1202 



in these results could not have given rise to such a difference. For 

 at the critical temperature 1 : RT = 8,2306,. so that with u = 0,06426 

 (see foregoing Paper, 2"^' table) the value of ƒ (a) becomes = 1,3180, 

 while at the BoYLEpoint, where 1 : /^ Z' is := 2,545, the value of this 

 function is = 1 ,0864. That of the temperature function ƒ (/;) becomes, 

 hovi^ever, in the two cases resp. 1,6971 and 1,1777, so that b(,: a 

 would become = (6,)^ : a^ X (1,697 : 1,318) = 1,288 {b,)^ -. a^ in 

 the first case, on the other hand = id X 1,178 : 1 ,086 = 1,084 (6,,)^ : a^ 



in the second case. 



Experimentally the same value (viz. 2,545) was found for the two 

 relations. With Boi.tzmann's distribution factor they would not be 

 the same, but be in the ratio of 1,288:1,084, '\.Q.b,,:a would have 

 to be 1,19 times gieater than at the BoYLKpoint, which would require 

 an error of almost 20 "/o in one of the two observations. And this 

 is very unlikely, indeed — unless the ratio of b,,:bk, for which we 

 assumed 1,044 (see foregoing Communication, ^ 2), should have to 

 be about 1,24. But since the value of the fictitious b in v — b at the 

 critical point will certainly not be 20 7o smaller than the limiting 

 value for great volume, this supposition is not particularly probable 

 either ^). 



The same thing applies to a still greater degree with respect to 

 the f {a) and f{b), calculated by Reinganum and Keesom '), in which 

 they started from the same distribution factor, but where r in the 

 virial of attraction was taken not almost constant r= r, (see § 9), but 

 varying between .v and oo . In order to render the integration pos- 

 sible, a definite form, viz. — c : r^, was then used for P, {q ^ 3). 



dP- qc dPr qc ^ n ^ ■ 



Then — =:-^, hence r' — = — -. If o were = or < 3, the integral 

 dr r<?+i dr r1~^ 



would become infinitely great (for ^ = 3 logarithmically infinite). 



For ^^or]>4 this difficulty disappears. 



From the general formula (42) on p. 32 of Suppl. 24 we can derive 



(Moo « 



>+#^,^.+ ^l^/^.T+*^,(7^.)V. 



2q—'óBT' '?,q—2>\RTJ " iq 

 for the quantity a [after subtraction of 



1) For this we should have to assume that the value of r^ in ^9") for a volume 

 corresponding with v^. were much greater at lower temperature than at higher 

 temperature, where the ratio 1,044 is determined. Possibly also the value of a on 

 the critical isotherm is slighter for large volume than for smaller volumes, because 

 the factor r^ could then play a part also in the sphere of attraction. (Cf. also the 

 conclusion of § 9, and the footnote in § 11). 



') Suppl. Gomm. Leiden No. 24, 25 en 26. 



