FOE AN EQUATION OF ANY OEDEE. 
99 
Calculation of coefficient 6^ in equation of differences for the quintic equation 
(«, b, c, d, e,f^v, 1)®=0. 
Calculation of Lo- 
j 
1 
1 
2ae 
-2bd 
+ c" 
2ce 
—d* 
In eq.of diff.for quartic. 
Coek fl®. 
Coek. 0'. 
Coek. 0^ 
! a*e* 
+ 512 
— 112 = 
+ 400 
1 a'bde^ 
-384 
— 512 
+ 56 
— 840 
a^c-e^ 
-256 
+ 256 
-384 
+ 24 
— 360 
a^cdre- 
+ 288 
+ 432 
+ 192 
+ 48 
+ 960 
aH^e 
- 54 
— 216 
—270 
c?h~c^ 
+ 288 
+ 144 
- 32 
+ 400 
drb^d'-e^ 
— 12 
+ 384 
- 72 
— 25 
+ 275 
a-b(rde‘ 
-160 
+ 256 
-192 
— 240 
- 54 
-390 
cchcd^e 
+ 36 
— 288 
— 108 
+ 120 
— 240 
ahd'’ 
+ 54 
+ 54 
+ 108 
j 
+ 32 
— 128 
+ 64 
+ 17 
— 15 
a'c^dre 
— 8 
+ 144 
-f- 36 
- 32 
+ 140 
aVc?^ 
- 27 
— 18 
— 45 
ab^er 
- 54 
+ 6 
— 48 
ab^cde^ 
+ 36 
-288 
+ 36 
+ 38 
— 178 
a¥d^e 
— 8 
+ 12 
— 18 
— 14 
ab-<?e^ 
— 8 
+ 144 
- 12 
- 12 
+ 112 
ab^e^d^e 
+ 2 
. +160 
- 6 
+ 84 
+ 6 
+ 246 
ab'cd^ 
— 36 
— 42 
- 78 
abdde 
- 32 
- 80 
- 52 
-164 
abc^d^ 
+ 8 
+ 18 
+ 26 
+ 52 
ad'e 
+ 16 
+ 8 
+ 24 
add* 
— 4 
— 4 
— 8 
b^’de* 
+ 54 
- 6 
+ 48 
bV-e* 
- 27 
+ 2 
— 25 
b^cd*e 
- 36 
— 18 
— 54 
¥d^ 
+ 8 
+ 9 
+ 17 
b*c*de 
+ 8 
+ 18 
+ 12 
+ 38 
b*(rd* 
— 2 
— 4 
- 6 
— 12 
b^de 
— 4 
- 2 
- 6 
b*c*d* 
+ 1 
+ 1 
+ 2 
+ suppose, then, 
1 -B= 
-C = 
-D= 
-E= 
d-d* + 270 
a*cd* — 960 
a*bd + 840 
d -400 
a*bcd* + 240 
ddd* -275 
a*c* + 360 
a*c*d* — 1 40 
a*bdd +390 
a*dc —400 
add* + 14 
aV + 15 
ad + 48 
addd* —246 
adcd + 1 78 
abc*d +l64 
adc* -112 
ac* — 24 
dd - 48 
b*cd* + 54 
b*c*d — 38 
dc* + 6 
dc* + 25 
