462 



C,H,F the value of yu i» =0,95; hence hi.:b, — '2yk = ^,^^, and 

 {h,,.h,)i. = 1,^0 y^l,0Q = '2,0\, whereas 1/2,01 =142. Further for 

 Argon 7jfc=rO,75, hence />/,: /^, = 1,50 and (z';^: 6,)^; = 1,49X1.018 

 (See II, p. 936) =1,516, whereas 1/1,516 = 1,231. 

 It follows from this that with great accuracy 



y„ = Vi^K)k = i^27 (41) 



may be written /or the Umitimj value at low temperature of the 

 characteristic fimction <f. 



It is therefore again only for "ideal" substances {b r= const.) that 

 (f^ = 1, and hence (f continually = 1 from Tk (then = 0) lo the 

 absolute zero. But for all the other substances the value of (f will 

 increase from 1 to a limiting value, which will depend on the 

 degree of variability of b. 



As according to (36) {h,—b„% : b„ = 2/' - 1 = 0,041 y/ Tk (see III 

 § 15), we have also : 



y„ = ]/TTOMVn (41a) 



We shall not enter any further into this subject, leaving it for a 

 possible later discussion. 



In conclusion we shall just repeat what we have already remai-ked 

 in I, p. 820, that the temperature dependence at extremely low 

 temperatures, where the departures from the equipartition law make 

 themselves felt, undergo a modification. But we shall not enter into 

 this any further either, and we only mention that for Argon the 

 departures from the said law fall entirely within the errors of ob- 

 servation even at 90" absolute (the lowest temperature at which 

 observations have been made). Besides, at those extremely low tem- 

 peratures all substances will probably have passed into the solid 

 state, and this state is controlled by other laws than the liquid and 

 the gaseous state, for which our considerations exclusively hold. 



20. Conclusion. Though there are still many questions to be 

 answered, and many difficulties left, we may already conclude in 

 virtue of the foregoing to this : 



1. The quantity a of van dek Waals' equation of state seems 

 within a large range not to depend on the density, so that the 



molecular attraction can be represented by ^^, both in the gaseous 



and in the liquid state. ^). 



1) Gf. also the conclusions in a paper by Tyrer in the just published number 

 of the Zeilschr. f. Ph. Ch. (87, Heft 2) p. 195. 



