( 80^ ) 



ineiitioiiod. For in flic laller wo sn|)|)o,so llie oxislciK'e of I'cally 

 [)ermaii(Mil sysliMus of alorns, anIioivjis in oiii- caso two molecules 

 u'lioso (lislancc spheres cover cacli oilier parfially, and wlilcli are 

 therefore lhoii<i'lil as a sysleui, remain only (ooether foi- an excee(lin<>iy 

 slioii lime. I)iil we see that we n'cl lo Hie rig'lil resnll by assuming, 

 that also I he pari of tlie snrface of im[>acl lying williin the (iistance 

 sphei-es, is jiarl of a "system", and thai therefore the force exei'ted 

 on it, does not count ^). This resnlt is a priori hy no means im|»robal>le, 

 for this part of the snrface of impact has exactly the same essential 

 property as the other parts of "systems" viz. of falling within distance 

 spheres, whereas in the commnnications mentioned this hypothesis 

 for the snrface of impact was not necessary, because thei-e the 

 systems are characterized by other properties which do not distinguish 

 the snrface of impact viz. that it is part of the same system for a 

 comparatively long time. 



§ 5. The resnlt obtained in the jireceding §, enables ns now to 

 use also the lirst method of reasoning of van dkr Waals for the 

 determination of the tinal form without making use of the ^•irial. 

 For Ave have seen that the pressure /-* on the ^vall, when the 

 pressure on the distance spheres F' is determined by 



free 



,-, area of surface of impact 

 P total ^ 



surface oi distance spheres 



(10) 



total 



No\N' the pressure on the distance spheres is, as appears from 



Clausus' formula for the length of [lath, proportional to: 



free ,. „ ,. , 



— r~T surmce or distance spheres / 

 total 



available volume 

 so that we tind from this for /-*: 



free 



j,^^.U^ 



area of the surface of impact 



available volume 



^) The real significance of [lie introiliiclion of llicse .system;; may he expressed 

 in this way, that we think tiie siliiati(jn f)!' one given moment as lixed. and lake 

 into account tlie systems ot more tlian one distance spliere formed in lliis way. 

 This removes also wliat is paradoxal in tlie supposition (see v. u. Waals Jr. loc. 

 cit. p. 644-) that the pressure is () in those places wliicli have just experienced a 

 collision or will soon experience one, viz. the points in the dishmce spheres. Kor 

 in this fixed state those points are really exempUHl from collisions fi-om all o/lier 

 molecules than those lielonging to their system, and whose pressure may therefore 

 be considered as an intra-molecular force. 



