440 
DR. ANDREWS ON THE GASEOUS STATE OE MATTER. 
From the results given in the last three tables, it is manifest that the values of p, 
which in the case of a perfect (ideal) gas would always be unit, steadily diminish for 
the same temperature as the pressure increases. An important exception to this remark 
occurs in the last recorded result in Table XV., from which it appears that at the tem- 
perature of 64° the value of p, which had diminished from 0-9478 to 0-4466 as the 
pressure was raised from 17-6 to 145-5 atmospheres, instead of continuing to diminish 
with a further increase of pressure, actually changes its direction, and at 223 atmospheres 
has increased to 0-4994. No change of this kind occurs at 100°, although the experi- 
ments were carried to 224 atmospheres. The explanation of this change in the value 
of p, after a certain pressure has been reached, I have already anticipated when referring 
to a similar change in the coefficient of expansion by heat at high pressures, as shown 
in Table VIII. At the temperature of 64°, and under a pressure of 223 atmospheres, 
carbonic acid has in fact approached the liquid volume, while passing through those 
intermediate conditions of matter which, in a former Bakerian Lecture, I have described 
as establishing an unbroken continuity between the ordinary gaseous and ordinary liquid 
states. At 100° carbonic acid under the same external pressure has not reached this 
stage of the process ; but if the experiment had been carried to higher pressures, a like 
change in the value of p would no doubt have occurred. These remarks will be fully 
confirmed when I give the values of p for the gaseous and liquid states at the same tem- 
perature, as calculated from my former experiments*. The true import of the values 
of p at a constant temperature will be considered hereafter. 
From Tables XIV., XV., and XVI. it further appears that the values of p approach more 
nearly to unit the higher the temperature, in accordance with the principle I deduced 
from my former experiments, that as the temperature becomes higher the curves repre- 
senting the change of volume of carbonic acid at different pressures approach more 
nearly to the curve of a perfect gas. But to find the actual relation which exists between 
these curves it will be necessary to make a preliminary calculation. 
In the curves representing the changes of volume of a gas by pressure at different 
temperatures, I propose to designate those points where the values of p are equal, homo- 
logues, or homologous points, and the lines passing through corresponding homologues, 
homologous lines. Let p be the ratio between the external pressures p and p' at 
homologous points on the curves of any two temperatures, or 
In Tables XVII. and XVIII. the values of p are calculated for the respective tem- 
peratures of 6 0, 5 and 64°, and of 64° and 100°, from the values of p in the preceding 
tables. The necessary reductions to obtain the homologous points at each temperature 
were carefully made. 
* Philosophical Transactions for 1869, p. 581. 
