( 657 ) 



The greatest chance to only one intersection with the binodal curve 



liquid-vapour presents, of course, as is best seen from the v, ^-figure, 

 the ease under 1, more particularly when in this case the line A==() 

 cats the axis at such small volumes, that it has no longer any point 

 in common not only with the spinodal curve, but even with the binodal 

 curve of the transverse plait. Only , ith a very exceptional course 

 of the binodal curve of the transverse plait double intersection could 

 take place in this case. Ón the other hand it will be highly probable 

 that always when the line N = cuts the binodal curve of the 

 transverse plait (which will always have to take place in the cases under 

 2 and 3), also double intersection of the two binodals will be found. 



This shows at the same time the connection of this investigation 

 with that of the preceding communication. For it appears now that 

 the shape of the p,x-\ines holding for 1 with single intersection is, 

 after all, by far the most frequently occurring, i. e. in almost all 

 cases where no temperature maximum occurs in the three phase line ; 

 for in this case the triple point temperature is the highest tempera- 

 ture for which a three phase coexistence exists. 



For a complete survey I have also indicated in figs 13 — 16, how 

 the binodal curve for the other solid phase gets detached from the trans- 

 verse plait. This is only possible in one way, because here there 

 cannot be intersection of the lines Z) = and A r — 0. For a? = 1 

 for this binodal curve, and so the expression for T at the rim becomes : 



dp\ MRT 



~ (« - *>s) + 



OxJ r X 



so always positive for both rims. The line N = would therefore, 

 have to become a closed curve, which on account of the shape of 

 the </-lines may be considered as excluded 1 ). 



In the TV-lines double intersection will, of course, always occur 

 above the triple point when the three phase line has a maximum 

 pressure. For the rest nothing of interest is to be said of the '/',,/- 

 lines ; they have the same general course as the p,#-lines given here, 

 provided the figures are made to turn J 80° round the „r-axis, or in 

 other words, provided a negative 7 7 -axis is made of the ü-axis. Then 

 the points with vertical tangent lie here, of course, on the line 

 W s j = 0, instead of on the locus D = ; only at the rim they coin- 



l ) At least as long as the complications, which are in connection with the 



</> 

 existence of a locus -— - = 0, do not present themselves. (See v. d. waals, Proc. 

 d.vr 



of this meeting p. 037). I shall perhaps revert later on to the changes which art; 

 to be made in what precedes in consequence of this. 



