( 290 ) 



equal to 3^, the value furnished by the equation of state, in 



which h is put constant, but that this equation is found rather 



nearer to '2b. This maj be accounted for by taking into account 



that b is variable and decreases with the Aolume. In a mixture b 



db 

 also depends on the composition. Accordingly the quantity — is an 



ax 



intricate expression for mixtures, and must in general be distin- 

 guished from ( — I . If the way in which b depends on volume and 



composition, was accurately known, then there would not be left 

 any difficulties but those of toilsome and intricate calculations. But 

 it is sufticiently known, that the way in which b, even for a simple 

 substance, depends on v, has not yet been fixed with perfect cer- 

 tainty, and that in any case the knowledge of the numerical values, 

 which occur in given forms of b, is wanting. These considerations 

 led me to believe that this would be an objection to deriving theo- 

 retically the properties of the beginning of the plaitpoint line with perfect 

 certainty — and also to deterniining the numerical values exactly. 

 It has however, appeared to me that the knowledge of how b 

 depends on .*■ and v is not required for this exact determination; 

 but that for this purpose it suffices to know two quantities which 

 have been experimentally determineil for the critical state of a 



simple substance. 



T /dp \ T dp^ ^ . , 

 Let us call /' the value which -—-=——- has m the criti- 



p \o^Jü p dl 



cal conditions of the component, and v., the critical coefficient, so that 



MET. = y.{pi-). . 



MET a ^. ,, MET . , « , , 



From p = ^ follows = / and _ - = / — 1. 



V — U V p{v — 0) pv 



The equality of MET= a pv =f{v—b)p, gives the value 



v = - h 



for the critical volume, in which we have to keep in view, that 

 now that b is put variable with the volume, b represents the value 

 w^hich this quantity has in the critical state. With ƒ = 7 and 



15 f 28 , . , . . , ^ u 1^ 



jt =^ we find — = — , wdiereas with / == 4 and x = — we should 



4 6 13 ' 3 



find the value — = 3. For carbonic acid Keesom has found ƒ r= 6,7 

 h 



V 6,7 

 and -/. = 3,56, from which would follow - = — — = 2,134. 



b 0,14 



