( 632 ) 



of higher order, whereas l(-p-) dv can a 8 ain diminish the order of 



V 



infinity by a unit, because the factor of dv has this higher order of 

 infinity only for an infinitesimal value of dv. But still the thesis 



00 



remains true that l(-~- J dv is infinitely great for v = b. 



V 



So there is strong asymmetry in the shape of the (/-lines. Whereas 



q=z — oo holds for x = and every value of v > b lt q = + °° holds 



all over the line of the limiting volumes, and for all volumes on the 



line a? = l which are larger than b s . We derive immediately from 



this, that all the (/-lines without exception start from the point x = 



and v = b x . In this point the value of q is indefinite, as also follows 



from the value of q as it is given by the approximate equation of 



state, viz. : 



db dv 



x dx dx 

 q = MRT I f- MET . 



1 1 — X V — V 



It also follows from the approximate equation of state that at 

 their starting point all the r/-lines touch the line v = b, of course 

 with the exception of the line q = — co. For we derive from 



\dx~J~ q 



\dxdvj \dxj q dx* 

 or 



dv\ dx* 



dxjq d* »p 



dxdv 



For — - the approximate equation of state yields 



dx' 



d*b ,, fdb\* d*a 

 MRT — MRT — — - 



d*ip MRT dx 2 \ds J dx* 



= -n—. x + — 7- + 



dx* ' x{l—x) v—b (v—b)* v 



d*ip (dp\ , _, fdv\ 



We already found the value of — — — = ( — J above. For 1—1 



we find therefore: 



