914 
PROFESSOR A. CAYLEY ON THE SINGLE 
A.A 
0 , 0 
V+“V 
— it = 
XX' +YY', 
(square-set) 
B.B 
*0 ” ^0 
5 ) 
YX' +XY', 
C.C 
d. 
• d 
5 5 
xx' -yy; 
D.D 
d . 
- d 
57 
-YX' +XY'; 
C.A 
0 , ,0 
3-ii-\-u S-u 
1 0 
— 11 = 
xx; +y y;, 
(first product-set) 
A.C 
D.B 
0 0 
\l » 
^1 ” ^0 
3 ? 
37 
X X' — Y Y ', 
Y.X/ +X.Y/, 
B.D 
d 1 d 1 
Cl ” 1 
33 
Y/ x;—XY/; 
B.A 
d^w+Ad% 
0 n 0 
—u — 
pf +qq; 
(second product-set) 
A.B 
si , 
0 
d 1 
’ 0 
3 3 
PQ +QPj 
D.C 
d 1 d° 
1 ” 1 
73 
?PF -iQQ', 
C.L) 
9° d 1 
1 „ ^ 
3 3 
tPQ' — iQP'; 
D.A 
3^u-\-u 'due 
1 1 0 
_ 
P/P/ + Q,Q/, 
(third product-set) 
A.D 
$9 d 1 
0 ” 1 
37 
^qz-^qp;, 
B.C 
9 1 d° 
H) ” H 
33 
—^P/P/ ~MQ,Q, ^ 
C.B 
d° „ d 1 
l ” u 
3 3 
pq; +qp;- 
33. Here, and subsequently, we have 
®o- @ 1 0’ e °v ®1 = x ’ Y > A Y , 
(2 u')=x', r, x/, y; 
(0) =a, /3, a, /3, 
33 3 ? 37 73 
5 ; 33 77 3 3 
0 o 5 0 O’ 0 1’ 0 1 Q’ P '’ Q/ 
( 20 =f, q', p/, q; 
(0) =p, q, p,, q. 
33 37 73 37 
7 ? 33 75 55 
viz., we use also a, (3, a, /3 and p, q, p /} q, to denote the zero-functions; /3 / is= 0, but 
we use B' to denote the zero-value of ~Y.. 
' civ 
