352 
EEV. E. HAELEY ON THE METHOD OF STMMETEIC PEODHCTS. 
Then introducing the first coefficient («) of the quintic and restoring the constant 
numerical factor (5®), we have, for the complete form 
the symmetric product 
(a, b, c, d, e, l/ = 0, 
n =^4 multiplied into 
5"X 
— 
125 d^cdef^ 
+ 
25 d^ce^f “ 
+ 
25 d^d~e-f“ 
— 
10 ff'W/ 
+ 
1 a‘V 
+ 5'X 
+ 
250 d'b'def^ 
— 
50 d'‘b-e'f - 
+ 
375 d'‘bc-ef^ 
+ 
250 d'bcd-f^ 
+ 
'Jo d‘bcde~/'' 
— 
20 d'bce^f 
— 
100 d'bd^ef- 
+ 
30 d'‘bd-e^f 
— 
2 d'bde' 
+ 
125 d~ddf^ 
— 
100 d'‘de~f“ 
— 
150 d"<rd-ef~ 
+ 
175 d'dddf 
— 
32 d'de' 
— 
25 d'cd^f^ 
— 
35 d'cd^e"f 
+ 
7 d'‘cd-d' 
+ 
10 d'd'^ef 
— 
2 e''(7+^ 
+ 5'''X 
1250 dHdcef^ 
— 
500 d%H-j^ 
— 
250 d%^ddp 
+ 
60 dHdd^f 
1875 d^dddf^ 
— 
75 d^dde-f^ 
+ 
525 d^dcd^ef^ 
— 
785 d^dcddf 
! + 
141 d%^cd 
+ 
150 dHdddf 
+ 
80 dHdd^df 
— 
19 d%^-d^d 
— 
375 d%dp 
+ 
925 d^bddef^ 
— 
325 d^hddf 
+ 
600 d%ddY- 
— 
435 dHjddrdf 
+ 
103 d^dde^ 
+ 
40 d%cddef 
+ 
3 d%cd^d 
— 
20 d%dy 
+ 
2 d%d^d 
+ 
125 
d^def^ 
+ 
150 
d^dd"f‘ 
— 
1340 
d'''dde“f 
+ 
336 
d^de' 
+ 
510 
d'''dd^ef 
— 
58 
d’"dd~d 
— 
70 
d^dd'^f 
+ 
14 
d^dd^d 
— 
7 
d^cd^'e 
+ 
1 
d\d 
+ 55x 
+ 
1000 
d^def^ 
+ 
5125 
d'^dcdf^ 
+ 
1275 
d^dce^f“ 
+ 
100 
d^'dd'^ef- 
+ 
790 
d%\ldf 
— 
156 
d'ddd 
+ 
3875 
d^ddf^ 
— 
2775 
d'^dddef- 
+ 
2135 
d^dddf 
— 
2550 
d^dcd^f” 
+ 
2140 
d^dcd-e‘f 
— 
445 
d'^dcde^ 
— 
260 
d^dd^ef 
d^dd^d 
+ 
20 
— 
2075 
d^ddef'^ 
— 
4825 
d'^dddy- 
+ 12075 (t>[h"cye‘f 
— 268O 
— 3030 a}'^h‘^c-cPef 
+ 140 a}-^h”c~d-e^ 
+ 420 a^^h^ccVf 
— 100 a}'’h'^cd''e^ 
+ 20 a}^h‘^d^e 
— 1150 a^'^hedf- 
+ 3770 a}°ljd’ey 
+ 470 a^'^bc^d-ef 
— 1000 a^-^bc^de^ 
\ + 30 a}'^bc^dy 
— 330 cd^bc^d^e‘- 
+ 140 cd'^b^d^e 
— 10 a}^bcd'‘ 
— 50 
+ 2800 a}^d‘def 
— 1330 a‘Ve» 
— 425 
— 95 
+ 115 a’W‘'e 
— 10 d^^c^d^ 
+ 5®X 
750 
d^ddf^ 
— 
270 
d'^dey^ 
— 
2475 
d^ddy^ 
+ 
45 
d^dcdey^ 
— 
880 
d^dcdy 
+ 
400 
d^ddy- 
— 
540 
d%hi‘dy 
+ 
102 
d^ddd 
+ 
1495 
d^ddey- 
+ 
4320 
d%^ddy^ 
— 
8250 
d'^ddddy 
+ 
1568 
d'^dde* 
+ 
1195 
d'^dcd^ey 
+ 
6 
d‘^dcd'^d 
— 
58 
d%^dy 
+ 
27 
d^dd^d 
+ 
3740 
d^dddy- 
— 
