IN THE HIGHER ALGEBRA. 141 
§ 29. 
The relations 
POL M+ OLO=L 
LOL?) XPOL?O=1E) 1); 
enable us to determine f”(7) f"(#) and f”(#*) /”(2) mm terms 
of Iand7,. Similar relations hold for J and 7. 
‘ 
ow tela = I 
vip wiplatp'y+p ztp 
This, on reduction, becomes 
3 f@®@ a, J') ect Ors 
Pay Py P+ 8 FHS = 
and the relation 
fi) _ P@Or@) 
PO ru’) 
will enable us to express p in terms of I and 7. 
§ 31. 
When, therefore, 0 is known, p can be determined ; and, 
if in (1) we substitute : —p for u and reduce the result 
to the usual form, the equation in ¢ will be solvible, for a 
factor of the symmetric product vanishes. The solution 
of (19) may be made to depend upon that of (1), and the 
latter, in its turn, upon that of (11) and of the equation 
in ¢. 
§ 82. 
Mr. Harley has discovered that in certain cases U be- 
comes a square, and equals 7. This circumstance may 
throw a light upon the question of the solvibility of the 
equation in 0. 
Norg. — Mr. Cockle’s original communication, consisting of the 
