1053 



be only 1,07 according to fSr)). However ~ at very high tempe- 

 ratures /;/, : />„ and .so also h,, : h„ will approach (o a limitiiKj value, 

 so that the coeHicient 0,038 tbi' 1/ 7'/, will probably gradually decrease 

 at higher temperatures. But as yet nothing is known about this, and 

 I shall therefore refrain from giving a more general expression derived 

 from theoretical considerations founded on the calculus of probabili- 

 ties (statistical mechanics), of which (35) or rather (36) would only 

 be a special case, holding only for temperatures up to about 600° 

 absolute. This expression too is characterized by particular sim{)Iicity. 



Finally some indications of the sources of the given values of 

 Tk and yk (found). 



Helium. The value of 71=5,2 is tiiat of Kamerlingh Onnes in 

 Comm. 124 (see also Suppl. N" 21). The earlier value- given in 

 Comm. 102a, 'J 12, and 119 deviate but little from this tinal value. 

 The value of y^ (found) follows from that given for ƒ in Comm. 124, 

 viz. 4,46 as lowest limit. If ƒ is ideutitied with ƒ ', which is certainly 

 permissible here on account of the slight variability of b for Helium, 

 n — V8/=0.56 would follow from ƒ ' = 4,5. I do not know a 

 direct determination of y^. 



Hydrogen. In Comm. 119 is given 71 — 32,3. From /=:4,83 

 (see KuENEN, die Zustandsgleichung, p. 142) would follow y/, = 0,604. 

 I do not know a direct determination of yic either. 



Argon. According toComm. 115, 71 = - -122,44+273,09=150,65. 

 By direct observation (Comm. 131) ;'a, = 0,7446 = 0,745') was found 

 here. 



Xenon. Here 1 find given 71 = 16,6 -|- 273,1 = 289,7, and further 

 y^ = 0,813, as the boundary line coincides entirely with that of 

 0„ where «7: = 0,813. 



We may therefore with close approximation di-aw up the formula 

 2yx: — 1=: 0,038 \^ Tk for substances, the critical temperature of 

 which lies no higher than =t 600° absolute (330° C), and with 

 extension to aibitrary temperatures: 



2y — 1 = 0,0:^8 y/T (85a) 



For {l),i — h^) :h^=z2y' — 1, also holding wlieii a substance is 

 considered at arbitrary temperatures, and not only at tlie critical, 

 we may j)ut : 



^— = 2y'- 1=0,041 1/7' (36) 



i) From 8 = 8 y^. :(1 -f 7/,) = 8, t2i (Uuinm. 181) would I'ullow 7^• = U,7i8, 

 which is in peilecl haimony willi the found value. 



