66 
Proceedings of Royal Society of Edinburgh. 
takes, to a first approximation at least, the value 
-bp, 
and the whole becomes 
p(V-b) = l$(mv 2 ). 
The principles on which the Yirial equation was itself based for- 
bid us to introduce any change in the meaning of the factor p, 
which has already been strictly defined as external pressure. Van 
der Waals, however, retains this form of the Yirial equation (derived 
without the assumption of molecular attraction), modifying it simply 
by the addition to p of a term a/ Y 2 , which is the internal pressure 
(K of Laplace) due to the molecular forces. Undoubtedly the com- 
plete Yirial equation, when molecular forces are taken into account, 
must contain a term somewhat of this nature ; but it ought to be 
obtained (with its proper factor) directly as a part of the expression 
J^(Rr). It seems to me that this must be the main point to which 
Clerk-Maxwell referred in the passage above quoted. It is curious 
that Clausius did not raise this objection to Yan der Waals’ equation, 
but contented himself with making modifications derived from 
general considerations, by which it was changed from 
kt a 
+ kt c 
t0 P = T^a.~WVpf' 
The close agreement of Yan der Waals’ equation, the first of these, 
with Andrews’ experimental results was exceedingly remarkable : — 
and Clausius’ modified form seems to suit them almost exactly ! 
But Clerk-Maxwell says (loc. cit.), “though this agreement would 
be strong evidence in favour of the accuracy of -an empirical formula 
devised to represent the experimental results, the equation of M. Yan 
der Waals, professing as it does to be derived from the dynamical 
theory, must be subjected to a much more severe criticism.” 
Along with the objection just mentioned, there is another and 
serious one. Van der Waals’ equation appears to be unwarrantably 
simple, as it contains (besides the k of the “perfect gas” formula 
pY = kt) only two disposable constants. A little thought shows 
that (even if the laic of molecular force were the same for all bodies, 
which we have no right to assume) we should expect to find three 
