399 



*(D) 



Ordinary Meeting, March 4tb, .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 



is, in general, (D denoting as usual the differential symbol 

 fl 



^^, and £ being written for the independent variable x,) 

 where 



D (D— 1) (D— 2) . . . (D— w+2) 

 The quadratic equation 



is an exception ; for, in this case the sum of the roots (S?/) 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 resolvent 

 is 



p-4 . 1 . 



PaOCEEDINGS-LlT. & PhIL. SOCIETY -No. 12.— SESSION 1861-62. 



