1888-89.] Prof. Tait on Virial Equation for Molecular Forces. 65 
On the Virial Equation for Molecular Forces, being 
Part IV. of a Paper on the Foundations of the 
Kinetic Theory of Gases. By Prof. Tait. 
In the preceding part of this paper I considered the consequences 
of a special assumption as to the nature of the molecular force between 
two particles, the particles themselves being still treated as hard 
spheres. My object was to obtain, by means of rigorous calculation, 
in as simple a form as possible, a general notion of the effects due 
to the molecular forces. My present object is to apply this general 
notion to the formation and interpretation of the Virial Equation. 
In the extremely ingenious Thesis of Van der Waals, who first 
succeeded in representing by a simple formula the main results of 
the researches of Andrews on the Isothermals of Carbonic Acid, 
the Virial Equation was employed; but, as was remarked by Clerk- 
Maxwell (Nature, Oct. 15, 1874), “ where he has borrowed results 
from Clausius and others, he has applied them in a manner which 
appears to me to be erroneous.” The object of the present paper is 
to attempt a legitimate (though, of course, only roughly approximate) 
application of the Virial Equation to the same question. The result 
cannot differ much quantitatively (though it may be widely different 
qualitatively) from that of Van der Waals, if it also can represent 
Andrews’ experimental data. 
The Virial Equation is 
From this Van der Waals derives the following expression 
in which the right-hand member is treated as a constant multiple of 
the absolute temperature. Now it is certain that, when there is lio 
molecular force except that of impact, the term 
(Read January 21, 1889.) 
(Abstract.) 
P(mii 2 ) = |^V + P(Rr). 
**(Rr) 
VOL. XVI. 28/2/89 
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