199 
<?!> P) 
Ordinary Meeting, March 4th, 1862. 
J. P. Joule, LL.D., F.R.S., President, in the Chair. 
The Rev. Robert Harley, F.R.A.S., made the following 
statement : — 
I am induced by the interest and attention excited by my 
communication on the Theory of the Transcendental Solution 
of Algebraic Equations (see pp. 181 — 184 of the current 
volume of the Proceedings) to offer to the Society some 
supplementary observations on the subject. 
The Boolian or symbolical form of the differential resolvent 
for the equation 
y n — ny+(n— 1 ) x=0 =f{y, x) 
is, in general, (D denoting as usual the differential symbol 
d 6 
ami t being written for the independent variable x,) 
y — 0 (D) y— 0, 
where 
n 2 — n+1 
n 
D (D— 1) (D — 2) . . . (D — rc+2) 
The quadratic equation 
y 2 — 2y+*= 0 
is an exception ; for, in this case the sum of the roots (Sy) is 
not, as in the other cases, equal to zero, and therefore the 
differential resolvent must contain a term independent of y. 
In fact, for this equation, the symbolical form of the resolved 
is 
3^ 
D 2 o i e 
y— j) 6 y ~ 2 d 6 ’ 
Proceedings— Lit, & Phil. Society— No. 12.— Session 1S61-62. 
