134 FLUIDITY AND PLASTICITY
curve which contains these properties. The linear curve for
substances like mercury is of course but a special and extreme
case. It is very important that we find out whether other mon-
atoniic liquids, such as, for example, liquid sodium, argon, et ceL
have a linear volume temperature and fluidity-temperature curve.
, Given the properties of a general fluidity-temperature curve
it is easy to obtain the curve which contains these properties.
The simplest is
T = Aq> + C - - (53)
9
For the simplest case, which we have in mercury, the constants
B and C are each zero and our equation, becomes that of Batschin-
ski (41); for other substances at high temperatures the term B/<p
becomes negligible and the equation becomes that of the asymp-
tote
T = A<p'+ C
This linear equation can be transformed into the formula of
Meyer and Rosencranz. Thus while our formula (51) agrees
with' some of the simpler formulas which have been proposed,
it is at variance with those which have had the widest usefulness.
For example, the Meyer-Poiseuille formula may be written
^ = A + BTC + C2V (53a)
which is the equation of a parabola. Were it valid as a general
equation, the fluidity would have a minimum value at 0°C,
and at high temperatures the fluidity curve would tend to be-
come parallel to the fluidity-axis. It needs no argument to show
that this equation cannot be general.
By increasing the number of terms, the formula of Meyer-
Poiseuille becomes the second formula of Slotte,
? = A(B + Tcy
The effect of the additional terms is to increase the curvature
but it does not remedy the defects noted. The equation of
Stoel and others may be regarded as a special case of Slotte's
equation where the number of terms is infinite.
The formula of Graetz is defective in that it assumes that the
fluidity becomes zero at a definite positive temperature and that
at the critical temperature the fluidity is infinite. Neither of
these assumptions can longer be held.