EEV. E. HAELEY THE METHOD OE STIilMETEIC PEODTJCTS. 
349 
and if we write 
n=n,+n,b+n,b^+ . . . +u,b% 
Ho is known, being what IT becomes when the quintic is deprived of its second term, 
and III, ria, . . . may be found from it by means of the formulse 
n,=- i v'n„ 
n,= -^(V'n,+ 43 .n.), 
wher: 
Assume 
and 
then 
and if w*e write 
then will 
so, in general, if 
we shall have 
V'=V_( 5 b 4 + 45 b,)= 3 cb,+ 2 (Zb,+eb^. 
^o=Ao+Bo/-^Co/^+Do/^ 
V" = V' - e^f= 3 cb , + 2 fZb, ; 
— 5 nj=v'no= v"Ao+Boe 
+/ (V"B„+2Co^) 
+/^(V"C„+3Do^) 
n,=A,+Biy+Ci^/’^+B,/ ^ 
-2.5n,=V'n,+4B,no= V"A.+ B.e + i'b.A, 
+/(V"B,+ 2 C ,6 + 4 B,B„) 
+/^(V''C. + 3D.6+4bA) 
+/^(V'D. + 4 bA); 
^,=A,+B,/+C,/•^+D,/^ 
— 5(^+l)n,+, = V'n^+4Bcni_,= V'hVi+ B^e+4bcA|;_i 
~^f (^”Bi+ 2 C|;e+ 4 bcB;_j) 
-{-f%V''Ct + 3D^e+ 4bcQ_ J 
+/^(V"D,+ 4 bA-. ). 
These formulee •will enable us with comparative ease and great rapidity to derive the 
symmetric product for the complete quintic from that for the quintic wanting in its 
second term. 
