( '^^ ) 



But there is still ca ,^econd metliod, wliit'li leads to the purpose 

 quicker aud uioi'e accurately in my opinion, viz. iho, theiinodnnnrnu' 

 method. What can hardly be taken into account in the first method: 

 attraction, the staying together for some time of' the molecules, for- 

 mation of so-called chisters of molecules, etc. is here implicitly 

 directly reckoned with. 



The thermodynamic (or statistic) method simply briefly summarizes, 

 what the kinetic method would be able to reach only in a very 

 circuitous way. The thermodynamic method does not occupy itself 

 with the vicissitudes of every molecule separately, but only directs 

 its attention to the most probable pial state of the system. And the 

 collisions and the temporary molecule aggregations considered in tlie 

 kinetie theory are — from a thermodynamic point of view — nothing 

 but the double, triple, quadruple etc. molecules, the varying quantities 

 of which are only functions of v and T. 



It is this method which more than ten years ago I wanted to 

 apply to the solution of this problem, and I repeatedly discussed it 

 orally, but I abandoned the attempt, because at the time the solution 

 was sought in an entirely different — in my opinion — impracti- 

 cable direction. I am now perfectly justified in using the qualification 

 "impracticable", as I myself am more or less competent to judge 

 about it. 



There is, however, one difference between the two methods. The 

 kinetic method gives some quantitive results, which the thermodynamic 

 method would never be able to give. E.g. that for v = ao the volume 

 V must be diminished by four-WmQ^ the molecular volume, to enable 

 us to find the correct value for the pressure. For this is a question 

 which is in connection with the collision of molecules considered 

 as perfectly elastic spheres. 



But the corrections which were applied later on for the overlapping 

 of two, three, aud more "distance spheres", can also be obtained 

 thermodynamically, in my opinion, by examining how many double, 

 triple etc. ujolecules are temporarily formed. It is true that w^e do 

 not arrive at the quantitative value of the coefficients «, ^?, etc. of 

 before, but yet at quantities corresponding with them. Where, 

 namely, these coefficients a, (3, etc. were calculated from the consi- 

 deration of segments cut off from purely geometrical spheres, now 

 the quantities A/>, hjj, etc. are entered into the calculation, i.e. the 

 variation of the molecular volum«i in consequence of the formation 

 of double, triple, etc. molecules. These last quantities remain purely 

 empirical, and can be considered kinetically as the apparent change 

 of 4/> for simple molecules, when two, three etc. of them get into 



7 

 Proceedings Royal Acad. Amsterdam. Vol. XIV. 



