PROFESSOR CAYLEY’S TENTH MEMOIR ON QUANTICS. 
651 
Table No. 99 (concluded). 
20 
21 
22 
24 
0 
2 
4 
1 
0 
2 
0 
9 5 
biv 
bY 
g 4 j 
gw 
W 
9 S 9 
c/r 
frc r q 
919 
bg s q 
g 4 q 
c/u 
g°i° 
Wgu 
0 
g-v 
bghi 
gho 
9<f 
■ ■ oft 
bY 
93 u 
bgq” 
gY 
qu 
99?' 
bg*m 
39 2 
bqu 
99 u 
■ ■ j°9 
bc/f 
qv 
g‘hi 
qi 
. . OV 
brjviq 
Q -O 
9T 
u 3 
rn 
. . Igo* 
TO 1 
g°mq 
kni 
0 O 
• • 9*0' 
tv 1 
■ ■ tyv 
gfq 
brmu 
• • qp 
. . bot 
gmu 
cYq 
■ . got 
dgjq 
•0 
fu 
. . dgv 
771 p 1 
dju 
■ . <rq 
g'h 
. . V 
rfhq 
. . cfho 
SV 
1 
. . g^rri" 
ghu 
• • 9T m 
• . gkt 
. . gos 
■ . gr 3 
1Y 
■ -i 4 
• • jor 
. . Jcoq 
. . vfiq 
. . m o 2 
. . st 
ov 1 
pv 
i 
sv 
i 
8 derivs. 
1 deriv. 
1 deriv. 
1 deriv. 
384. The Canonical form (using the divided expressions, Table No. 98) is peculiarly 
convenient for the calculation of the derivatives. Some attention is required in regard 
to the numerical determination : it will be observed that A is given in the standard form 
(A 0 , A b A 2 , A 3 , A 4 , A-4f.r, y) 5 , while the other covariants are given in the denumerate 
forms B=(B 0 , B,, B.^a?, y) 2 &c. : these must be converted into the other form 
B =(B„, Pl B ; Ix, yf, C=(C 0 , JC„ JjA, *C 3 , *C 4 , |C 5 , C&x, </)“, Ac., the 
numerical coefficients being of course the reciprocals of the binomial coefficients. We 
thus have, for instance, the leading coefficients. 
l.c. of AC2=A 0 . t l 5 -C 3 - 2. A^Ci + Ao.C 0 , but 
„ „ BC2 = B 0 . 1 i-C 3 -2.iB 1 iC 1 + B 2 .C 0 . 
5 ? 
