( 330 ) 



«■n«(14e 1 )(l + 8 1 ) = {2« + «, + »' *,}' 

 the quantity /'-' is > 1, and this equation represents a hyperbola. 



For / 3 > 1 the two points of intersection with the f 3 axis lie on 

 the negative side of the origin. For V' 1 one of the points Oj 

 intersection has got into the point 0, and for A' > 1 one of the 

 points of intersection lies on the righthand side of 0, SO at a value 

 of f 2 which is positive. The branch of the hyperbola passing through 

 this point, then intersects the first parabola and the line PQ, or 



onlv the tirst parabola; a line - -<1 can then cut the hyper- 



hola in points for which f, and e, ure positive, and then absence 

 of three-phase-pressure may again be expected. 



But let us return to the examination of the equation [a') after 

 our digression. Till now we have discussed the condition on which 

 this equation has no real root. Let us now pass to other possible 

 cases. The roots of this equation have the form: 



/db 

 . das 



1± V i- 



1 + *(!-*) 



//-' 



!_.,;(!_ X ) 



or 



1 ± 



,r,l-,') 



'db 



\da 



a lr 



L \- X ! • ,r{\-.r) 



(n-\)^ (n -ly 



I— a; (1—a:) — 



a 



We shall continue to suppose the denominator to be positive. For 

 x = the expression under the radical sign is equal to 



n?E v 



!_' an d for these values — is, there- 

 fa - l) s & 



and for x = 1 equal to 

 fore, imaginary for positive *, and e 3 . Now we put |/c, + n |/s, > n— 1 

 before; this supposition implies that is imaginary all over the width 

 from .i'=0 to a=l. Let us now put l/^ + wl/c^n — 1. 



Then the equation - - . *' + * *' a — at (1 — *) = has two 



1 fa — l) a fa — 1)" 



roots for x between and 1. For these definite values of x — has 



it 



