﻿192 Mr. William Sutherland on the 



others involving the exceptional alcohol or complex petro- 

 leum. Before proceeding with an account of my own expe- 

 riments on normal liquid pairs, I will illustrate the application 

 of equation (6) to Rodenbeck's mixtures of the normal pair of 

 liquids ethyl oxide and chloroform. The following table 

 contains the data for the two liquids and five mixtures along 

 with the value of lAg/^Ax 2 A 2 )* calculated by equation (6) 

 from the data for each mixture: — 



Ethyl Mixture. Mixture. Mixture. Mixture. Mixture. Chloro- 

 Oxide. I. II. III. IV. V. form. 



Pi l'O -68 -44 -262 -125 -064 0-0 



P-2 00 -32 -56 -738 '875 -936 1-0 



P ■ -727 -870 1020 1-170 1-320 1400 1-494 



" 1-83 2-01 2-22 2-44 2'52 2-60 2-78 



1 A 2 /( 1 A 1 2 A 2 )I 1-02 1-05 1-07 -97 -89 



In the table ethyl oxide is liquid 1 and chloroform is 2, 

 and the surface-tensions are given in mgrms. weight per 

 millim. The mean value of iA 2 /(iA 12 A 2 )^ is l'O; or, ex- 

 cluding mixtures IV. and V., in which the proportion of 

 ethyl oxide is too small to favour an accurate value of 

 iA^Ax 2 A 2 )* from equation (6), the mean value is T05. 

 Thus the theoretical formula (6) is proved to apply well to 

 mixtures of ethyl oxide and chloroform, for which also X A 2 is 

 proved to be equal to ( 1 A 12 A 2 )*. 



Two other sets of Rodenbeck's experiments may be dis- 

 cussed here, although they relate to mixtures involving 

 petroleum, which is itself a mixture, for the equation 



can be generalized so as to apply to any mixture of any 

 number of liquids. Suppose a gramme of any such mixture 

 to contain jh, V^ Pz • • • gramme of liquids 1, 2 ; 3 . . . , and have 

 a density p and surface-tension a, then 



cc/p 2 = (pi«i*/Pi + p^lpi +iW/?3 + • • • ) 2 - 



If the liquids 2, 3, 4 ... in proportions p 2 , ps, p± . . . are sup- 

 posed to form a separate liquid n, as for instance Rodenbeck's 

 petroleum, then 



"/P 2 = {pi«lVpl+ (P2+PB + • • • )4lp n Y I 



so that the law for a mixture of mixtures is the same as for a 

 mixture of pure liquids, and we ought to be able to apply 

 equation (6) to a mixture of mixtures. Thus we can utilize 

 Rodenbeck's measurements on mixtures of rectified petroleum 

 and chloroform, and also of ordinary petroleum and ethyl 



