( 788 ) 



It is clear that at least one of these formulae must be wrong and 

 it does not seem doubtfnl to me that (1) is so. As is known, formula 

 (1) has been found by van dek Waals by applying a correction to 

 Clausius' original formula ^) 



jr ns^ — 

 Pi=- r (3) 



,. V 



Now it is easy to shou' that this correction has been wrongly 

 applied to (8). We caji do this without much difficulty either by 

 making the original proof of Clausius for (3) applicable, taking into 

 account the reasons which lead to the correction in question, or by 

 making use of van dek Waals' reasoning for (1), which leads really 

 to (3). For shortness I shall confine myself here to pointing out the 

 mistake in the train of thought, which led van der Waals ^) and 

 after him Koktewec; •') to the application of this correction. This 

 reasoning is chiefly this. Fii-st it is demonstrated that formula (3) 

 holds for a gas, the molecules of which are discs of the same diameter 

 and nature as the spheres iji Cjuestion, which discs have further the 

 property to take a position normal to the direction of their relative 

 motion with regard to a molecule, with which they are going to 

 collide. Then it is thns demonstrated that formula (3) must hold for 

 spheres. (I derive this passage from the proof of Korteweg''), with 

 which that of van der Waals agrees perfectly). 



"Now, however, the moment has come, to remove the incorrect 

 hypothesis — introduced in § 3 — and replace the discs again by 

 spheres. The consequence of this will not be that the nature of the 

 collisions is changed, for any molecule M, which pursuing its way 

 would have reached any disc, ^^'ill infallibly first reach the surface 

 of the sphere, which we now put in its place. All the molecides 

 will therefore strike against the same molecules, whose discs we have 

 supposed to be cut by their centres; but all these collisions will lake 

 place somewhat earlier, in other words, the paths will be shortened." 

 From this shortening of the mean path follows the increase of the 

 number of collisions, as this number is in inverse ratio to the length 

 of path. 



That this reasoning has been able to deceive not only its inven- 

 tors, but so many after them, is exclusively due to the and)iguous 



1) Pogg. 105, p. 239. 



~) Verslagen Kon. Ak. Afd. Natuurk. Tweede reeks, X. 321. Gonlinuitat 1899. 

 p. 4.5 et seq. 



•^) Verslagen Kon. Ak. Afd. Natuiiik. Tweede reeks, X. p. 349. 

 ■^) ], c, p. 355. 



