Mixtures of Liquids and of Solutions. 131 



solution of the equations (1), (2), (3) above, for this case 

 gives for the viscosity rj 



1 °g 7 7=2( 1 °g 7 7i + lo g 7 ?2). 



If 1 c.c. of the mixture contains v x c.c. of the rj l and v 2 c.c. 

 of the rj 2 constituent 



log r i =v 1 logrj l + v 2 logi] 2 . 



For a mixture containing in 1 c.c. v i9 v 2 , v s , &c. c.c. of media 

 of viscosities r] u rj 2 , rj 3 , &c* 



log r) = v l \ogr jl +v 2 logr) 2 + v 3 log7] 3 + . . . . 



This result is independent o£ the number of the elementary 

 prisms of each constituent present. In the tables which 

 follow this will be referred to as the iC logarithmic formula. 5 ' 



The number of mixtures of liquids, of which the viscosities 

 have been observed and are available for comparison with the 

 results of theory, is small, and some of them, for which the 

 observed values of the viscosities do not fall within those of 

 the constituents, e.g. mixtures of water and alcohols or certain 

 acids fj are seen to be outside the limits of the above theory. 

 Of the rest some, e.g. chloroform or carbon bisulphide and 

 ether J have points of inflection on the curve connecting- 

 viscosity and constitution, and of such singularities none of 

 the above formulae can take account. The conclusion may at 

 once be drawn that the viscosity of a mixture of liquids is in 

 general not dependent solely on the viscosities and amounts 

 of the constituents present, but is influenced by some other 

 action of which none of the above theories takes account. 

 Notwithstanding this fact, it may be of use in the case of 

 mixtures in which the action of this unknown disturbing effect 

 appears to be least, to compare the values given by the three 

 formulae with those found by experiment ; and in the following- 

 Tables these observed values are compared with the values 

 calculated from the recorded percentage compositions by 

 weight, and the densities, on the assumption that no contrac- 



* Lees, Phil. Mag. xlix. p. 225 (1900). 



t Wijkander, Wied. Ann. Beibl. iii. p. 8 (1879) ; Thorpe & Rodger, 

 J. Chem. Soc. lxxi. p. 367 (1897). 



\ Traube, Ber. Chem. Ges. xix. p. 871 (1886) ; Pagliani & Battelli, 

 Ann. JR. 1st. Torino, xiii. p. 37 (1885). 



K2 



