MR. A. CAYLEY’S THIRD MEMOIR UPON QUANTICS. 
631 
No. 29. 
- 1 
a^<rd~f^ 
+ 
2 
''dddeY 
324 d^dd^ef 
+ 
18 ab&Y 
+ 
194 kddy- 
-1- 2 
a^(?de-f^ 
— 
1 
d-ddf 
— 
440 a?dd^d‘ 
+ 
242 abddeY 
— 
652 ddidey 
— 1 
a^ccP'ef^ 
— 
16 
db^ddf* 
+ 
78 d^dddf 
— 
128 abddy 
+ 
71.3 iddd"d 
+ 6 
+ 
16 
dWdeY 
+ 
428 a^^d^'d 
— 
324 abdd\f 
-j- 
1 36 dcd^’e/ 
-16 
a^cd'e^f" 
+ 
82 
(tb^cd‘eY 
a~b^cdeY 
— 
180 arcdPe 
— 
498 abdd-ey 
— 
246 b^cd^e^ 
+ 14 
a^cdd'f 
— 
132 
+ 
27 d^d}'^ 
+ 
136 abddd' 
+ 
16 b^dy 
— 4 
d^ce' 
+ 
50 
dWcdf 
+ 
14 ab^cdY 
14 ab^cdY 
+ 1078 abdd*ef 
+ 
4 bH^d 
— 4 
ddY 
— 
16 
a-PdY 
a-b^d^eY 
— 
+ 
206 abdd'^d 
— 
14 b^dY 
+ 11 
— 
14 
— 
32 ab^d~eY 
— 
342 abd'dy 
— 
294 b^ddef - 
-10 
dd?e^f 
+ 
60 
dWdPe^f 
+ 
50 ab^ddY 
— 
804 ahddJ'd 
+ 
138 b^dey 
+ 3 
dd-d 
— 
30 
db^dd 
— 
18 ab^df 
+ 
506 abdd'e 
— 
440 dd(iy^ 
+ 2 
aWcff-f* 
+ 
11 
dd-cY 
— 
10 ab^dY 
— 
90 abcd^ 
-1-1246 h^ddrdy 
— 4 
db^cde‘f^ 
— 
30 
aWc^deY 
— 
30 adddeY 
— 
72 adeY 
— 
246 b^dde* 
+ 2 
dVce\f 
— 
14 
a-JdddY 
+ 
60 ab^ddf- 
+ 
78 adky^ 
+ 
206 ddd'ef 
- 6 
cdlrd^ef^ 
— 
50 
a'b^ddy^ 
— 
48 ab*cd^eY 
+ 
224 adddf 
_ 
866 b^dd?d 
+ 16 
o?hHhY“ 
+ 168 
db^ddrdY 
+ 
16 ab^cdY 
+ 
1 6 add 
— 
220 dddy 
-14 
dh^de'f 
— 
48 
d^Wddey 
+ 
38 ab^cde*/ 
— 
342 add^ef 
+ 
550 IdddJ'd 
+ 4 
dlre‘ 
— 
4 
db'^dd’ 
— 
36 adcd" 
_ 
220 add“d 
_ 
56 b^^cd'e 
+ 6 
o?hddf^ 
— 
48 
(db'^cd^eY 
+ 
112 ab^d^eY 
+ 
106 addy 
— 
4 Vd 
- 6 
dbdeY 
— 
2 
(rWcd/ey 
— 
204 ab‘^d^e^f 
+ 
392 add^d 
+ 
78 b-def- 
-50 
c?b(?<tef^ 
+ 
6 
aVdcdre^ 
+ 
102 ab^drdf 
— 
222 add^e 
+ 
428 Wdd?y" 
+ 82 
dhdddf 
+ 
62 
d-bHY 
+ 
50 ab^deY 
+ 
40 ad(P 
— 
516 b‘ddey 
— 32 
dbde’f 
— 
90 
d^Wd^df 
+ 
46 odc^dY 
— 
4 ddY 
+ 
4 b~de* 
+ 36 
dbcdY 
+ 
39 
arh^d^e* 
— 
2 addddY 
+ 
4 b'ey^ 
— 
804 b-dd^ef 
— 30 
dbcd^eY 
— 
28 
d~bdeY 
— 
204 a¥ddf 
+ 
3 b^dY 
+ 
550 Iddd/d' 
-30 
