489] 
AND THE (2, 2) CORRESPONDENCE OF POINTS ON A CONIC. 
21 
If the original matrix be symmetrical = 
a, h, g 
h, b, f 
g, f, c 
, this is 
that is 
(fh - by + (ag - h 2 ) (eg -f 2 ) 
+ b 2 {-eg) 
+ b 2 (— ac — g 2 — 2fh) 
+f 2 (-ag) 
+ 2 bf(af+gh) 
+ W l (~f h ) 
+ 2 bh (fg + eh) 
- 2d 
a, 
h, 
K g 
f 
9, f> o 
+ Ö' 2 [2 (fh - b 2 ) - ac - g 2 + 2hf] 
+ 6 4 = 0, 
(b — g) {(6 2 — ac) (b+g) + 2 (a/ 2 + eh 2 — 2bfh)} 
-26 (abc - af 2 - bg 2 - eh 2 + 2fgh) + 6 2 (4fh - 2b 2 -ae- g 2 ) + 6+ = 0, 
satisfied by 
0 + b - g = 0, 
viz. the equation in 6 is 
(6 + b—g) {6 s — (b — g)6 2 + (4fh -ac- 2 bg - 6 2 ) 6 + (b 2 - ac) (b + g)+2 (af 2 + eh 2 - 2 bfh)\ = 0.