﻿190 Mr. William Sutherland on the 



where el, e 2 , and ie 2 are distances corresponding to e and 

 representing the distances to be left between continuums 

 which may be supposed to replace the molecular mediums 

 whose attractions have just been enumerated. For a single 

 liquid, for instance liquid 1 for which the value of e may be 

 denoted by e x , e\ is proportional to (mi/pi) 5 ; and then for its 

 surface-tension relation (1) may be written 



* 1 =k 1 A lPl 2 {m 1 /p 1 )*, (4) 



where k is the same for all liquids. Similarly for liquid 2, 



ct 2 = k 2 A 2 p 2 2 (m 2 /p 2 )$ (4) 



Now if e x is taken as represented by (rn^/pi)^, we cannot take 

 el as represented by (rn-Jpl) 15 ; because if we did so and then 

 in (3) put pi=p 2 an d suppose liquid 2 to become identical 

 with liquid 1, in which case el=.e 2 — x e 2 , we should find that 

 (3) would not reduce to \Aiple x , as it ought. The most 

 appropriate way in which to represent el is to take it as given 

 by {m-JplY reduced in the ratio of the cube root of the space 

 Pi/ Pi occupied by liquid 1 to the cube root of the total space 

 1/p. Thus el is represented by (jn 1 /p l , )^(p 1 p/p 1 )^, e 2 ' by 



(. ni 2/p2 f )*(P2P/P2)*) an( i 1*2 D J \el + e l)/2 ; so that for the 

 surface-tension of the mixtr , we get 



/. i« 2 //3 2 =^l 2a l/Pl 2 +iVWf>2 2 



xPiP*{*i"*) 9f , , u , //iUli ; (6) 



GA 12 A 2 )^ i7 ^ 2{( W i 1 /Pi)*Wf> 8 )¥ 3 



which is an equation for determining the ratio 1 A 2 /(iA 1 2 A 2 )£ 

 by a measurement of the surface-tension of a mixture of the 

 liquids 1 and 2 of known surface-tensions a x and a 2 . In these 

 expressions, if we put p 1 =p 2 = l/2 and suppose liquid 2 to 

 become identical with 1, we get the identity 1 a 1 = a 1 as we 

 ought ; also if we put p 2 = and p 1 = 1 we get the same 

 identity. There is doubtless something arbitrary in the 

 manner in which we have fixed the values of el, e%, and x ej y 

 but we must remember that, in the original establishment of 

 the relation a=kAp 2 e, there is an arbitrary step in the 



