( 427 ) 



by differentiating </ ' with respect to x, and by keeping v constant, viz. : 



- ,« d A _ 2v (6,-ftJ + V-6^ = . . . . (<?") 



By eliminating v from (<//) and (</"), we obtain an equation in x 

 only — and for the values of # which satisfy this resulting equation, 



civ 



— will be = 0. We shall, however, seek a resulting equation in x 



da 



in a somewhat different way. 



If we subtract x (<p") from (y '), we get : 



I dA) 



v* I — A 4- as — — 2vb, 4 b.* = 0, 



1 I J I 111 



d.v \ 



and adding this last equation to (</>"), we get : 



dA 

 dx 



dA) 

 1 — A — (1 — a) — — 2vb, 4- b t ' = 0. 



Hence 



:l±l/U-a 



_L — ldz|/A — * 



and 



Now — is certainly smaller than J , hence in the expression for 



b. 



only the sign — can be retained before the radical sign. And 



r 



leaving undecided for the present whether v ^> 6 S or v <^ 6 2 , we tind 



ft s b, 



when we divide — by — : 

 v v 



dA 



1±|/ A + (l-«) 



1 — 1/ L 1 — .? — 

 I dx 



or 



IcLl J I dA) 



A — x — qr t/ L4 4- (1 - x) — = . {(f w ) 

 dx ) dx \ 



Now 



dA c I £ efa 



(1--*) — = (1 -.<■)- 1--T- 



do; a / a a.i; 



and 



