( 135 ) 



fig. 3, These Proc. March 30, 1907 with a maximum and a mini- 

 dp 



mum volume, but moreover when they afterwards cut — =0, with 



dx 



d'i|> 

 a maximum value of x. But when the point in which —- =0 must 



disappear lies at larger volume than — = 0, then with rise of Tthe 



left-hand point where = is directed parallel to the w-axis, must 



il.r' 2 



dp 



pass through the point where — =0 lias minimum volume. Then 



intersection still takes place, hut with further rise of T the curves 



touch and get detached — and then the '/-lines run as lias been 



d'tb </> 



drawn in lig. 5. So contact between — = and - =0 may 

 ° dx 1 dxdv 



take place in two ways and we may already conclude to this from 



dv 



the condition for contact. From the equality of — for the two curves 



dx 



follows namely : 



d'y d z p _fd , p\ i 

 dx' dxdv \dx'J 



d*p dp d'lb 



The value of being negative for the points of — = 0, — - 



dxdv dx dx 



must be positive in the point of contact. That is to say, that for 



</> 



the curve = the point of contact must lie to the right of the 



dx* 



line which joins the minimum and the maximum volume. Only with 

 the two kinds of contact which we have described, this condition 

 can be fulfilled. If the first described contact takes place, the mini- 

 dp 

 mum volume of — = must lie to the right of the point of contact. 

 dx 



In the second case of contact this point must lie on the left, or 



dv 



even be entirely wanting in the figure, in which case — is positive 



dx 



in all points of the line = 0. 

 dx 



From all this follows that if the spinodal curve entirely envelops 



the curve = in a closed line, and the latter remains entirely 



dx 1 J 



dp 



restricted to smaller volume than the volumes of — = 0, there are 



dx 



