108 
MR. A. CAYLEY’S SECOND MEMOIR UPON QUANTICS. 
ah 
ac 
ad 
hd 
cd j 
¥ 
he 
1 
a’ 
a^b 
etc 
(td 
ahd 
acd 
adP 
bdP 
ceP 
dP 
aV 
abc 
a(? 
Pd 
bed 
Pd 
P 
Pc 
hc^ 
P 
a* 
a^b 
a^c 
a^d 
Phd 
Ped 
a^P 
ahd‘ 
acP 
ad^ 
bd^ 
cP 
d* 
a^P 
Pbc 
PP 
aPd 
abed 
aPd 
PP 
beP 
Pd‘ 
aP 
aPe 
abc‘ 
aP 
Ped 
bPd 
Pd 
P 
Pc 
Pd 
bP 
Pc~ 
ab 
ac 
ad 
ae 
be 
bd 
cd 
P 
P 
be 
bd 
cd 
(? 
P 
Pb 
etc 
Pd 
Pe 
abe 
ace 
ade 
aP 
bP 
cP 
dP 
P 
aP 
abc 
abd 
acd 
aP 
bee 
bde 
ede 
Pe 
P 
aP 
Pd 
We 
bP 
c^e 
d^ 
b“c 
bP 
bed 
Pd 
cP 
P 
34. Thus in the case of a cubic (a, h, c, d\x,yY, the tables show that there will 
be a single invariant of the degree 4. Represent this by 
-\-^ahcd 
-\-Cac^ 
-\-jyjfd 
which is to be operated upon with This gives 
c^cd 
aPd 
ahc^ 
b^c 
+ B 
+ 6A 
+ 3D 
+ 2B 
+ 2E 
+ 6C 
+ 3B 
+ 4E 
+ 3D 
