74 G. PLARR ON THE SOLUTION OF THE EQUATION Vpgp=0. 
0 = Se[Ak? —v(—h,)*] x Se [hh +(—h,)*]- 
The vector \h? —v(—h,)? being perpendicular to the «’ which we want, we get 
(60) Me = 'M—h,)3 + v(h,)? , 
and then the normal v; for Swe’ =0 becomes parallel to : 
(M’v, sue-0 = [M—As) (2, —h,) —vh3(h, —h,) 
M’ being another scalar factor whose expression is unimportant. It is directed 
towards —v, and towards +). 
Likewise, the normal v, corresponding to the generating line ¢ in the plane 
pv, is directed parallel to : 
(Mv,)(sre=0) = [—H(hs)*(l4 — he) —vho4(In — hs) , 
that is, it is directed towards —p and —v. 


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Then : (se a (E—W), ae Tey. : oP’ ? 
(#) = 
dE J, (je? 
which is positive, so that e is increasing when E passes through E,. 
For E= E,, also on the cone 0 = 2hiS*ke’", the equation I’ = 0 gives 
also : 
é, = . —Pf’ 
as radius of the sphere of the spherical conic. And we have already remarked 
that this solution corresponds to 
P= 07 /@=)0, 
annulling separately the two terms of I’; for this reason, and for others too, 
this solution is of the kind termed a singular solution. 
We have evidently 
é,, >e,, namely —P’ oe which gives —4P° >F = —4P°—27Q”, 
