Mixtures of Liquids and of Solutions. 145 



of the viscosity of a physical mixture in terms of the viscosities 

 and natures of its constituents. Like other empirical formulae, 

 it will in time be replaced by a formula founded on theory 

 and capable of including cases in which the liquids, owing 

 to some chemical action on each other, give rise to mixtures 

 having viscosities outside the limits of those of their con- 

 stituents. 



Since a liquid at temperature t may be regarded as pro- 

 duced by a mixture of suitable proportions of the liquid at 

 temperatures and t ± respectively, the above formula for the 

 viscosities of mixtures should be capable of expressing the 

 variation of the viscosity of a liquid with temperature. 



If 1 c.c. of a mixture at temperature t is supposed to result 

 from mixing v c.c. of liquid at 0° C. and v } c.c. of liquid at 

 £j° C, £=01*1 ; and if the viscosity is rj at 0° C, tj at t° 0., and 

 77! at *!° 0., then 



©-©'-©"' 



h 



'here 



»-K(?)"-'} 



Hence t? 



v= r> 



an empirical formula proposed by Slotte *, and found by him, 

 and more extensively by Thorpe and Rodgerf , to be applicable 

 to all liquids on which experiments have been made. 



The values of m for most of the mixtures mentioned in the 

 preceding tables vary between '20 and *50 ; and Thorpe and 

 Rodger have found its values in Slotte's temperature-variation 

 formula to lie between *22 and *3 for alcohols, and to be about 

 6 for water, benzine, ether, and chloroform. In the following 

 table the values found suitable for expressing the viscosity of 

 a mixture in terms of the viscosities of its constituents, are 

 compared with those found best for expressing the variation 

 of the viscosity of each constituent with temperature. 



* Ofv. Finska Vet. Sac. Forhand. xxxii. p. 127, formula (11) (1890). 

 t Phil. Trans. A. 189. p. 96 (1897). 



Phil. Mag. S. 6. Vol. 1. No. 1. Jan. 1901. L 



