( 804 ) 



the axiom from which van der Waals started, viz. that we must 



equate tlie pressure on the distance spheres and that on the outer 



wall, is true, if onlv we apply it to the pressure p' . This result is 



only in apparent contradiction with the result of van der Waals Jr., 



that the pressure P on a fixed plane wall stands to the pressure P' 



3 b 

 on the distance spheres in the ratio of 1 : 1 — — - . For these pressures 



P and P' liaA'e been found by supposing the quantity of moment 

 furnished by the Avail (and the distance spheres) in the collisions to 

 be distributed over the toUd surface, so by assuming that every 

 surface element contributes an equal amount to the inq^ulsc; the 

 pressure />' of Avhich there is question here, and which proNed to be 

 the same for both, is found on the other hand by supposing, that 

 only the mean free surface contributes to the quantity of motion, 

 and that the rest is therefore subjected to a pressure = 0. 

 From this follows: 



, free area of surface of impact , / h 



total area of surface of impact \^ v 



, , free surface of distance spheres ,/ 11 /> 



■' total surface of distance spheres \^ 8 t- 



lib 

 1 _ __ 



P' 8 V 3 b 

 and so — = = 1 — with neglect of the terms of higher 



P b Br 



V 



order. 



The importance of the proof completed in this way, lies for me 

 in the fact, that it makes use of the idea, of systems of molecules 

 whose intra-nu:)lecular forces need not be introduced into the equation 

 of the \irial, pro\ided Ave adopt the pressure integrated o\ er the 

 whole Aolume of these systems in the virial. I need not point out 

 tiie great advantages of such a point of AieAv, already cursorily 

 mentioned by van der Waals in his dissertation, and later worked 

 out; the communications of van der Waals on the equation of state 

 and the theory of cyclic motion are striking evidences of its \alue. 



Now it is true that there is a difference between our case and 

 the cases, to which this view is applied in the communications 



in connection with the volume ut llie di.sLance spheres, wliich are cut by the sui-- 

 facc of impact. TJiis correction would come to an increase ot the volume to be 

 integrated with that part of the distance spheres that is found between the surface 

 of impact and tlie outer v»'all, but it is clear that this volume may he neglected 

 with the same riaht as the total volume enclosed bv those two surfaces. 