dbcd?ey 
+ 
54 
dbdd?f 
— 
170 addd^eY 
+ 
24 dcdeY 
+ 
392 dddy 
+ 24 
dhcdd' 
— 
48 
dbddeY 
+ 
308 ab^ddd" 
— 
30 dceY 
+ 
139 b^dd^d 
— 28 
dbd’ef" 
-1- 
112 
dbddf 
+ 
42 ab^dd'^ey 
+ 
16 ddY 
— 
354 Vdd^'e 
+ 50 
dbd^df 
+ 
82 
(rbdd?eY 
— 
164 aWcd^Y 
— 
4 dd'df - 
+ 
83 b^dd^ 
-22 
dbd?d 
— 
170 
dbc"(Pey 
dbddd 
+ 
674 ab\d^df 
— 
36 b^dey 
— 
180 bddY 
48 bdey 
— 4 
dcY 
— 
104 
— 
590 ab^cd^e^ 
+ 
27 b^d 
+ 
+ 36 
dddeY 
dd/p 
— 
108 
dbdd?f 
— 
128 aWd^ef 
— 
104 b^ccPef- 
+ 
506 bdd~ef 
-16 
— 
42 
dbdd^df 
+ 
138 add^d' 
— 
22 b^deY 
— 
56 bddd 
— 22 
aWY 
+ 298 
(tbddPe^ 
— 
70 ab^ddY 
— 
60 dddrf^ 
— 
222 bddy 
-50 
ddd‘eY 
+ 242 
crbcd^ef 
— 
90 ab~ddf" 
+ 
6 dc^dey^ 
— 
354 bdd^d 
+ 16 
ddde'^f 
— 
294 
cdbcd^d 
— 
42 alddddeY 
+ 
102' b^de^f 
+ 
330 bddj'e 
+ 16 
— 
72 
d-bdy 
+ 
674 aJddddf 
+ 
CO 
0 
CO 
— 
72 hdd? 
+ 54 
ddd*eY 
+ 
78 
(rbd^d 
— 
4 ad^dd' 
— 
234 dcdd' 
+ 
27 dy- 
+ 46 
o?dd}e^f 
— 
6 
dddY 
+ 
394 ab^ddy^ 
— 
24 WdPp 
— 
90 ddef ' 
-60 
d'dd?d‘ 
+ 
62 
ddeY 
— 
652 ad^ddP'd' 
— 
4 dd^df 
— 
4 dd ! 
- 6 
dcdY 
— 
108 
(ddd^eY 
— 
714 alrdd^e-f 
+ 
32 dd?d 
+ 
40 ddy 
-70 
dcdPe^f 
— 
164 
ddddf 
— 
498 iddddJ'ef 
+ 
56 b^ddf 
+ 
83 dd-d 
+ 56 
dcd*e^ 
— 
24 
dde’ 
+ 1246 ah^dd^d 
+ 
39 Idddf^^ 
— 
72 dd!^e 
+ 18 
dddef 
+ 
63 
a‘ddY 
+ 
224 adcdJf 
+ 
298 bVd-ef 
+ 
16 dd^ 
-14 
aW 
+ 394 
cddd^df 
— 
516 ab“cd^d 
— 
590 ddddf 
— 1 
awr 
l 
+ 194 
ddd^e' 
+ 
48 ub"d^e 
+ 
32 ddd 
1 
The tables Nos. 30 to 35 relate to a sextic. No. 30 is the sextic itself; No. 31 the 
qaadrinvariant; Nos. 32 and 33 the quadricovariants (the latter of them the Hessian); 
No. 34 is the quartinvariant or catalecticant ; and No. 35 is the sextinvariant in its 
best form, i. e. a form not containing any power higher than the second of the lead- 
ing coefficient a. 
g Rt,?/)® 
No. 30. 
a 
6 b 
15 c 
20 d 
15 e 
6/ 
