( 803 ) 



to experience a pressure =: 0. He has, however, not worked out 

 this thoiiglit further; as it seems to me, l)e('ause he has not fully 

 appreciated the ideas which led his father to the correction ^V»?- He 

 has, therefore, substituted for this view, another, undoubtedly correct 

 one, but he luxs not explained, how the former might be completed in 

 order to yield also the true result. If, however, we make use of 

 the oi)servation made by him, then it is clear that the pressure 



\vhich seems to be P z=i p -\ — ~ per unit of surface when we think 



it as working in the usual way on the total area of the surface 

 of impact (J, must be really largei- in the gas, viz, equal to 





 p' = i^ —y , when this pressure />' acts only on the free surface 0' . 



.0 

 Now it is clear that this quantity — , which hereby gets into the 



denominator of the first member of the e(piation of state is identical 



with the quantity introduced by Boltzmann in this place. For he, 



too, determines this denominator by examining what part of the 



surface of inq^act falls within the distance spheres. This shows us 



at the same time another point. In the few words which van dkr 



Waals ^) bestows on this derivation of the e(piation of state, he says, 



that the pressure is not to be integrated over the total volume of 



the distance S[)heres, as we might ex[)ect, l)ut over half of it. Now 



I ha\e been struck with this from the beginning, aiul 1 have tried 



to tind the reason in vain. It appears from what precedes that we 



have really to integrate over the total \oliime and that van dkk 



Waals has only introduced the division by two as conq^ensation for 



the circumstance overlooked by him, but which we take here into 



v-2h 

 account. So he got r — h, instead of — , which evidently does 



not make any difference by tirst approximation. But already the 

 second approximation cannot properly be found in this way. 



It appears now, that we must integrate the pressure />', determined in the 

 way above indicated, over the whole outer surface, that of the distance 

 spheres included in so far as they fall outside each other '), and that 



1) Gontinuitat 1899, p. ()2. 



-) The logical inference from this tiieoreni : tlial the true ecjuation of state is found 

 by assuming that every surface element, lying either on a plane or a curved wall, 

 experiences a pressure: // |)er unit of surface provided it does not lie within a distance 

 sphere, in which case the pressure must he put e(|nal to 0, would involve, that 

 we did not integrate the pressuie over liie available voliune (volume diminished 

 by the free volume of the distance spheres), l)ut that another correction was applied 



53- 



