EEV. E. HAELEY ON THE I^IETHOD OF SYMMETEIC PEODHCTS. 
353 
+ 52 X 
— 
26 
am/ 
+ 
9 
— 
394 
a^d'^df 
+ 
142 
a^d^cde 
+ 
4 
a^d'^d^ 
+ 
792 
am^e 
+ 
196 
a^d^dd^ 
+ 
1140 
+ 
1345 
+ 
52 X 
+ 
190 
dd^cf 
— 
34 
a^d^de 
— 
596 
a^d^de 
— 
118 
a?d^cd‘ 
— 
1400 
aPd^dd 
2550 
aJ-d^d 
+ 5'X 
— 
8 a^dy 
+ 
52 a^d^ce 
+ 
6 a^d^d^ 
+ 
220 a'^d‘dd 
+ 
690 a^d'^d 
+ 5=X 
— 
2 am 
— 
20 amd 
— 
130 a^6'V 
+ 5 X 
+ 
4 a^d^d 
+ 
81 a-b-°d 
+ 5 X 
(- 
6 ab~^c) 
+ 1 X 
— 4 
— 9550 
+ 5670 
+ 2640 
_ 60 
-6835 
+ 7025 
+ 30 
+ 4800 
+ 700 
+ 1100 
+ 405 
a}%We 
a}%‘cy 
c^%^e‘de 
a}'>b'c^d^ 
a^®5®e"e 
0}%^ 
a}^^c^d 
+ 5^X 
— 105 a^b^-cf^ 
+ 120 a^b^-def 
— 18 a^b^e^ 
+ 1590 
+ 330 a?b^^cd'f 
— 354 a^b^^cde^ 
— 22 a^b^'di'e 
+ 3555 
— 1816 
— 825 
+ 2 
+ 4282 
-3766 
— 112 
-3716 
- 778 
-1400 
— 650 
a^b^^^df 
a^b^^(Pdre 
a?b^'^cd^ 
a»6V/ 
a^b^c^de 
a^b^c^e 
a^b^c^d' 
a^b'&d 
a^b^c^ 
+ 5^X 
+ 30 aWY- 
— 990 aW^cef 
— 120 a^b^^dY 
+ 108 a%^^de- 
-3985 a%^(rdf 
+ 1772 a®6’Ve^ 
+ 657 a^b^^cd^e 
+ 3 
-8755 
+ 6265 
+ 270 
+ 9620 
+ 2410 
+ 5700 
+ 3450 
a®5"cy 
a^b^^c^de 
a®5'Ve 
db^^dd- 
dddd 
aW 
+ 5^X 
+ 52 
+ 494 
— 193 
— 42 
+ 2339 
— 1265 
— 54 
-3374 
— 892 
— 3100 
— 2550 
a'd^ef 
a'd^cdf 
a'd^ce" 
a'd^d‘e 
a'd^cy 
dd^dde 
a'bV 
a'd-de 
a~d~dd“ 
a'd^dd 
(+1 
24. A partial verification of this value is afibrded by supposing the last two coefficients 
of the quintic, \iz. e and/*, or (what in effect is the same thing) two of its roots, say 
Xt, and x-^, to vanish. We have then (art. 11 ei seq.) 
6s=0,= ^3{^a+6dx,), 
^4 = ^6=^3(aa+5d.r,), 
where I have for the moment written a in place of 
da^hd-i-ba^c^—bab'^c+b*. 
And, consequently, in this case the product is 
^ X the square of 
.... 1 1 
- 6^ a^d* 
— 2'^ 5^ d’ddd 
-11.5* a^dd 
+ 5'^ d’bcd^ 
— 3.5^ ddd’ 
+ 2.5 d‘dd 
+ 5^ a'dd- 
+ 5” d^dd'^ 
+ 18.5 crdd 
+ 2.5^ dhc^d 
+ 14. 5" a'ddd 
— 3.5 ad'^c 
+ 5® fiV 
+ 18. 52 aW 
+ 1 6'- 
-2-. d ddcd’^ 
- 2\da^dcd 
1 
1 
Developing this expression, all the terms in n not affected by e or /will be verified. 
* It is noticeable that tbe following combinations do not enter into the above expression for n, vhs. 
dW* d^HK 
3c2 
d^ef^ d^bdf' 
d^df* d^df* 
