FLUIDITY AND CONDUCTIVITY. 163 



where ^ and 772 are the viscosities of the components and H that of the mix- 

 ture 



where K 1 has the same significance as in equation (1). 



Since ^ - is a constant, equation (2) is considered to represent an equilat- 



eral hyperbola, the F-axis of which is at a distance - - to the left of the 



172 - f]i 



origin to which equation (1) is referred. Thus, the conclusion is drawn that 

 the hyperbola is the normal curve for viscosities and not the straight line. This 

 fact accounts for the sagging of the viscosity curves, or, in other words, the 

 viscosities of the mixtures are not proportional directly to the amounts of 

 the components. The above only holds in case we have a mixture of two 

 liquids which are made up of particles that do not interact in any way with 

 each other, as in the case of acetone and ethyl alcohol. 



When we have contraction or expansion on mixing two liquids, the hyper- 

 bola would not represent the viscosity curve of the mixtures, but we get a 

 curve of the form already described. 



By examining the viscosity data of the mixtures of acetone with methyl 

 alcohol and ethyl alcohol, and also the data for lithium bromide in these 

 mixtures, we see that the viscosity of a mixture is, in most instances, slightly 

 lower than would be expected from the law of averages. In these cases the 

 fluidity curves are straight lines. In the recent work of Bingham this has 

 been shown to be frequently true where organic solvents are mixed. 



Let us now consider the maximum in conductivity obtained with lithium 

 bromide in mixtures of acetone with methyl and ethyl alcohols. Cobalt 

 chloride gave a maximum in conductivity only in the case of acetone with 

 ethyl alcohol. In the former case the maximum occurs entirely in the 75 

 per cent mixture, while in the latter only in the 25 per cent mixture. 



This phenomenon had also been observed by Jones and Bingham, working 

 with lithium nitrate and calcium nitrate in mixtures of acetone with the 

 alcohols. As pointed out by them, this must be due either to an increase in 

 dissociation in the 75 per cent mixture, or to the diminution in the size of the 

 ionic spheres. 



In discussing the fluidity curves, we pointed out that when acetone was 

 mixed with the alcohols, we did not obtain complex molecular aggregates. 

 It is, then, impossible for the mixture to be more associated than the pure 

 solvents, and we therefore can not have an increase in dissociation if the 

 hypothesis of Dutoit and Aston is true. 



From an examination of the conductivity tables of lithium bromide we see 

 that we have by no means reached the limiting conductivity values in the 



