( 331 ) 

 two equal values. Kor x outside these values is Imaginary, and 

 within these limits two positive values of > 1 satisfy. Thai ">1 or 



v—b 



is positive may among others be seen when we have developed 



the equation (a) as quadratic equation in (v b). The two real values of 



dbV 



v—b \d®s 



are both positive, if — >• ; and lite equation in x requires 



t> b a 



that this condition is fulfilled for real values of . from this follows 



o 

 that it' the conditions r-,>0, f,>0 and ^vfn V<> — 1 are fulfilled 



Hie loens of the points ot intersection of =0 and — ■ - = is 



dx % dv* 



a closed figure. The limiting values lor N '= have been °iven 



1-— x 



(see formula (y)) by : 



{n-\f J (n-1) 2 j (n-1) 8 



coincided, and arc equal to -. The existence of such a 



For these values of x, the volumes for a given value of x have 



b 



a 



closed figure with volumes larger than U means thai al exceedingly 



,/-i|< d'xp 



low temperature the two curves — = and = do not inter- 



</,/■- <//■'-' 



sect. Not before a certain value of 7' e.g. 7', these two meet. At the 



d?q 

 lower temperatures the whole curve ■ — lies in the space where 



is negative. At 7', the branch of the small volumes of - = Ü 



</r- dv* 



has overtaken the branch of the small volumes of = \t 



d'i\> . . . '/'-'if' 



1^> l\ part of = lies in the region where is positive. Bui 



<l,r" dv 1 



with further rise of the temperature a change is brought altoul in 

 the relative movement of the two curves inter se, and at certain 

 temperature equal to 7', the branches of the -mall volumes of the 



Tl 

 Proceedings Royal Acad. Amsterdam. Vol. XI. 



