■ H i 
- — ^ . — 
ON THE RECIPROCAL OF A CERTAIN EQUATION OF A CONIC. 
523 
541] 
or, as it may be written, 
i 2 66'c"c'" + 2 6"6'"cc' 
{X (6c' - b'c) ± /x (b"c'" - 6"'c")} 2 + 2\/i - (bc'+ b'c) (6V" + 6 /,, c") 
(+ (be'— b'c) (b"c'" — b'"c") 
Taking the upper signs, this is 
{X (6c' - b'c) + fx (6"c- 6"'c")} 2 + 4X/a / 66'c"c"' + 6"6'"cc' 
V- 6c'6V" - 6'c6 / "c" 
viz. the term in \/x is 
+ 4Xya(6c"'-6'"c) (6'c"-6"c'). 
Taking the lower signs, it is 
{X (6c' - b'c) - /a (6"c'" - 6"'c")} 2 + 4X^ 
viz. the term in X/a is 
66'c"c'" + 6"6'"cc'\ 
6c'6'"c"-6'c6"c"7 
+ 4X/a (6c" - 6"c) (6'c'" - 6"'c'). 
And it is thence easy to infer the forms of the other coefficients, and to arrive at 
the foregoing result. 
66—2