and 



( 318 ) 



drip MRT 2a _ 



fa? (r-6) 5 v' 



When we eliminate T from these two equations, wo net for the 

 locus of the points of intersection of the two curves : 



(v—b>) fdb\ da? 



x{l—xy\da}J 2a 



This locus, in which v occurs in the 2"' 1 degree, and x in the 4 th , 

 may present a different shape, and in order to ,i, r et a survey of the 

 different shapes of this curve, we shall introduce some auxiliary 

 quantities. 



These auxiliary quantities will recommend themselves in the dis- 

 cussion of one of the special cases, and for this we choose the case 

 that the whole locus is imaginary for all the values of .?' between 

 and 1. Let us for this purpose write the equation («) in the fol- 

 lowing form : 



d*a 



( -" ) f \''''V 1 



For the case that this locus is imaginary 



<Pa 



I A//»YM da?) 



&'<&' + *(!-.*) - U—d -m) — 



or 



<r<i d*a 



{fdb\ dx' fdb'ydx* 



<'< 1 ->|(sj-aT*' — ^UJ *> 



or for .f between and 1 : 



</,/•/ </,/■' \dx) das 9 



d*a , , 



or for — =z 2 («j -j- (/„ — 2a la ) positive, which we always assume in 



all our considerations : 



a lr 

 < _ _ x (1 — x) . 



A/ 



