specific heat_ over the range 18 deg. to _t_. The specific heat itself
can be deduced only by differentiating the curve of observation, which
greatly increases the uncertainty. The peculiar advantage of the
electric method of Callendar and Barnes, already referred to, is that
the specific heat itself is determined over a range of 8 deg. to 10
deg. at each point, by adding accurately measured quantities of heat
to the water at the desired temperature in an isothermal enclosure,
under perfectly steady conditions, without any possibility of
evaporation or loss of heat in transference. These experiments, which
have been extended by Barnes over the whole range 0 deg. to 100 deg.,
agree very well with Rowland and Griffiths in the rate of variation at
20 deg. C., but show a rather flat minimum of specific heat in the
neighbourhood of 38 deg. to 40 deg. C. At higher points the rate of
variation is very similar to that of Regnault's curve, but taking the
specific heat at 20 deg. as the standard of reference, the actual
values are nearly 0.56% less than Regnault's. It appears probable that
his values for higher temperatures may be adopted with this reduction,
which is further confirmed by the results of Reynolds and Moorby, and
by those of Ludin. According to the electric method, the whole range
of variation of the specific heat between 10 deg. and 80 deg. is only
0.5%. Comparatively simple formulae, therefore, suffice for its
expression to 1 in 10,000, which is beyond the limits of accuracy of
the observations. It is more convenient in practice to use a few
simple formulae, than to attempt to represent the whole range by a
single complicated expression:--

Below 20 deg. C. s = 0.9982 + 0.0000045(t - 40)^2 - 0.0000005(t - 20)^3.

From 20 deg. to 60 deg., s = 0.9982 + 0.0000045(t - 40)^2 (5).

/ s = 0.9944 + .00004t + 0.0000009t^2
Above 60 deg. to 200 deg. < (Regnault corrd.)
\ s = 1.000 + 0.00022(t - 60), (Bosscha corrd.)

The addition of the cubic term below 20 deg. is intended to represent
the somewhat more rapid change near the freezing-point. This effect is
probably due, as suggested by Rowland, to the presence of a certain
proportion of ice molecules in the liquid, which is also no doubt the
cause of the anomalous expansion. Above 60 deg. C. Regnault's formula
is adopted, t