311] 
TO EQUATIONS OF THE FIFTH ORDER. 
61 
Putting for a its value — (x — 6), and for b, c, d, e their values, the quintic equation 
in x is 
(x — 6) 5 
+ (x — Ô) 3 . — 5 (AG + BD) a(3y8 
+ (x — fff. — 5 (A 2 ByS + B 2 C8a + G 2 Da(3 + D 2 A/3y ) a/3y8 
f— 5 (A 3 D/3y‘ 2 8 + B 3 Ay8 2 a + C 3 B8a?/3 + D s Ga/3 2 y) a/3y8 
+ (x — 6) -! 
t+ 5 (A 2 C 2 +B 2 D 2 — A BCD) a 2 /3 2 y 2 8 2 
f (A r, /3y ] 8 2 + B 5 y8 3 u 2 4- G 5 8a 3 /3 2 + D 5 a/3 3 y 2 ) a/3y8 
+ •! - 5 (A 3 BCy8 + B 3 GB8a + C 3 DAa(3 + DAB/3y) a 2 /3 2 y 2 8 2 
\ +o(A B 2 C 2 a8 + BC 2 D 2 (3a + GD 2 A 2 y/3 + DE 2 A 2 8a) tf/3 2 y 2 8 2 
where as before 
A = K + La + My + Nay, 
B=K + L/3 + M8 + N/38, 
G — K + Ly + Ma + Nya, 
D = K + L8 + M/3 + N8/3; 
and the coefficients of the quintic equation are, as they should be, cyclical functions 
with the cycle a/3yS. 
2, Stone Buildings, W.G., February 10, 1861.