(801 ) 



11 b'' b' b 



b \-B \-C — 



'' + ? =ir ' + tt^— ^S ■ ■ («> 



26 + -T- + CV 



or 



a \_RT i . b o b^ b' 



i-' + Tr) = -!i+7 + 8^ + .V •••('> 



but this conclusion would be unjustifiable. For it is possible, nay 

 even probable, that the coefficients of numerator and denominator in 

 (6) decrease rapidly ; it is therefore possible, that the true form is 

 accurately represented by a quotient of two forms, which have each 

 only three or four terms; from this folloAvs by no means, that also 

 in the form (7) we should get a close approximation with three or 

 four terms, for the coefticients of the higher powers in (7) do not 

 depend only on the coefficients of the li'ujlier powers in numerator 

 and denominator of (6), l)ut they are also fimctions of the coefficients 

 of the lower powers 1; '\/g; 2; ^''l^^; and in such a way that they 

 do not become zero, when the coefficients of the higher powers in 



(6) do so. Now the difference between (6) and (7) vanishes, of course, 

 for such large values of v, that the series (7) converges strongly, 

 but for the critical volume and even more so for licpiid volumes the 

 difference is very pronounced. This appears already from the simple 

 fact, that a form as (6) can easily yield a minimum volume ; but 



(7) only when an infinite number of tei'uis is taken into account. 

 And also the before mentioned difference l)etween the resuhs of 

 DiETERici on one side, and van Laah and van dek Waat.s on the 

 other side, prove how careful we must be \\\i\\ the introduction of 

 simplifications which seem perfectly allowable. 



§ 4. Also the other ways proposed for finding the equation of 

 state, arrive at similar final results. 



Tiiis is easy to see for the most direct way, indicated l)y Boi/pzmann ^). 

 For it is clear, that liis formula (4), which leads to the form: 



a \ c — 2b 

 /' + ;tJ JT"^^'^ (^> 



r 



requires another correction on account of the fact that the distance 

 spheres cover each otliei- partially. The mimeratoi' of tliis fraction 



') Gastheorie p. 'J. 



53 

 Proceedings Royal Acad. Amsterdam. Vol. VI. 



