( 658 ) 



cide. If the pressure maximum of the three phase line should be 

 found at higher pressure than the point A of fig. 1, we must, of 

 course, have the case mentioned under 3, i. e. the point of contrac- 

 tion must lie within the figure. 



It has been assumed in the above that throughout the region 



/dp\ 



I — I = positive, and that a decreases with increasing b. The case 



that a increases with increasing b does not present any new points 

 of view. If we have a system where a strongly increases, so that 



/d/A 

 the critical temperature rises with b and I y- I ' s negative, the ex- 

 pression 



/d/A MRT 



(w — w») T- + (*« — Xf) - 



dxj Xf{\—Xf) 



is evidently always negative for x 8 = 0. And this is obvious, 



because this axis is now also that of the more volatile component; 



on the other hand the reversal of sign may now take place with 



the other axis. What happened on the left just now. will now take 



place on the right, and vice versa. It is only worthy of notice that 



now the line N~z=0, if it exists, must intersect the axis a? = l in 



two points. For the expression 



\ MRT db da/dx) 



(r — v 8 ) — 4- MRT 



v "J (v-b)* dx v 1 I 



where dbjdx and dajdx are positive, becomes positive for v = b&nd 



v=z<x>. From this follows that besides the just mentioned cases, 



another possibility may be found, i. e. that the point of contraction 



does fall within the figure, but not the point of detachment. For 



the p, x- and T, x- figures it makes only this difference that a loop 



formed in the way of fig. 12, (which always disappeared in the 



rim in the other cases) may now also disappear like the loop of 



fig. 10 in a point within the figure. It is further clear, that in this 



case the point of contraction will much sooner fall within the figure 



db 

 than in the preceding case. For according to formula (1) — must 



dx 



have an excessively high value for the expression to be able 

 still to become positive with a volume v = 10/;. If, however, 

 dajdx = 2a 2 — 2« 12 = 1.8 a 2 1 ), then : 



l ) With the values for a and b of Landolt and Börnstein's table 82 we find 



about 12 for the highest value of — , about 250 for that of — ; if hydrogen is 



h «i 



excluded, tbe values become resp. 8 and 40. So, whereas with exclusion of 



b 2 — bi a* — a x 



hydrogen, pairs with a ratio > 7 cannot occur, — can reach the 



b L ax 



value 39. 



