( 60 ) 



linos of every degree. .1A, ;«i = — oc for v=. s-. \iv decreases, .lA,f, 



increases lili the potential has reached a highest value in t lie point 



(dp \ 

 oi maximum pressure = J. Willi further decrease ol v the 



potential diminishes, till the final point, of the unstable state is reached, 



dp 

 where — is again equal to 0. There M 1 (i. is minimum. If the point 

 dv 



v = b is reached, M 1 (i 1 = cc. With very large volume M 1 (i } is 



1 — ,)• 



approximately equal to MRTlog , in which also a function ot 



v 



T is left out, which may generally be left out in the construction 



of the ijj-surface for definite value of T; from this shape for M 1 (i 1 



it is seen that the portions of the potential lines which start from 



the 1 st axis for large volume, may almost lie considered as straight 



Inns directed to the point .r = 1 and v = 0. If the potential line 



starts from the volume /\, the equation of the initial portion is 



v=v 1 (l — x). If Vj should be — oo, and so Af i (i 1 = — oo, the value 



of .l/,Mi is negative infinite for every value of x for v = oo, which 



it is also all along the second axis. The rule that for very large 



volumes the initial portions of' the potential lines may be considered 



as straight lines already follows from the law of Dalton that each 



of the components in a mixture of gases behaves as if it alone was 



present in the volume. If v = v 1 (l — x), the density of the first 



component has the same value, and the quantities determined by the 



density, are the same; e.g. the pressure and the potential. If the 



circumstances are as assumed in fig. 15. there is of course also a 



(d 3 v\ 



locus where : J = 0, which is again a loop-line passing through 

 \dx Jm xH 



dv 

 the double point ol the potential lines. It the locus v — x — = 



daiq 



docs not intersect the other /• — ./■ ■ - -- , all the potential lines have 



<A<> 



the simple shape which they have on the left side and on the right 



side in tig. J 5. 



It' we suppose a left region at a value of T above 7'/.,, the locus 



r — x— = <> is subjected to a modification. Then the two branches 



'!■>■,, 



of ^=0 have joined, and in the same way the two branches of 

 dv 



dp 



this locus will join; hut both lying outside =0 the point ot 



