( 211 ) 



equal to 0. The projection of the section of the two surfaces on the 

 v,x-p\sine is then a curve which starts at x = 1 and v = /; 3 , and 



has an asymptote for the value of x for which - - = 0. The T x- 



dx 



projection of the section is then a line which has a value for T 



equal to zero at ,/■ = 1 and x = — — , and which has a maximum 



T somewhere between these two values of x. It is clear that at this 



value of T, at which the curves ( 1 — and ( — ) = touch 



\d®*JvT \<l>rJvT 



the contact takes place as in the case discussed last, and that the 



cPtf> dp 



top of — ^ = lies in the region where — is positive. And in the 

 dx % das 



third place we draw attention to the special case that B = 0, or 



a lt = a i or k = oo. Then the value of x, for which -- = 0, is 



das 



itself equal to 0. The equation for the determination of v—b of the 



section of the two surfaces simplifies then to : 



(x — bY v — b 1—as 



'db\* V ' db n-1 



. dx ) dx 



or 



v — b 1 — x t /{ 



dx 



This represents a branch of a hyperbola which passes through 

 the point x = l and v = b, and cuts the axis x = for a value of: 



/b.—b, 

 v — b. - 



2 



The quantity k = , on which it depends in so high a degree 



o la -a, 



whether the considered surfaces intersect or not, and the way in 

 which they intersect, is, for the same value of a, and a lt entirely 

 determined by the value which we must assign to a 13 . If « ls de- 

 creases from a„ to a A , k increases from tot oo. For n l ,=[/a l a t 



ralue I / - a 



it has the value \/ - and then one of the transition cases k = 



it 



would be — =:«!, or the critical pressure of the two components 



