( 734 ) 



passes through this curve for the second time, reaches its highest 



A//A 

 point, after which it. meets the curve I — I = in vertical direction, 



and then pursues its course downward after having been directed 

 horizontally twice more. 



It must then again approach asymptotically that value of a?, at 



rdp 



which it intersected the line I — dv — shortly after the beginning: 



J ax 



of its course. This line has also been drawn in tig. 6. It is evident 



that it may not intersect the curve = 0. In fig. 6 it has, aceord- 



dx 1 



ingly, remained restricted to smaller volumes than those of the curve 



(Ptb ... 



— = 0. For the assumption of intersection involves that a «-line 



dx* 



ƒ dp x 

 — dv = several times. As # = MET I- in 

 dx 1 — x 



such a meeting point, it follows from this that only one value of 

 x can belong to given q. It deserves notice that in this way without 



d'ty 

 any calculation w T e can state this thesis : "The curves - — = and 

 J dx* 



I- 



— dv = Q can never intersect." According to the equation of state 

 dx 



it would run like this : "The equations : 



fdb\ d % a db da 



— MRT — — 



II \dxj I dx 2 , dx dx 



—r, : + r— ttA = — and i~ =~ 

 x (1 — x) (v — by) v v — b v 



can have no solution in common. Indeed, if v from the second equation 

 is expressed in x and T, and if this value is substituted in the first 

 equation, we get the following quadratic equation in MRT: 



d 2 a 

 2 ] 1 1 /db\* 1 db dx* 



* ^ x (1—x) ¥ [dxj ~b dx ~da ( 



' dx ' 



( 1 dbda 11 d*a) 1 /day 



— 2(MRT)\ — -f — [— =0. 



V ; |è 3 dxdx b 2 dx*\ ^6 a \daj 



A value of MRT, which must necessarily be positive to have 



