THE FLUIDITY OF SOLUTIONS 165

Av = avi + bvz
= (a — mX — (n — 6)02
= (a - m) (P! — »2) (60)
since a — m = n — b.
If the fluidity is directly proportional to the free volume (Eq. 56),
it seems reasonable to assume that if the volume is decreased
for any reason by an amount Av, the fluidity will be decreased
by an amount which is some function of this fAv. Since in the
ideal mixture the fluidity is only slightly less than that given
by the linear formula (Eq. 25), we may assume as a first approxi-
mation that the decrease in fluidity is directly proportional to the
specific volume difference. We then obtain as our formula for
the true fluidity $
$ = k(v — w) — KAv
= v — KAv
= a<pi + b<pz — K(a — m) (vi — v2). (61)
It may be possible later to evaluate the above function, but
it is only necessary to know the fluidity of one or more mixtures
in order to determine a value for the constant K, from which the
fluidities of all other mixtures of the two components may be
calculated. The physical significance of K will be explained later.
We may take for an example carbon tetrachloride and benzene,
the mixtures of which were studied carefully by Thorpe andRodger,
and at a single temperature by Linebarger. (C/. Table XLII.)
In the first line at each temperature are given the fluidities
observed. In the second line are given the fluidities (<i>) as
calculated with the use of Eq. (61), using 40 as the value for K.
The fluidities (<p) as given by the simple additive formula,
Eq. (25), are given in the third line. These last are invariably
higher than the observed values, but when corrected for the
volume the agreement is very close, the average deviation
being less than half of 1 per cent.
It is worth noting in passing to what extent Batschinski's Law
applies to the ideal mixture, with which we assume to be dealing
in this case. Using the limiting specific volumes of carbon
tetrachloride and benzene as 0.5782 and 1.0476 respectively,
we have calculated the values of w by the admixture rule to be
0.683, 0.784, and 0.896, using weight percentages. This accords