( 797 ) 



11 h 

 1_. 



|/2rr;<.s- 8 v 



be changed bv first approximation into P = — or 



V b 



1—2- 



V 



neglecting- the terms of higlier order F= 1 -f ~ - . 



/' V 8 ^V 



The other theorem says that the [)ressure on the wall (or an 



imaginary partition) is inversely proportionate to the mean length of 



path. Already Kortewkg^) has felt an objection to this tiieorem,and 



has therefore looked for another way of deriving the equation of 



state ; though convinced of the vahdity of the theorem, van der Waals ■') 



has later on given another proof, because he considered this theorem 



as a not to be pro\ed dictum. After the appearance of the already 



cited paper by van dek Waals Jr., however, it is in my opinion 



beyond doubt, that this theorem does not contain an unprovalde truth, 



but — at least in the tei-ms given here — a provable untruth. For 



it says the same thing as the statemeut, that the pressure exerted 



by the collisions on the distance-spheres per plane unity is equal to 



that on an imaginary or real wall. It seems to me, however, that 



van der W\aals Jr. has convincingly proved, that when the terms 



b 

 of the order - are taken into account, the relation between these 



V 



, . , • , 3 6 



pressnres detmed in the usual Avav, is 1 . 



8 V 



If this result is combined with the just mentioned value for the 

 number of collisions, which determine the pressure on the distance- 

 spheres, it is seen, that also in this way the fourfold of the volume 

 of the molecules is found as tirst correction, but for the present this 

 does not teach us anything about the tinal form, because in the 

 communication of van der Waals Jr. the relation of the pressures 

 is not given in its true form, but developed to an intbiitely extended 

 series with neglect of the higher powers, which are, however, material 

 to the determination of the tinal form. 



In order to derive the iinal form, we may, if we want to avoid 

 speaking of repulsive forces, make use of the method based on the 

 increase of the trans|)ort of moment brought about by the collisions. 

 We start in this from the observation, that the quantity of motion, 

 which, bound to the molecules, generally moves on with the velocity 

 of them, proceeds in a collision over a certain distance with infinite 



1) Verslagen der Kon. Ak. Afd. Natuiuk. Tweede reeks, X, p. 3G2. 



2) GontinuitUl 189'.l, p. 00 cf. 



