( 730 ) 



d'tp /d*v\ 



same time = 0. Hence — = 0, which appears also immedia- 

 te" \dx*J ( , ' ' 



tely from the figure. 



Within the curve - — = every (/-line that intersects it, has also 

 dx* 



a point of inflection, because the latter must pass from minimum 



volume to maximum volume in its course. So there is a continuous 



series of points in which (/-lines possess points of inflection between 



the two points in which horizontal tangents may be drawn to 



d*xp 



= 0. But there is also a continuous series of points in which the 



dx* 



(/-lines must possess points of inflection on the left of the curve 

 = 0, so with smaller value of x. For every (/-line has its convex 



side turned to the ,r-axis just after it has left the starting point. If' 



d*\p 



it is to enter the curve — — = in horizontal direction and to pass 



aar 



then to smaller volume, it must turn its concave side to the «-axis 



in that point, and so it must have previously possessed a point of 



inflection. Most probably the last-mentioned branch is somewhere 



continuously joined to the first mentioned one. If so, there is a closed 



d*v 

 curve in which — — = — and then it may be expected that this 

 dx ■ g 



closed curve contracts with rise of T, and has disappeared above a 



certain temperature. But these and other particulars may be left to 



a later investigation. 



We have now described the shape of the (/-lines, 1 • in the case 



that neither , nor — — is equal to 0, 2. in the case that the 



dx* dxdv 



d*ib d*\p 



curve = exists, 3. in the case that the curve — — = is found. 



dxdv dx* 



It remains to examine the course of the (/-lines when both curves 



d*\b d*\l> 



—^ = and — — = exist, 



dx* dxdv 



d 2 ty , • , , cPa 



For the occurrence of the = it is only required that — 



dx* dx* 



be positive, as we shall always suppose, and that T is below the 



d*xp 

 value of the temperature at which the curve — = has contracted 



to a single point. It may, therefore, occur with every binary system, 

 without our having to pay attention to the choice of the components. 



