(;42 



sitioii that in van dek Waals' equation />w i^^ independent of Tand 

 (i\y is proportional to 7'-'. Tlie latter assumption was already made 

 by Ci.AUsius, with a view to tiie vaponr pressures of carbon dioxide. 

 A relation agreeing with 



B = B^^l + ^,J (19) 



(with a negative value of />,) was also found by D. Berthklot ') 

 to be suitable to represent the compressibility at densities near the 

 normal. In these investigations the approximate validity of that 

 I'elation was extended lo much lower temperatures than those 

 indicated above. It will a|)pear in the next §, that equation (18) 

 actually agrees with an equation of the form (19) down to an 

 appreciably lower temperature than those indicated above. 



§ 4. For the purpose of a closer comparison between the second 

 \irial coefficients of quadruplet-bearing molecules and of doublet- 

 bearing molecules we shall introduce as a reduction temperature a 

 temperature which is specific for each gas ''). According to what 

 was said in § 3 about the region in which equation (18) is applicable 

 the inversion temperature of the Joui.E-KELViN-effect at small densities 

 is a suitable one for this purpose. This temperature is found from 

 the relation : 



dB 



B—T — = 0, 



dT 



or 



dB 



B + hv = 0. 



d{hv) 



Equation (18), and Suppl. N". 2416 equation (59) give respectively, 

 for quadruplets: 



hüinv{pz=0) = 0.576, 



for doublets : 



/K'm„(.=o) = 0.969. 



T 



If we call =: f ,■/„„), it follows further, that: 



for quadruplets: 



_i> u — 4 i 



(20) 



B = ^^ jl — 0.3589 to„r) + 0.03327 tiht) — 0.05215 i(,„t) -1- 



+ 03964 t(i,l.) — 0.00862 t,W) + 0.00285 t(;,'„) — 0.00123 t („,-,. 



1) D. Berthelot. Tiav. el Mém. Bur. Internal, des Poids el Mesures, t. 13 (1907). 

 -) Gf. H. Kamerlingh Onnes and W. H. Keesom. Die Zustandgleichung. Math. 

 Enc. V 10. Leiden Gomm. Suppl. No 23 § 28a. 



