( 227 ) 



tions of the normal substances themselves. Still a beginning has been 

 made with calculations which aim at a represcnialion of those deviations. 



§ 4. Determmatlon of the critical quantities of the mixtures taken 

 as homogeneous. As we neglect the deviations from the law of cor- 

 responding states, we may derive these quantities (occurring in the 

 unstable region and hence not to be detei'mined directly) from any 

 observed range of the equation of state of any mixture. 



The most obvious means is the shifting of logarithmical or partly 



invariant diagrams of isothermals in the area near the critical state. 



pv 

 In Comm. N". 59/; it was applied to — isothermals with regard to 



logv, in Comm. N". 65 to /o^^MSOthermals with regard to hxjv, in 



pv 

 Comm. N°. 88 to log —-isothermals with regard to log p and to 



pv 

 log —-isothermals ^vith regard to log v. We may also imagine, 



however, that we have at our disposal a sufficient number of obser- 

 vations of another range. Thus, to give a simple instance, we know 

 the critical temperature of a mixture if the temperature is found, at 

 which under relatively small pressures it does not deviate from the 

 law of Boyle. And it is also possible that we may derive the data 

 from observed conditions of coexistence. If the critical quantities for 

 some mixtures are found, it will in graphical solutions be preferable 

 to derive the T^-k J^nd pi:k as a function of x also graphicall3% For 

 the experiments of Kuenen have made us doubt whether the suppo- 

 sition made ad 3° is in general possible, and this doubt is strengthened 

 by Keesom's experiments. 



If on the other hand we confine ourselves to qualitative investi- 

 gations of mixtures of substances about which all the data which 

 belong to the mixing are lacking, the supposition lirst lies at hand that 



§ 5. The reduced y^-curves. In Comm. N". ^^a is briefly set forth 

 how the different i|vcurves can be derived from those that have 

 been calculated once for all for a simple substance. If we write a 

 little more extensively, and if v^ indicates such a large volume that 

 with this the mixtures are in the ideal gaseous state, 



V 



ipa^ = — ipdv 4- RT \x log X + (1— A') log (1— .r)| 



omitting a temperature function linear in x. This with 

 1) Gautzine and D. Berthelot. 



