( 574 ; 



The quaiititv « in llie equation of state {d) depends on the forces, 

 which keep flie atoms together in the molecule. These forces are 

 supposed to be proportional to the linear deviation tVoui the })osition 

 of equilibrium r — 1\. 



The equation of state {n) for a tri-atomic gas, c. g. CO.^ — \vhicii 

 in tins case is the combination of two similar equations — will con- 

 tain besides RT still a factor f, whose value Avill vary from 1 to 2 

 according as the different cases occur, which w^e may distinguish in the 

 motion of the atoms. For CO^ a value of nearly 2 is found for ƒ. 

 As, however, this quantity /'for a certain substance is, strictly speaking, 

 variable (see the paper in the "Li^re dédié a Bosscha", quoted above) 

 and as the accurate equation is therefore very complicate, I have 

 chosen a bi-atomic gas, namely hydrogen, in order to test the new 

 equation of van der Waals. In this case /*= 1 and the relation 

 between h and r is represented by the sinq)le equation (1). I hope 

 later to test the equations for oxygen and nitrogen, in order to 

 examine whether the residts f(nmd for hydrogen also hold for these 

 gases. 



II. An (iccuratc kiu)\\ ledge of '/ is re([uired tor the exact calcu- 

 lation of h. This is still a great dil'licully. Alisolnfc certainty as to 

 this value cannot be obtained as yet, but still it ai)pears to me that 

 the value « = 300X1^"^ ^) ^^^^ ^ ''i^l^ degree of probal)ility. Assu- 

 ming another ^•alue for a, I found namely that the values calculated 

 for J> decrease nnich too rapidly, — much more rapidly than agrees 

 with formula (1); this is principally the case in the beginning, i. e. 

 for large values of r. Only the values of />, calculated for a^^'iOOy^iO ^ 

 varied in such a way, that their course was represented by ecpiation 

 (1) with nearly perfect accuracy. Schalkwijk ^) also calculated from 

 his last experiments 10' a = 300 (10" h,, = 910). I therefore thought 

 myself justified in assuming 300 for 10^ a. In the following table 

 we And the values for b at 0° Centigrade, calculated from the equation 



P + ^^ {v-b) = (1 + a) {l-h) (l+«0- 



For (l-j-a)(l — h) we put 0,9994. All values have been multiplied 

 by 10"; the same will be the case with all values of h which we 

 give in what follows. 



At 0° C. we have 



0.9994 



-hz=- . 



a 



1) All values of r, b, etc. have been expressed in the usual practical units. 



2) These Proceedings, June 1901, p. 124. 



