MK. A. CAYLEY’S THIRD MEMOIR UPON QUANTICS. 
633 
The tables Nos. 36 and 37 relate to a septic. No. 36 is the septic itself ; No. 37 
the quartinvariant. 
No. 36. 
1 a 
7 b 
21 c 
35 d 
35 e 
21 / 
7 9 
h 
J^x, y) 
7 
No. 37. 
— 1 a~h^ 
+ 14 altffh 
— 18 acfk 
— 24 acg- 
+ 10 adeh 
+ 60 adfg 
— 40 ae-g 
— 24 bjh 
— 25 by 
+ 234 bcfg 
+ 60 bceh 
— 40 bdrh 
— 50 bdeg 
-360 bdf- 
+ 240 bey 
— 360 c'gff 
— 81 cy- 
+ 240 cd"g 
+ 990 cdef 
— 600 ce^ 
-600 dy 
+ 375 dre^ 
The tables Nos. 38 to 45 relate to the octavic. No. 38 is the octavic itself; 
No. 39 the quadrinvariant ; Nos. 40, 41 and 42 are the quadricovariants, the last of 
them being the Hessian ; No. 43 is the cnbinvariant ; No. 44 the quartinvariant, and 
No. 45 the quintinvariant, which is also the catalecticant. 
No. 38. 
a 
8 b 
00 
56 d 
70 e 
56/ 
00 
8 h 
i 
yf 
No. 39. 
+ 1 
ai 
- 8 
bh 
+ 28 
C9 
— 06 
if 
+ 35 
No. 40. 
+ 1 ag 
+ 2 ah 
+ 1 ai 
+ 2 bi 
+ 1 ci 
- 6 by 
-10 bg 
— 2 bh 
— 10 eh 
- & dh 
+ 15 ce 
+ 18 e/ 
— % eg 
dg 
+ 15 eg 
-10 d^ 
— 10 de 
+ 34 dy 
— 25 
-10 ey 
-loy 
No. 41. 
+ 1 ae 
+ 4 «/ 
4 - & ag 
-}- 4 (xJi 
+ 1 ai 
+ 4 bi 
+ 6 ci 
+ 4 di 
+ 1 ei 
-4 bd 
— 12 be 
— 8 bf 
+ ^ bg 
+ 12 bh 
+ 8 eh 
— S dh 
-12 eh 
— 4 yh 
+ 3 c" 
“1“ 8 cd 
— 22 ce 
+ 24 <72 
— 48 e/ 
+ 36 de 
— 22 eg 
-36 dy 
+ 45 e^ 
-48 dg 
+ 36 ey 
+ 1 
+ 8/y 
4-^ g‘ 

