246 
Proceedings of Royal Society of Edinburgh. [sess. 
The agreement with the experimental data wonld be somewhat 
closer if II for any one temperature were (in accordance with theory) 
regarded as a quantity which increases with the compression produced. 
For the present, as no definite theoretical basis has been assigned 
for it, the formula must be regarded merely as an exceedingly con- 
venient mode of summarizing the experimental results ; justified by 
the closeness of its general agreement with them. 
On these numbers remark 
First., that e is nearly the same for all the liquids in the table : — 
its lowest value being for propylic alcohol, and its highest for 
water. But the differences of these extremes from the mean of all 
are less than 7 per cent. Hence it seems that ordinary liquids, as 
a rule, would be reduced by infinite pressure to about 70 per cent, 
of their usual volume : — provided, of course, that the formula 
remains applicable for pressures immensely exceeding even' the 
enormous ones applied by Amagat. 
Second, e increases, as a rule, with rise of temperature. [But it 
does not appear to increase, in any case, so much as to make the 
ultimate volume diminish when temperature rises.] 
Third. Except in the case of water, H falls off rapidly with rise 
of temperature. This was, of course, to be expected from the 
increase of volume ; and it is the chief cause of the increase of 
compressibility as given by the formula. But the value of H does 
not seem to vary inversely as the square of the volume. 
Fourth. In the exceptional case of water, H increases steadily 
with rise of temperature, at least up to 40° C. This is the im- 
mediate cause of the diminution of compressibility given by the 
formula as the temperature is raised. But, so far as the present rough 
calculations go, Amagat’s data would seem to make the temperature 
of minimum compressibility considerably lower than that assigned 
by Pagliani and Vincentini. [This may be due to the great range 
of pressure, or to the fact that the formula treats H as a constant 
instead of taking account of its increase with compression.] 
It is interesting to compare, with these, some (necessarily very 
rough) results for a substance which requires considerable external 
pressure to keep it in the liquid state. It is shown that if the 
empirical formula, above, be true generally for any substance, it holds 
from any initial value of Vq, provided that we give e and H proper 
