522 
[541 
541. 
ON THE RECIPROCAL OF A CERTAIN EQUATION OF A CONIC. 
[From the Messenger of Mathematics, vol. I. (1872), pp. 120, 121.] 
The following formula is useful in various problems relating to conics: the 
reciprocal equation of the conic 
X (ax + by + cz) (a'x + b'y + c'z) - ¡jl (a"x + b"y + c"z) (a'"x + b"'y + c'"z) — 0 
may be written indifferent in either of the forms 
{X 
v, £ 
+ P 
Ï , V , t 
} 2 4- 4X/a 
£ > V , Ç 
V > Ç 
a', b', c' 
a", b", c" 
a , b , c 
a! , b' , c 
a, b, c 
a'", bc” 
a'", V", c'" 
a , b , c 
and 
{*■ 
f, V, f 
% , V > Ç 
} 2 + 4X/a 
f » V > £ 
£ > V > K 
a', b', c 
a", b", c" 
a , b , c 
a , b' , c' 
a, b, c 
a'", b'", c'" 
a", b", c" 
a"', 6"', c"' 
In fact, in the reciprocal equation, seeking for the coefficient of f 2 , it is 
{X (ibe' + b'c) - n (lV'c+ b’"c")Y - (2Xbb' - 2fxb"b m ) (2Xcc' - 2/xc'V"), 
X 2 (be - b'c) 2 + /a 2 (b"c'" - b"'c’J + 2Xya 
f 2bb , c"c'"+2b"b'"cc Ï 
t -(bc' + b'c)(b"c ,,, + b' ,, c")j > 
viz. this is