130

FLUIDITY AND PLASTICITY

where Tcr is the critical temperature and Ts is the temperature of
solidification.

Applying this formula to the data of Rellstab, and Pribram
and Handl, Graetz found that it was satisfactory in some fifty
cases, but it is inapplicable to the fatty alcohols.

This formula is a particular form of the one already given by
Slotte. Slotte (1883-90) reached the conclusion that none of
the preceding formulas gives satisfactory results with substances
whose viscosity changes rapidly with the temperature, as is
generally true of very viscous substances. He proposed the
formula

where T is the temperature centigrade and a, b, and n are arbi-
trary constants. Slotte found that this formula gave better
results than any other and Thorpe and Rodger adopted it in
their great work as the most satisfactory formula at their disposal,
but this formula like the others breaks down when applied to the
alcohols. In the case of several of the alcohols it was necessary
to apply the formula three times with different constants over
different parts of the curves in order to reproduce the observed
values with anything like the desired accuracy. The values of
n vary from 1.4 to 4.3.
Several exponential formulas have been proposed. Reynolds
(1886) and Stoel (1891) suggested the formula
rj = ae~^ (46)
which Reynolds found to apply to olive oil and Stoel and De Haas
(1894) found to apply to methyl chloride between the boiling-
point and the critical temperature. In this formula e is the
natural logarithmic base and a and 7 are constants. Heydweiller
in 1895 investigated benzene and ethyl ether over a similar
range of temperature, and found that the formula holds between
the reduced temperatures of 0.62 and 0.87 for the purposes of
interpolation; but that similar systematic deviations occur for all
substances, which is due to the fact that the temperature coef-
ficient of the viscosity is not constant but passes through a point of
inflection. Below the boiling-point the viscosity-temperature
curve is convex toward the temperature axis while near the