472 Proceedings of the Koyal Society of Edinburgh. [Sess. 
pyrometer scale was 10°, though quarters of a division could be estimated. 
The curves show that up to a certain point, which varies with the pressure, 
the volume increases more rapidly than the temperature ; but that above 
that point the isopiestic becomes a straight line. The greater divergences 
above 700° on the 1000 isopiestic can be explained thus: — a small error in 
the determination of the initial volume has a relatively large effect on the 
value of Y T , and, at these temperatures also, a small change in the pressure 
causes large deviations in the temperature and vice versa. As regards the 
1300 isopiestic, sufficient observations were not obtained to enable so 
complete curves to be drawn in. All the curves drawn show that for a 
given value of V the temperature is higher the greater the pressure. This 
means that above 200° water continues to behave as between 125° and 200°, 
it being remembered that for water the isopiestics have a crossing point 
between 100° and 200°, and that, in fact, below 125° for a given value of Y, 
the temperature is lower the higher the pressure. 
The third column for each pressure in the preceding table gives the 
value of the mean coefficient of expansion of the liquid between 0° and T° 
if we neglect the change in V 0 between 0° and room temperature. The 
change is approximately 4 in 1000, and therefore does not appreciably affect 
the results. It is seen that in general the mean coefficient of expansion 
increases with the temperature, and that the increase is relatively 
greater the lower the pressure. For a given temperature, also, the mean 
coefficient of expansion decreases with increasing pressure, the decrease 
being relatively greater the higher the temperature ; as can also be 
seen directly from the curves in fig. 4. These conclusions agree entirely 
with Amagat’s results for the coefficients of expansion of liquids at 
lower temperatures. 
To obtain values for the true coefficient of expansion — we can 
V 0 d 1 
proceed in two ways. We can either read off from the curves the tangents 
dV 
of the angles of inclination to the T — axis and find — — from these tangents 
a x 
by multiplying by a constant factor which depends on the scales used for V 
and T in the figure, or we can try to obtain equations for the curves, 
expressing Y in terms of T and calculating from them. Considering the 
Ob X 
comparatively large error limit involved in these experiments, and the 
complex formulae which previous observers have found necessary to express 
Yt in terms of Y 0 and T even for very small ranges of temperature, I 
adopted the first method of finding the true coefficient of expansion. The 
