1888 - 89 .] Prof. Tait on Virial Equation for Molecular Forces. 69 
special consideration. What is now to be taken as the measure of 
temperature ? Van der Waals and Clausius alike take the whole 
kinetic energy as proportional to the absolute temperature. And 
Clerk-Maxwell says ( [lx, .) “ The assumption that the kinetic energy 
is determined by the absolute temperature is true for perfect gases, 
and we have no evidence that any other law holds for gases, even 
near their liquefying point.” 
On this question I differ completely from these great authorities, 
and may err entirely. For it appears to me that only if E (with a 
constant added, when required, as shown below) is regarded as pro- 
portional to the absolute temperature, is the equation that of an 
Q 
Isothermal. But if the whole kinetic energy, E -j- ^ , is to be 
considered as proportional to the absolute temperature, the equation 
would seem to be that of a species of Adiabatic. Van der Waals 
and Clausius do not call attention to the fact that the whole kinetic 
energy necessarily varies with the volume (when there are inter- 
molecular forces, and the mean-square speed of a free particle is 
regarded as constant), and therefore cannot be regarded as constant 
in the Yirial Equation unless heat is given to (or taken from) the 
particles. 
The answer would seem to be : — difference of temperature, as 
measured experimentally, depends upon the gross rate of heat 
transactions between two bodies in contact; so that, as change 
of relative speed of pairs of particles will not affect their heat- 
transactions with the walls of the containing vessel, or with a 
thermometer, the part E, alone, is entitled to be interpreted as 
proportional to the absolute temperature. This will, apparently, 
be the case so long as, at every instant, the majority of the particles 
are free from molecular force. But a different result may be 
expected when none (or a small minority only) are free from mole- 
cular force. And here I may mention, in passing, another con- 
nected complication. There must be molecular force between the 
particles and the walls of the vessel ; so that p, as defined in the 
Virial equation , is necessarily greater than the value calculated from 
h, even when the volume is so great that the effect of the molecular 
force between the particles is insensible. [It is possible that this 
consideration may help to explain the serious differences between 
