PROFESSOR CAYLEY’S TENTH MEMOIR ON QUANTICS. 
659 
(continued from last page.) 
fib 0 fief 
- 63 
a l b d 7 

27 
cdb°fid 3 e 2 

234 
a°b 4 d 2 ef 2 
- 18 
chi 2 / 
+ 66 
„ b°fi/ 2 
— 
27 
fid 3 e 
+ 141 
de 3 / 
+ 45 
fide 2 
+ 99 
fidef 
+ 
24 
cd 7 
— 
27 
e 5 
- 27 
fid 3 e 
-147 
+ 
54 
aPbhlf 3 
— 
18 
„ bh 3 / 3 
+ 7 
fid 3 
+ 45 
fid 3 / 
+ 
27 
e/ 2 
+ 
18 
fidef 2 
+ 51 
a%/ 3 
+ 2 
cW 
— 
93 
„ bh/ 3 
+ 
15 
fie 3 / 
- 72 
b 3 cef 3 
- 15 
fid 4 e 
+ 
6 
cdef 2 
+ 
33 
cd 3 / 2 
+ 63 
dr 2 
- 6 
fid 3 
+ 
9 
ce 3 / 
— 
63 
cd 2 fif 
-213 
de 2 / 
- 18 
a°b 3 cf 3 
+ 
3 
d/ 2 
+ 
54 
cde 4 
+ 171 
e 4 
+ 27 
def 2 
— 
30 
dhf 
— 
66 
dhf 
+ 36 
„ fifidf 2 
+ 24 
ej 
+ 
27 
de 4 
+ 
27 
d 3 e 3 
- 43 
cV/ 
+ 51 
„ bhd/ 2 
+ 
51 
., b 3 fief 3 
— 
54 
„ fifief 2 
- 39 
cdfief 
+ 102 
cde/ 
— 
39 
fid/ 2 
— 
129 
fid/ 2 
-150 
cdfi 
-171 
ce 4 
— 
27 
fide 2 / 
+ 
186 
fide/ 
+ 303 
dff 
+ 6 
d 3 ef 
+ 
60 
fie 4 
+ 
45 
fie 4 
- 18 
d 3 e 2 
+ 18 
d 2 fi 
— 
45 
cd 3 ef 
+ 
54 
fid 3 ef 
+ 174 
„ b 3 fif 
- 9 
„ b 3 fidf 2 
— 
39 
cd 2 e 3 
— 
96 
fidfifi 
-345 
fide/ 
-210 
c 3 e 3 / 
+ 
45 
d 5 f 
— 
54 
cd/ 
- 99 
fifi 
+ 43 
c 2 d 2 ef 
— 
108 
d 4 fi 
+ 
48 
cdhfi 
+ 192 
cWf 
-120 
fidfi 
+ 
96 
„ b 2 fidf 2 
+ 114 
d G e 
- 18 
+ 345 
cd/ 
— 
111 
fifif 
+ 
9 
„ b fid/ 2 
+ 117 
cd i e 
- 87 
cd 3 e 2 
+ 
147 
fid 2 ef 
— 
150 
fie/ 
- 51 
d 6 
2 
d 3 e 
— 
30 
fidfi 
— 
147 
fid 2 ef 
-330 
„ b 2 fief 
+ 72 
„ b 2 fi/ 2 
+ 
9 
fid 4 f 
+ 
93 
fide 3 
+ 87 
chi 2 / 
+ 240 
chief 
+ 
6 
O 74 O 
c-cre" 
+ 150 
fid / 
+ 147 
fide 2 
-192 
c 4 e 3 
— 
48 
cd 3 e 
— 
87 • 
fid 3 fi 
+ 186 
fid 3 e 
-186 
fids/ 
+ 234 
d 7 
+ 
18 
fid 3 e 
-201 
fid 3 
+ 96 
fid 2 fi 
— 
150 
„ b fif 2 
— 
27 
cd 7 
+ 45 
„ b fidf 
-144 
fit l 4 e 
— 
108 
fidef 
— 
30 
„ m 2 
- 27 
c 6 e 2 
+ 18 
cd° 
+ 
57 
fie 3 
+ 
30 
fidef 
+ 99 
fid 2 e 
+ 201 
„ b fief 
+ 
9 
fid 3 / 
— 
6 
fie 3 
+ 2 
fid 4 
- 87 
fid 2 f 
— 
141 
fid?fi 
+ 
108 
fid/ 
- 45 
„ b°fif 
+ 27 
fide 2 
+ 
87 
fid 4 e 
— 
96 
fid 2 e 2 
- 96 
fide 
- 45 
fid 3 e 
+ 
96 
fid 6 
+ 
21 
fid 4 e 
+ 87 
fid 3 
+ 20 
chi 3 
— 
51 
„ b°fief 
+ 
27 
chi 6 
- 20 
„ b°c 7 df 
+ 
27 
fid 2 / 
— 
9 
fifi 
— 
18 
fide 2 
— 
57 
fid 2 e 
— 
21 
fid 3 e 
+ 
51 
* 
chi 4 
+ 
12 
fid 3 
— 
12 
I remark that I calculated the first two coefficients S 0 , S l5 and deduced the other 
two S 2 from S l5 and S 3 from S 0 , by reversing the order of the letters (or which is the 
same thing, interchanging a and f b and e, c and cl) and reversing also the signs of the 
numerical coefficients. This process for So, S 3 is to a very great extent a verification 
of the values of S 0 , S : . For, as presently mentioned, the terms of S 0 form sub- 
divisions such that in each subdivision the sum of the numerical coefficients is =0 : 
m passing by the reversal process to the value of S 3 , the terms are distributed into an 
entirely new set of subdivisions, and then in each of these subdivisions the sum of the 
numerical coefficients is found to be =0 ; and the like as regards S : and S 3 . 
Ii in the expressions for S 0 , S 1? S 3 , S 3 we first write d—e—f— 1, thus in effect 
combining the numerical coefficients for the terms which contain the same powers in 
«, b, c, we find 
