430 Prof. A. L. Selby on the Variation of 



Multiplying 



-iAC -ABC 



-*AB' 

 iAA' 



iBB' 

 -*BA' 



JOCK 

 -*CB' 

 -JOA' 



AB 



CA 



BC 



by D we obtain 











. . . AiA'CT-BBO 



B(B'C'-AA') 



C(AB-C /2 ) 





. . . A(A'B'-CC') 



B(AC-B' 2 ] 





C(B / C / -AA / ) 





. ; . A(BC-A /2 ) 



B(A'B'-CC') 



C(A'C'-BB') 





B A . 



. 





-2C 





C . A 



-2B' 





. 





. C B -2A' 



. 





• 



? 



so that we have at once the identity 









A'C'-BB' 



B'C 



'-AA' AB-C /2 



5 2 C 2 D = -2ABC.ABC 



A'B'-CC 



AC-B /2 B'C'-AA' 





BC-A /2 



A'B'-CC' A'C- 



BB' 



But the determinant on the right here is such that if we alter 

 the signs of the elements in its first row, third row, and second 

 column, it becomes the adjugate of 



B' A' C 



C B A' 



A C B' 



and consequently is equal to — K 2 . All that therefore 

 remains to be done is division by — A 2 B 2 C 2 . 



Bothwell, Glasgow, 

 April 7, 1891. 



LII. On the Variation of Surface-Tension with Temperature. 

 By Prof. A. L. Selby, M.A., University College, Cardiff 



MENDELEJEFF speaks of an ideal liquid as charac- 

 terized by two conditions : — 



(1) Y t =Y /(l — kt), Y t being the specific volume at f C. 



(2) T t = T (l — at), T t being the surface-tension at t° C. 

 * Communicated by the Physical Society : read March 20, 1891. 



