of which are quite arbitrary. 



Let us consider two fluids in contact and in equilibrium, 

 and the layer of transition between the fluids not charged 

 with electricity, except for the fact that the layer is a double 

 sheet. 



In this paper it is assumed that (i.) some of the chemical 

 constituents of which the two fluids in contact with each 

 other are made are electrolytic ions unless the contrary is 

 stated, and at eveiy point each of the densities pj, p 2 , . • . pn is 

 not absolutely zero, where pi is the density of the i-th 

 constituent ; (ii.) the free energy per unit volume F is a 

 function of the absolute temperature 6 and the n densities 

 pi, p 2 , . . . p n , but is independent of the space variations of 

 these quantities ; (iii.) F depends not only on a, but on 



s— ,s~- 5^~ > an ^ not on the higher space variations of c, 

 0£ oy Oz 



where a- is a scalar quantity defining the state of aggregation ; 

 (iv.) F is a continuous function of the n-f-8 independent 

 variables or, a x , <j y , a z , 6, p 1} p 2 . . . pn, D.r, D y , D~, where 

 "do- ~dcr (V 



D- are the components of the electric displacement ; (v.) all 

 the independent variables cr, g x , <fy, <? z , 6, Pi, p-2i • • • Pn, D#, 

 Dy, D z are continuous functions of the rectangular 

 co-ordinates oc, y, z ; (vi.) F is sensibly independent of 

 <r x . o y , <r z in all the points outside of the transition layer ; and 

 (vii.) the elementary work done per unit volume on the 

 electric field when the densities are kept constant is 



x , <r iJ} cr z stand for ^~?^~j^ respectively, and D x , D y , 



where E^, E y , E^ are the components of the electric force. 



The quantity cr above stated requires some explanation. 

 The functional form of F differs according as we take the 

 first fluid or the second. For the first fluid we put cr = a / i a 



* Communicated by Prof. A. W. Porter, F.RS. 



