( 633 ) 



MRifm tl 

 MRT MRT cPb \dx) da' 



dv ,r{l — x) v—b dx' 1 (v—by 



V 



db 



dx 



dxg- MRT db dd\l 



(v—by ^dx~ dösv* 

 If we multiply numerator and denominator by (v — by and if' we 



put v = b, we find for the starting point of the ^/-lines ( — J 



\dxj 



(v—by 



at least if we can prove that is equal to zero for x = and 



v = b x . To show this, we put & = 6,+ fix -f y^, and so v — b = 



v — b 



= (v — b x ) — xfi — yx % } and then we find for (v — b) the value: 



x 



Iv — b 1 | 

 ft — yx \ . 



v — b x 

 The term is indefinite, but nevertheless the given value 



x 



multiplied by v — b is really equal to zero. This result, too, is still 

 to be subjected to further consideration, because it has been obtained 

 by the aid of the equation of state, which is only known by approxi- 

 mation. And then 1 must confess that I cannot give a conclusive 

 proof for this thesis. But 1 have thought that 1 could accept it with 

 great certainty, because in all such cases where a whole group 

 of curves starts from one vertex of an angle, e. g. for the lines 

 of distillation of a ternary system, I have found this thesis confirmed 

 that then they all touch one side of the angle. Only in very 

 exceptional cases the thesis is not valid. 



Moreover, the theses which I shall give for the further course of 

 the ^-lines, are independent of the initial direction of these lines. 

 Only, the </-lines themselves present a more natural course when 

 their initial direction is the indicated one than in the opposite case. 



fdv\ 

 From the value given above for — I follows that they have a 



\dx y g 



fdp\ 

 tangent // v-axis, when 1 — 1 = 0, and a tangent // .i'-axis, when 



\dxj v 



d % tp 



-— = 0. Hence they have a very simple shape in a region where 



(XOu 



(dr>\ d 3 ifj 



the lines — =0 and — — = do not occur, btarting from the 

 \dxj v dar 



point x = and v = b x they always move to the right and towards 



43* 



