FLUIDITY AND TEMPERATURE 145

When the molecules of a liquid are closely packed, the volume
reaches its minimum value and the fluidity is zero. With
tetrahedral close-packing of the molecules, shear would require
rupture of the molecules themselves. If there are pore spaces
between or within the molecules, they do not give rise to fluidity,
so that the molecules somewhat resemble close-fitting solid
figures. As the fluid expands, due to molecular agitation, the
volume of the molecules themselves, i.e., the inner molecular
volume may remain the same, but the ordinary, i.e., the outer
molecular volume increases. The law states that the fluidity
originates solely in the free space which is the difference between
the outer molecular volume, or the volume occupied by the
molecules, and the inner molecular volume or the space filled by
the molecules in the sense indicated above. Given two sub-
stances with the same outer molecular volume, it is evident that
the one with the larger molecular kernel will have the smaller
fluidity. It is therefore natural to expect that the limiting
molecular volumes should be additive as Batschinski has found
to be the case. This opens the way to a study of the relation
between fluidity and chemical composition and constitution
which is most fascinating. It is very simple to measure the
outer molecular volume, and if this with the fluidity will give a
certain and easy method for determining the inner molecular
volume, it is a result much to be desired. It is apparent that
density and fluidity determinations should go hand in hand.
If the above reasoning held true for gases as well as liquids,
the fluidity isothermals of carbon dioxide should closely resemble
the familiar volume isothermals. By substituting for the volume
its value in terms of the fluidity given by Batschinski's law, we
would obtain a modified van der Waals' equation. As a matter
of fact van der Waals' equation may be written

P

T - v
* ~

- - -
R R Rv Rv*
but since viscosities are ordinarily measured at constant, i.e.,
atmospheric pressure, this may be written
B E
T = A.(f> -f" C -- : |=: T~ 7 f TN\9
<p + D (<p + D)2
where A, B, C, D and E are constants. This is identical with
Eq. (54) which is entirely satisfactory for liquids, except that it
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