FOE AN EQUATION OF ANY OEDEE. 
101 
Terms of Lj not involving e. 
-f(V"iB + 4diC) 
5dbt> 
459c 
3cdd 
4d 
-1C 
a^dT-f 
a?hcdf^- 
+ 3875 
-8700 
+ 6600 
+ 4650 
—2000 = 
—2800 
+ 1875 
— 250 
a^cY' 
(vl?df^ 
- 725 
+ 2000 
-3480 
+ 2475 
+ 1280 
+ 1750 
— 200 
d^b'cY 
aVcf" 
+ 2325 
— 1740 
—2610 
— 2025 
- 700 
+ 1240 
+ 300 
+ 840 
abY 
— 112 
— 112 
Terms of involving e\ 
-e/^V"lC 
bdbb 45de 3c9d 
viz. 
-1C 
a^cef- 
a^b'ef- 
— 3500 —1500 = 
+ 4800 -2800 
-5000 
+ 2000 
Calculation of L3 (gives L3=0). 
L2= 
1 
“"3 
B= 
a^c 
+ 1666| 
a^b^ 
- 666| 
Terms of L3 
. 45dc 3cdd 
VIZ. 
-IB 
j 
1 
1 
a'bp 
-6666| +6666| = 
0 
1 
And the required coefficient of is 
All the coefficients were calculated in this manner, except the last coefficient, which 
was deduced from the known value of the discriminant for the standard form. And we 
have thus the complete expression of the equation of differences for the general quin tic 
equation under the denumerate form («, h, c, d, €,f^v, 1)®=0, viz.— 
MDCCCLX. P 
