128 Dr. C. H. Lees on the Viscosities of 



For another specimen of the same glass we obtained 

 0-00181. 



A similar experiment was made with Jena " Verbundglas " 

 D.R.P. No. 61573, by removing the bulb E, and joining on 

 a bulb of the D.R.P. glass. 



The result of a single experiment showed its cubical 

 expansibility to be 0*0022 between 0° and 100° ; a result 

 not very different from thatiof ordinary German gliss. 



X. On the Viscosities of Mixtures of Liquids and of 

 Solutions. By Charles H. Lees, D.Sc* 



IN recent years many determinations of the viscosities of 

 mixtures of liquids and of solutions have been made in 

 the endeavour to discover the law of connexion of the vis- 

 cosity ol: a mixture with the relative amounts and viscosities 

 of its constituents. As a result several empirical formulae 

 have be 3ii proposed which represent the observations with 

 more or less accuracy. Of the^e formulae, the one first used 

 by Arrhenius in 1887, and since then by Reyer, Wagner, 

 Lauenstein, and Kanitz, for weak salt-solutions or for 

 mixtures of liquids when one liquid is present to the extent of 

 DO per cent, or more, seems to be the most valuable. Accord- 

 ing to it the viscosity y ul a temperature t. of a mixture which 

 contains in 1 c.c, i\ c.c. of a liquid of viscosity ^ 1? v 2 c.c. 

 of one of viscosity 7? 2 , &c, at temperature /, is given by the 

 equation 



V = Vi Vl -V2 V2 -Vs' 3 



or 



so long as one constituent i^i present to the extent of 90 per 

 cent, or more. It is the object of the present paper to con- 

 sider whether this formula can be supported on theoretical 

 grounds, to see how far it agrees with the observed facts for 

 mixtures generally, and if the agreement is unsatisfactory 

 to replace it by a more suitable expression. 



To arrive at a theory for mixtures of fluids which have no 

 chemical action on each other, we may suppose the volume of 

 a mixture to be divided into elementary volumes by, say, 

 three series of parallel planes. Each of these elementary 

 volumes we may suppose occupied exclusively by one con- 

 stituent. The limit of the calculated viscosity of a medium 

 so built up when the elementarv parts are taken indefinitely 

 small, may be taken as the viscosity of the mixture. 



* Communicated by the Physical Society .: read June 8, 1900. 



