t 
na 
■ ... '' 
144] 
A THIRD MEMOIR UPON QUANTICS. 
311 
the different columns of the matrix. No. 28 gives the values of certain linear 
functions of these determinants, viz. 
L= 1256 + 2345-2.1346, 
¿'=3.1256 - 1346, 
8 iff = - 1345 + 2.1246, 
8iff'= - 2346 + 2.1356, 
8N=- 1245 +3.1236, 
8N'=- 2356 +3.1456, 
SOP = L' - 3P = 5.1346 - 3.2345, 
16P'=-5L'~ L = - 16.1256 - 3 .1346 - 2356. 
At the end of the two tables there are given certain relations which exist between 
the terms of Tables 14, 16, 25, 26, 27 and 28. 
No. 27. 
1234 
1235. 
1236. 
1245. 
1246. 
1345. 
1256. 
2345. 
a?bf 
a 2 cf 
_ 
4 
a 2 df + 
6 
a 2 df — 
6 
a 2 ef + 
4 
a?ef 
a 2 f 2 + 
1 
a 2 / 2 
....! 
a 2 ce 
— 
16 
a?de 
+ 
24 
a 2 e 2 
a 2 e 2 + 
16 
abdf— 
4 
abdf— 
24 
abef— 
2 
abef 
... 
a 2 d? 
+ 
36 
ab 2 f 
4 
abef— 
22 
abef + 
6 
abe 2 — 
4 
abe 2 + 
64 
aedf— 
16 
aedf+ 
20 1 
ab 2 e 
+ 
16 
abce 
— 
84 
■abde— 
6 
abde— 
26 
ac 2 f — 
24 
acf + 
24 
ace 2 + 
16 
ace 2 — 
80 j 
abed 
— 
152 
abd 2 
— 
24 
ac 2 e + 
16 
ac 2 e - 
96 
accle + 
24 
aede — 
208 
ad 2 e + 
16 
ad?e + 
60 
aP 
+ 
96 
aPd 
+ 
64 
acd 2 
acd 2 + 
96. 
ad? 
ad 3 + 
144 
b 2 df- 
15 
bW- 
80 
b 3 d 
+ 
80 
b 3 e 
+ 
60 
by + 
16 
by 
b 2 cf + 
24 
b‘V 
b 2 e 2 
b 2 e 2 + 
240 
b 2 c 2 
_ 
60 
b 2 cd 
— 
40 
b 2 ce — 
10 
b 2 ce + 
90 
b 2 de — 
20 
b 2 de - 
40 
bef 
bc 2 f + 
60 
be 3 
b 2 d 2 
b 2 d 2 - 
80 
bc?e 
bc 2 e + 
60 
bede 
bede — 
860 
bc 2 d 
bc 2 d 
bed 2 
bed 2 - 
40 
bd 3 
bd 3 + 
960 
c 4 
c 4 
<?d 
c 3 d 
c 3 e 
c 3 e + 
960 
c 2 d 2 
c\P - 
320 ! 
1346. 
2346. 
1356. 
2356. 
1456. 
2456. 
3456. 
a 2 f 2 ... 
abf 2 ... 
abf 2 + 4 
acf 2 — 6 
acf 2 + 6 
adf 2 - 4 
aef 2 
abef + 16 
acef — 24 
acef — 4 
adef + 6 
adef — 22 
aPf + 4 
bdf 2 — 16 
aedf — 36 
ad 2 f+ 24 
ad?f— 24 
a<? 
ae 3 +16 
bef 2 + 24 
be 2 f + 16 
ace 2 — 16 
ade 2 
ade 2 + 24 
b 2 f 2 + 16 
by 2 ... 
bdef— 84 
c 2 f 2 + 36 
ad 2 e + 36 
b 2 ef + 64 
b 2 ef - 4 
beef — 26 
beef — 6 
be 3 + 60 
edef- 152 
b 2 df - 16 
bedf- 208 
bedf + 24 
b 2 df- 96 
bdf+ 16 
Pef - 24 
ce 3 + 80 
b 2 e 2 
bee 2 — 40 
bee 2 - 20 
bde 2 +90 
bde 2 - 10 
cdPf + 64 
d?f + 96 
bc 2 f + 36 
bd 2 e + 60 
bd?e ... 
Pdf + 96 
Pdf ... 
ede 2 - 40 
d 2 P - 60 
bede — 20 
c 3 f + 144 
cf 
c 2 e 2 - 80 
pep 
d 3 e 
bd 3 
c 2 de — 40 
c 2 de 
cd 2 e 
cd?e 
c 3 e 
cd 3 
cd 3 
d 4 
d 4 
c 2 d 2