70 Proceedings of Royal Society of Edinburgh. [sess. 
the results of the ablest experimenters, such as Mendel6ef and 
Amagat, regarding the relation between p and V in air, hydrogen, 
&c., at pressures considerably less than an atmosphere.] 
Consider, for a moment, the case of a gas, in which the kinetic 
energy is not much greater than that due to the molecular forces 
alone, these being so intense as to aggregate its particles into a 
group, so that scarcely any of them ever escape from the thick of 
the encounter. Its external pressure would be practically nil , and 
its temperature (as measured by a thermometer) close to absolute 
zero, although the mean kinetic energy per particle may be very 
high. Such a group would no more communicate heat to a thermo- 
meter plunged in it than would water (in consequence of Laplace’s 
K) squeeze a finger dipped into it. Next, consider the case of a 
liquid in contact with its saturated vapour, at a temperature so 
low that there is great difference of density between the states. 
On the hypothesis which underlies the whole of my work (viz., 
that the particles are hard spheres, with unit coefficient of resti- 
tution) permanently double or multiple particles cannot occur in 
the vapour. Here the average kinetic energy per particle, in the 
liquid, should apparently be much greater than in the vapour, yet 
their temperature and their ( external ) pressure are the same. On the 
other hand, the condensation of part of the vapour produces a rise 
of temperature. It seems to follow that E (defined as above) be- 
comes less in the liquid than in the vapour state, if the temperature be 
maintained constant. In other words, no formation of liquid is pos- 
sible isothermally unless heat be abstracted ; not even if the walls of 
the containing vessel could be made to shrink in, bit by bit where 
no impact is impending, without doing work on the gas. And, con- 
versely, a liquid cannot, without supply of heat, be dissipated into 
vapour even in vacuo. The effect on the above equation would be 
to make E + L, and not E, proportional to the absolute temperature, 
L being a quantity which becomes rapidly less as the temperature 
rises towards the critical point. The only noteworthy effects, of this, 
on the graphical representation of the Isothermals, would be to shift 
them parallel to the pressure axis, by amounts which increase from 
the critical point downwards; and to (slightly) modify their form 
in the neighbourhood of the minimum ordinate of each. Their 
general appearance will be unchanged, while our hypothetical 
