OF ARTS AND SCIENCES. 409 



Column 5 gives the differences between the vahies of P/ and 

 (Pi. ^\.~\~2h ^i) i^ percentages of PL Columns G, 7, 8, and 9 give 

 the percentages of the constituents of each mixture, as deduced from 

 the proportions taken by "WUlIner and given in Table II., and the per- 

 centages as calculated by the formula 



1 00 /= a /j + (100 — a) l^. 



In examining Table III., it will be seen that in the cases of mixtures 

 of water and chloride of zinc, of water and glycerine, and of alcohol and 

 glycerine, the differences between the values of P /and (/>j I-^-\- p.^ Z) 

 in no case exceed 0.2,1 (fo^ 3,nd that the signs of the differences are 

 about as often plus as minus. The comparison of the observed and 

 calculated percentages is less satisfactory, but is still sufficient to show 

 that the method is available in analyses of mixtures of liquids in 

 which extreme precision is not required and for which purely chemical 

 methods are wan tint;. 



But with mixtures of alcohol and carbonic disulphide the case is 

 otherwise. The differences between the value of P/and {p^ I^ -{-Pi ^>) 

 amount as a minimum to 1.14^ and as a maximum to 1.83%. I con- 

 sider it, to say the least, as probable that the mixture of alcohol and 

 the disulphide is accompanied by chemical action resulting in the for- 

 mation of new compounds. Wullner found that these mixtures, after 

 standing overnight in well stoppei"ed bottles, gave indices of refraction 

 differing materially from those of the freshly prepared solutions, the 

 differences being too large to be accounted for by a loss of carbonic 

 disulphide. It is difficult to explain this fact in any other way than 

 by supposing that a chemical change begins as soon as the liquids are 

 mixed, though no such change has been observed by chemists. 



In any event, my results, I think, render it probable that the method 

 of analysis based upon them will find useful applications. A much 

 larger and more varied series of observations of the indices and densi- 

 ties of different liquids and mixtures of tliese in various proportions is 

 extremely desirable. For saline solutions, we possess measurements 

 by Sauber, Hoffmann, and others, but unfortunately the densities and 

 indices of refraction have not, except in a very limited number of cases, 

 been determined for the same temperatures. In the particular case of 

 solutions of sugar, Obermayer * has given the following values for the 

 indices of refraction and densities, at 22.26 C : — 



* Wien. Acad. Ber. 61 (2 Abth.) p. 797. 



