378 ON dr. wiener’s model oe a cubic surface WITH 27 REAL LINES ; [521 
x y x y 
1 
m 
slM 
6 
VT4 = 3-742 
2 
0 
1 
0 
1 
3 
0 
-1 
0 
-1 
4 
6 
\/® 
" 1369 “ 1940 
2280 /T7 
-(37T V 
5 
<l> 
-i + A„ 0 -792 
6 
rn l 
~.^M X 
y = 4-333 
-|\/I4 = - 1-641 
1' 
m 
6 
-Vl4 = - 3-742 
2' 
(T 
VS 
1560(14 —Vl4) 
(31 V14-5) 2 
.. = + -676 
3' 
T 
Vt 
1560 (14 + vT4) _ 1>eg7 
(31 Vl4 + 5) 2 
.. = + -247 
4' 
c 
0 
- 1 
0 
5' 
b 
0 
2 
0 
6' 
m 1 
y/M x 
^ = 4-333 
o 
gVU= 1*641. 
The numerical values belong to the curve y* = (l — ^1 — ^1 + xj and to m = 6. 
Starting with the points 1, 2, 3, 1', 4', o' we have to find the remaining points 
6', 6, 4, 5, 2', 3'. 
Point 6' by means of the conic 1234 / 5'6', as follows. 
The equation of the conic is 
{x — b)(x — c)~ be y 2 + k xy = 0, (2, 3, 4', o'), 
and making this pass through the point 1 (x = m, y = Vif) we find 
(m — 6) (to — c) + = 0. (1). 
Hence taking the coordinates of 6' to be to 1( Vif l5 we have 
(nh — b) (mi — c) + ka Vifj = 0, (6'), 
Vilfj _ — b) (to x — c) _M 1 (m — a) 
\/M ( m — 5) (m — c) M (m 1 - a) ’ 
and thence