FOUNDATIONS OF THE KINETIC THEORY OF GASES. 261 



It is certain (§ 30) that, when there is no molecular force except elastic resilience, the 



term 



£2(Rr) 



in the virial equation takes, to a first approximation at least, the form of a numerical 



multiple of 



S(mu 2 ) 

 v ' 



and thus that, if this term be small in comparison with the other terms in the equation, 

 we may call it 



Thus the virial equation becomes 



p(v — /3) = }2(mtt 2 ) . 



[So far, all seems perfectly legitimate ; though, as will be seen later, I think it has led to 

 a good deal of confusion : — at all events, it has retarded progress, by introducing what was 

 taken as a direct representation of the " ultimate volume" to which a substance can be 

 reduced by infinite pressure. When this idea was once settled in men's minds, it seemed 

 natural and reasonable, and consequently the left-hand member of the virial equation 

 is now almost universally written p(v—fi) ; although, even in Van der Waals' Thesis, it 

 was pointed out that comparison with experiment shows that /3 cannot be regarded as a 

 constant. But its introduction is obviously indefensible, except in the special case of no 

 molecular force.] 



Van der Waals' next step is as follows : — Although p, in the virial equation, has 

 been strictly defined as external pressure (that exerted by the walls of the containing 

 vessel), he adds to it, in the last-written form of the equation (deduced on the express 

 assumption of the absence of molecular force), a term a/v 2 , which is to represent 

 Laplace's K. Thus he obtains his fundamental equation 



(p+^)(v-®=m™v>*), 



or, as it is more usually written (in consequence of the assumption about absolute tem- 

 perature, already noticed), 



_ kt a 



where h is an absolute constant, depending on the quantity of gas, and to be determined 

 by the condition that the gas has unit volume at 0° C. and 1 atmosphere. 



I do not profess to be able fully to comprehend the arguments by which Van der 

 Waals attempts to justify the mode in which he obtains the above equation. Their 

 nature is somewhat as follows. He repeats a good deal of Laplace's capillary work ; in 

 which the existence of a large, but unknown, internal molecular pressure is established, 



