1888 - 89 .] Prof. Tait on Virial Equation for Molecular Forces. 67 
disposable constants at least. For we must provide (1) for the 
diameters of the particles, on which the “ ultimate volume ” depends ; 
(2) for the range of molecular force ; (3) for the maximum relative 
potential energy of two particles. It is quite clear that these three 
must be assumed to be entirely independent of one another ; at 
least unless experiment should, some day, prove the existence of a 
relation among them. 
The general results obtained in Part III. of this paper show that, 
when molecular attraction is taken into account, the whole kinetic 
energy must exceed that of particles free from molecular forces by a 
term proportional to the fraction of the whole particles which are, 
at any and every time, within molecular range of one another. 
(This raises another point on which I cannot agree with previous 
writers. It will be discussed later.) Hence, if i; 2 = 3/27i when the 
volume is practically infinite, we have approximately 
& = 3/2h + ^-, 
where c and a may be treated (within certain limits at least) as 
constants. The negative sign is given to a because the particles (in 
consequence of the presumed intensity of the molecular force) move 
very much faster when under mutual influence, and therefore spend 
relatively less time in that part of their space. It is not easy to see 
what, if any, change of form this expression must take when V 
becomes so small that no single particle is ever free from the action 
of the molecular forces of a number of others. For the present we 
may employ it as it stands even when the volume is of the order a. 
It is possible that there may be gases (hydrogen ?) in which, on 
account of the comparative feebleness of the molecular force, a may 
be positive : the effect of the increased length of the relative path 
not being overcome by the increase of relative speed. But, in this 
abstract, I merely mention the question. 
The term J2i(Rr) gives the negative part -pfi due to the impacts, 
where j3 also may be regarded (at first, at least) as constant, though 
it certainly increases with diminution of volume. This is, at least, 
the result obtained when the only molecular forces considered are 
due to the elastic resilience. It evidently should be considerably 
modified by the introduction of the molecular attraction ; but we 
will not, for the present, insist on this point further than to say 