7165 
d^dddy 
— 
1260 
d%^dd^ey 
+ 
1635 
d'^dddd 
— 
40 
d'ddddy 
+ 
490 
d'ddd^d 
— 
100 
d^dcd^e 
+ 
485 
d^ddy^ 
— 
8280 
d^dddey 
+ 
3115 
d^ddd" 
+ 
720 
d^dddy 
+ 
1040 
d^ddd-d 
— 
265 
d^ddd^e 
+ 
5 
d%\H^ 
— 
1660 
d'^bdey 
— 
355 
ddjddf 
+ 
1150 
d'^bd’dd' 
— 
115 
d%dd^e 
— 
10 
d^bdd^ 
— 
325 
d^ddy 
+ 
480 
d^dd 
— 
45 
d^dd"e 
— 
5 
d^dd' 
+ 
5’ X 
+ 630 d^Ucf^ 
+ 90 d^bUef 
+ 116 d^Ue^f 
— 355 d^^def^ 
— 1275 dWcd-f~ 
+ 2481 dWcddf 
- 399 d^dce^ 
— 114 dWd^ef 
- 10 dWcPe^ 
- 3550 d^dddf 
+ 
5456 
d^ddey 
+ 
1149 
d^ddd^ey 
— 
958 
d^dddd 
— 
48 
dWcdy 
— 
219 
d^dcd^d 
+ 
14' 
d^ddl'e 
— 
1143 
d'^ddy^ 
+ 
9717 
d^dddey 
— 
3002 
d^ddd' 
— 
426 
d^dddy 
— 
1480 
d^ddd'^e^ 
-j- 
138 
d^ddd^e 
+ 
8 
d^^cd’^ 
+ 
4690 
d^ddey 
+ 
1240 
dWddy 
— 
2950 
d^dddd' 
+ 
40 
d^ddd?e 
+ 
40 
d^dddP 
+ 
1585 
d^dddy 
1715 
d^ddd 
— 
195 
d^ddd'^e 
+ 
50 
d^ddd^ 
+ 
195 
d^bdy 
— 
265 
d^bdde 
+ 
30 
d^bdd^ 
— 
80 
d^d^e 
+ 
10 
d^dd- 
+ 
5’x 
— 
56 
d^y^ 
+ 
17 
d’^dcey’^ 
+ 
123 
dvddy^ 
— 
270 
d^dddy 
+ 
37 
d'^de^ 
+ 
1456 
d-dddy^ 
— 
2063 
d'dde-y 
— 
444 
d“dcd?ey 
+ 
241 
d-dcdd 
+ 
12 
d^ddy 
+ 
30 
d-dd:^d 
+ 
1117 
d’^ddy- 
— 
5903 
d'^dddey 
+ 
1515 
d^ddd 
+ 
113 
d"dddy 
+ 
811 
d^^ddd'd 
13 
d’^dcd^e 
— 
2 
d^dd 
— 
5577 
d‘ddey 
— 
1616 
d^ddddy 
+ 
3047 
dWddd 
+ 
162 
d’^dddde 
36 
d^ddd^ 
— 
3060 
d'^dddy 
+ 
2609 
d^^dd 
+ 
744 
d^ddcPe 
— 
84 
d'^bVd* 
— 
785 
dWdy 
+ 
995 
dWdde 
— 
70 
d^W 
+ 
380 
d"dde 
— 
10 
d'^ddd? 
+ 
20 
d"bd^d 
+ 
5 
+ t 
>®x 
+ 
2 
— 
276 
d'-dcdy- 
+ 
384 
d^dcdy 
+ 
58 
d^dd~ef 
— 
22 
d^dde^ 
— 
556 
dWdf“ 
+ 
1971 
d^dddef 
— 
421 
d^dde^ 
— 
4 
d^dcdy 
— 
194 
d^dcd'^e- 
— 
2 
dWe 
+ 
3629 
d^ddey 
+ 
1047 
d^b'dd'y 
— 
1623 
d^dddd 
— 
147 
d^ddd^e 
+ 
10 
d^dcd^ 
+ 
3143 
d^dddy 
— 
2206 
d^ddd 
— 
897 
d^ddd^e 
+ 
52 
d^ddd^ 
+ 
1372 
d^ddy 
— 
1588 
d^ddde 
+ 
48 
d'ddd^ 
— 
794 
d'^dde 
~ 
52 
d^ddd~ 
— 
100 
d^ddd 
— 
30 
dW 
+ l 
>'x 
+ 100 d%^^df 
— 140 
+ 750 a'^s^vy- 
— 1710 d%'^^cdef 
+ 305 d'^d^cd 
— 10 d%'^H^f 
+ 85 d%'^^d‘^d 
— 6985 d'^ddef 
— 1830 d%\-d-f 
+ 2355 d%\'^dd 
+ 220 d%^cd^e 
