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Ordinary Meeting, November 3rd, 1863. 
E. W. Binney, F.R.S., F.G.S., President, in the Chair. 
Edward Hull, B.A., F.G.S., was elected an ordinary 
member of the Society. 
A Paper, entitled “ On the Theory of Equations,” by His 
Honour James Cockle, M.A., F.R.A.S., F.C.P.S., &c., 
the Chief Justice of Queensland, was communicated by the 
Rev. Robert Harley, F.R.S., F.R.A.S. 
Despite the accession to the subject of Mr. Harley and Mr. 
Cayley, there remains something to be done in the theory of 
quintics. I think that a root of the given equation should be 
expressed in terms of a single value of the resolvent product, 
and (in the Philosophical Magazine for March, 1860, and the 
Quarterhj Journal for June, 1860) I have taken some steps 
in that direction. The latter calculations are pushed some- 
what further in a manuscript which I forwarded to Mr. 
Harley some little time since, but as yet I am not aware 
whether that intrepid calculator has arrived at any conclusion 
as to which course it would be advisable to adopt. To 
express a root in terms of a single value of Mr. Harley’s r or 
of Mr. Cayley’s (p would, I believe, be desirable. 
Shortly before leaving England for Australia it had occurred 
to me that the theory of what I propose to call <( coresol vents” 
might throw light on such a question as “ What is the most 
general form of linear differential equation of the second order 
soluble by means of an algebraical (not necessarily a cubic) 
equation ?” and also on the determination of the points of 
Proceedings— Lit. & Phil. Society— No. 5.— Session, 1863-64. 
