141] 
A SECOND MEMOIR UPON QUANTICS. 
259 
i.e. £+34 -o, 30+2£ = O; or putting 4 = 1, we have £ = -3, 0=2, and the leading 
coefficient is 
a 2 d 
- 3 abc 
+ 2 b s . 
The coefficient of x 2 y is found by operating upon this with (3bd a + 2cd b + dd c ), this 
gives 
abd 
ac 2 
b 2 c 
i.e. the required coefficient of x 2 y is 
3 abd 
— 6 ac 2 
+ 3 b 2 c j 
and by operating upon this with £ (3bd a + 2cd b + dd e ), we have for the coefficient of xy- 
acd 
b 2 d 
be 2 
+ 3 
- 6 
+ 1 
+ 1 
- 9 
+ 6 
+ 6 
- 6 
- 3 
- 9 
+ 12 
i.e. the coefficient of xy 2 is 
— 3 acd 
+ 6 b 2 d 
- 3 be 2 . 
Finally, operating upon this with J (3bd a + 2cd b + dd c ), we have for the coefficient of y 5 , 
- 1 
- 3 
+ 8 
- 2 
* 
- 2 
i.e. the coefficient of y 3 is 
— ad 2 
+ 3 bed 
- 2 c 3 , 
and the co variant is 
a 2 d + 1 
abd + 3 
acd — 3 
ad 2 - 1 
abc - 3 
ac 2 — 6 
b 2 d + 6 
bed + 3 
b 3 + 2 
b 2 c +3 
be 2 -3 
c 3 - 2 
[I now write the numerical coefficients after instead of before the literal terms.] 
33—2