382 ON DR. wiener’s MODEL OF a CUBIC SURFACE WITH 27 REAL LINES ; 
and we have 
G + H = bc, 
Fm + G*/Il+H = 
Vi/ 
Fm x - G Vif x + H= (mi ~ ~ c) , 
-Vj/; 
(2) 
(1) 
(6). 
Eliminating f 7 , we have 
g (m, Vff + m Vg.) + H (m - m.) = ”*■' (m ~ ff (m ~ c) + ” (m ‘ ~ ^ 1 ^ ~ c >, 
Vif Vif 
which is easily reduced first to 
g 2mOT,-»(ro + m 1 ) w . „ ' 0» - <») 0» ~ &) 
(m-o)Vi + ( (m + mi) ViT 
and then to 
G [a A + 2m (a — b) (a — c)} — H - + a6c {— i. + 2m (i/i — a)} = 0 ; 
V i/ 
and combining herewith G + H = be, we have 
U _ 26c m [a (m — a) + (a — 6) (a — c)] 
a A + 2m (a — 6) (a — c) + 
and we have then 
that is, 
Vif 
G = bc-H; 
/^(m + m x ) + Cr (Vif — V ifj) + 2if = 0, 
i Vif 
J^m (m — a) — A] + G —2// (m — a) = 0, 
or, what is the same thing, 
4 Vif f J. VF) 
f 7 {2m (m — a) — A} = —be II j 2 (m — a) j-. 
m — a 
m — a) 
We then have 
Fx + H = y (— G + 
{x — b)(x — c) 
y* 
x— a 
that is, 
{Fx + H) 2 = 
^ ^ a6c \ _ y {Ha 4- Gx) 
~ y \ ~ x — a)~ " ’ 
{x — b)(x — c) 
abc {x — a) 
{Ha + Gx) 2 ,