(834) 



MRT 



db 

 dx 



da 

 dx 



(v g -by V* 



d*a Xg(l — Xg) l — yg db 1 



Jx~*~~~b (i+ y!J ydx(vg-by~~ v 



b x g (l—x g ) 



da 



dx 



and after the substitution of — = 



db 



dx 



I v„ — b 

 (1— y g ) and of — 



W 



(1+&) 



- , the sign proves to depend on the expression : 



d'a da 



_ ( l_2^)-._4^ 



dx 



d?a da 1 



In the first limiting case in which — — = 2a, , — = 2a i x g ,y q = — 



dx 1 1. r 2 



1 

 and x g =z — this expression = 0. Also in the second limiting case, 



Q 



1 



in which x g = - and y g = 0. So in the limiting cases the curve 



a 



d'ib </ 2 if' 



= intersects the curve up to the last moment in which 



dxdv dx* 



the latter disappears. Also in an intermediate case this quantity may 



he zero, but the value of x g , at which this takes place, depends on 



d'a 



da? ' (a a — g l9 ) — (« M — a,) 



da («u— «i) ( l — < v <j) + x <j («,— O 



a# 



If we write 



<Z 3 a 



^* A 



da 1 — .c 7 -f x g ( 1 + A) 



dx 



. We then derive the value of x a for this intermediate 



1 + ^A 9 



case from the equation : 

 A 



or 



A 



(1 - 2x g ) = 4 



(l—2xg)* !> 



= 4 



1— 2a 



i+A^ L 16 ^! 1 — ^) 3 _ 



