( 794 ) 



Physics. - -'On van dkk Waals' cquatioit of .'itate," by Dr. Ph. 

 KoHXSTAMM. (CoiuiHimicated In' Prof, van ])¥.r Waals), 



§ I. The way, in whu-li we ha\e to lake the extension ofmole- 

 eiiles into account lor tlie derivation of the equation of state, has been 

 repeatedly a subject of discussioiL It is known that, in order to avoid 

 the introduction of repulsive elastic forces and therefore the apparent 

 contradiction with the sup[)osilion that oidy attractive forces act, 

 VAN DER Waals lias, in tiie lirst derivation of his equation, not allowed 

 for this extension by means of the virial, but Uy quite other means. This 

 departure from the path lirst laken was disapproved of by Maxwell*), 

 and stron,ü,ly condomnod by Tait-), who himself from tiie equation 

 of the virial iiad an-ived at an ecpiation of stale, as also Lokentz 

 had derixed, \iz. : 



More llian ten years ago an interesling controversy was carried on 

 between Tait'), llAYLEKiH'') aii<l Koktkavk(;M on tlie value of this form 

 in comparison with the original form : 



p+~^i'•-f')-=f^"f' (2) 



Whereas Tati' considered an (M|ualion of the loi'in (1) as the only 



cori-ect one and the derivation of van dek Waals as decidedly 



wrong, because it could nexer lead to this foi-m, Koktewec; thought 



tbal he could pro\e, Ihat (ui the contrary the linal I'esull ought to 



have form (2), a form which he greatly preferred. This preference, 



xvhich is not to be Juslitied tVom a [>urely mathematical point of view 



as the two foi-mnlae ai'e identical when we take oidy the terms of 



A 

 the order - into account — and the terms of higher order are 



r 



neglected in both cases — may be easily understood when we con- 

 sider that we have here to do with |)hysical problems. For whereas 

 from the form (1) neither the existence of a minimum ^•olume, nor 



1) Nature 10, p. 477. 



2) Nature 44, p. 540, 027; 45, 199. 



3) Nature 44, p. 499, 597 ; 45, 80. 

 ^) Nature 45, p. 152, 277. 



