634 
MR. A. CAYLEY’S THIRD MEMOIR UPON QUANTICS. 
No. 42. 
+ 1 
+ 6 ad 
+ 15 ae 
+ 20 qf 
+ 15 ag 
+ 6 ah 
+ 1 ai 
+ 6 bi 
+ 1 5 c* 
+ 20 di 
+ 15 ei 
+ 6/2 
+ 1 yi 
-1 b- 
—6 be 
+ 6 bd 
+ 50 be 
+ 90 bf 
+ 78 bg 
+ 34 bh 
+ 78 ch 
+ 90 dh 
+ 50 eh 
+ Q fh 
-&gh 
-1 h^ 
— 21 e‘ 
-70 cd 
-105 d'^ 
+ 126 cf 
-210 de 
+ 154 eg 
- lidf 
-175 e- 
+ 126 dg 
— 210 ef 
-105 f 
-21/ 
No. 43. 
+ 1 
aei 
— 4 
afh 
+ 3 
ag- 
— 4 
bdi 
+ 12 
beh 
- 8 
kfy 
+ 3 
cH 
- 8 
cdh 
-22 
ceg 
+ 24 
<^f 
+ 24 
d-g 
-36 
def 
+ 15 
e^ 
No. 44 . 
— 
1 
aegi r 
+ 
1 
acJd- 
+ 
3 
adfi 
— 
3 
adgh 
— 
2 
aeH 
+ 
1 
aefh 
3 
aeg- 
— 
2 
afy 
+ 
1 
b‘^gi 
1 
b%^ 
— 
3 
befi 
+ 3 /jcffk 
+ 1 ddei 
-10 dc///i 
+ 9 
+ 1 1 de"k 
— 23 hefg 
+ 12 hf 
+ 3 c"e^ 
4- 9 c“fli 
— 12 (?g'“ 
- 2 
cdH 
— 23 
edeh 
+ 27 
cdfg 
+ 19 
ce^g 
-21 
cef^ 
+ 12 
d'^h 
-21 
d^-eg 
-13 
d'T 
— 32 
de^f 
— 10 
e^ 
No. 45. 
+ 1 acegi 
-H ar 
— 4 bdeg~ 
+ 1 edy 
— 1 aceJd 
— 1 b“egi 
+ 2 bdf-g 
— 2 edefg 
— 1 acfH 
+ 1 b”eh^ 
— 2 be^h 
— 2 cdy 
+ 2 aefgh 
— 1 
-2 b^gh 
+ 4 beyg 
— 3 ce^g 
+ 1 bji^ 
— 2 bef^ 
+ 4 ce-dh 
— 1 ad‘gi 
+ 1 by 
— 1 c^gi 
+ 3 cep 
+ 1 ad“h^ 
+ 2 bedgi 
+ 1 c^h^ 
+ 1 dH 
+ 2 adefi 
— 2 bcdh‘ 
+ 2 c^dfi 
— 2 d^eh 
— 2 adegh 
— 2 bcefi 
— 2 c^dgh 
— 2 d'^fg 
— 2 adf~h 
+ 2 bcegh 
+ 1 eVi 
+ 3 cTe^^ 
+ 2 adfg- 
+ 2 befh 
-4 cyji 
+ 3 d‘ef 
— 4 de^f 
— 1 aeH 
-2 befg- 
+ 2 e“eg- 
+ 2 ae^fh 
+ 1 ae-g- 
-3 aef-g 
— 2 hd‘fi 
+ 2 bd'^gh 
+ 2 bdeH 
+ 1 eyy 
— 3 cd“ei 
+ 2 cd^fh 
1 V 
+ 1 e' 
It we write 
No. 39=1 
No. 43=J 
No. 44 = K 
No. 45 = L, 
then tlie determinant called the lambdaic, viz. 
a , h , c , d , e— I2 a 
b , c , d , e-l-3?v, y 
c , d , e—2X, f , g 
d , e+3X, / , g , h 
e—l2X, f , g , h , i 
