FLUIDITY AND TEMPERATURE 131

critical temperature it is concave, and the deviations from the
formula are considerable. Heydweiller made the interesting
observation that within the series of compounds with which he
worked the temperatures of equal viscosity are in the ratio of
their critical temperatures. But to this rule water and the
alcohols are exceptional.

De Heen in his Theorie des Liquides (1888) found the following
formula satisfactory

77 = 770(1 + ae~bT*y (47)

The constant c varies little from liquid to liquid from 2.65 to 2.85.

Jaeger (1893) has worked out a kinetic theory of liquids on
the ground that the transfer of momentum takes place by the
molecules passing back and forth from one layer of molecules to
another. He gives the expression

. . .

where r is the radius of a molecule, v its mean velocity, X its
mean free path, and p is the density of the liquid.

Similarly Kamerling Onnes has derived a formula from the
theory of corresponding condition of van der Waals,

= Constant (49)

VMTcr
where V is the molecular volume, M the molecular weight,
Tcr the critical temperature, and 77 V^ is the molecular surface
friction. The formula does not apply at low temperatures and
perhaps only perfectly as the critical temperature is reached.
Perry (1893) states that sperm oil cannot be represented by
any single formula since a discontinuity occurs in the viscosity
and density curves at 40°. It should be added that he took care
that the velocity of flow did not exceed the critical value for
viscous flow. He employed two sets of constants in the formula
rj = a(T - &)-* (50)
Examining a considerable number of the formulas which
had already proved of value and given above, Duff (1896)
obtained the following formula by integrating the curve of
subtangents derived from them:
f .
(5D