262 PEOFESSOR TAIT ON THE 



entirely from a statical point of view. He then gives reasons (which seem, on the 

 whole, satisfactory from this point of view) for assuming that the magnitude of this 

 force is as the square of the density of the aggregate of particles considered. But his 

 justification of the introduction of the term a/v 2 into an account already closed, as it 

 were, escapes me. He seems to treat the surface-skin of the group of particles as if it 

 were an additional bounding-surface, exerting an additional, and enormous, pressure on 

 the contents. Even were this justifiable, nothing could justify the multiplying of this 

 term by (v — /3) instead of by v alone. But the whole procedure is erroneous. If one 

 begins with the virial equation, one must keep strictly to the assumptions made in 

 obtaining it, and consequently everything connected with molecular force, whether of 

 attraction or of elastic resilience, must be extracted from the term 2(Rr). 



It is very strange that Clausius,"* to whom we owe the virial equation, should not 

 have protested against this striking misuse of it, but should have contented himself with 

 making modifications (derived from general considerations, such as aggregation of par- 

 ticles, &c.) which put Van der Waals' equation in the form 



_ kt a 



P ~v~=p~t(v + a) 2 ' 



65. Van der Waals' equation gives curves, whose general resemblance to those plotted 

 by Andrews for C0 2 is certainly remarkable : — and it has the further advantage of repro- 

 ducing, for temperatures below the critical point, the form of isothermals (with physically 

 unstable, and therefore experimentally unrealisable, portions) which was suggested by 

 James Thomson, as an extension of Andrews' work. For a reason which will presently 

 appear (§ 67), Van der Waals' curves cannot be made to coincide with those of Andrews. 



The modified equation of Clausius, however, seems to fit Andrews' work much 

 better : — but the coincidence with the true isothermals is much more apparent than real, 

 because Clausius' work is based on the measurement of pressures by the air-manometer, 

 as they were originally given by Andrews, who had not the means of reducing them to 

 absolute measure. 



But a further remark of Clerk-Maxwell's (in the review above cited) is quite as 

 applicable to the results of Clausius as to those of Van der Waals, viz. : — " 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. Van der Waals, pro- 

 fessing as it does to be deduced from the dynamical theory, must be subjected to a much 

 more severe criticism." 



66. Before I leave this part of the subject, I will, for the sake of future reference, put 

 the equations of Van der Waals and Clausius in a form which I have found to be 

 very convenient, viz. : — 



*-K i -£3P+iV-» (A > 



* Annalen der Physik, ix, 1880. 



