128 FLUIDITY AND PLASTICITY

In 1881 Slotte gave a formula to cover the entire range of
viscosities from 0 to 100°

, = a-^ (39)

c -}- Tc

or

which accords with the values of Sprung to 0.7 per cent.

Most of the formulas which have been proposed have been
I applied primarily to water. But Koch (1881) and Wagner (1883)

found that a formula of a different type is necessary for mercury
and Koch proposed the formula

which holds from —20 to 340°C with a maximum deviation of
less than 2 per cent. But Slotte has applied the much simpler
formula of Meyer and Rosencranz with good results. On the
f other hand, Batschinski (1900) has given a formula for mercury

„ = ± + b + cT (42)

where T is the temperature absolute. As a first approximation

iT = a, (43)

which can be deduced from Jaeger's theory of fluid friction.

Graetz (1883—5) is one of the few who have attempted to derive
a formula from theoretical considerations. We may therefore
give his argument in some detail.

According to Maxwell (1868) the viscosity of a body is the
product of two factors, the modulus of rigidity E and the time
of relaxation T. The time of relaxation was defined as the time
necessary for the strain after deformation in a body to sink to
l/E of its original value. The reciprocal of the time of relaxation
is called the relaxation number, n} or

This is the number of times per second that the strain will sink
to l/E per second if the strain is renewed. For absolutely rigid
solids the value of r is infinite and for ductile solid bodies which
show elastic after-effect the relaxation may continue for hours or
days. But if, through raising the temperature, the substance is