80 The Rev. Robert Harley on 



will be found in the writings of Boole, 3 Cayley, 4 Spottis- 

 woode, 5 Russell, 6 Rawson, 7 and others. 



3. In early numbers of the Proceedings of this Society, 8 

 I showed that every differential resolvent is satisfied not 

 only by the roots, but also by the constituents of the roots 

 of the co-resolvent : these constituents are, in fact, particular 

 integrals of the differential equation. In the same series 

 of papers, I also showed that any homogeneous linear 

 function of the roots will satisfy the differential resolvent 

 provided only that such resolvent be also homogeneous. 



4. In a later paper 9 I have enunciated and proved the 



y Boole. "On the Differential Equations which determine the form of 

 the Roots of Algebraic Equations." Philosophical Transactions for 1864, 



PP- 733-755- 



" Differential Equations." Supplementary Volume, 1865, pp. 190-199. 



* Cayley. "Note on a Differential Equation." Manchester Memoirs, 

 Vol. II., Third Series, 1861-2, pp. 111-114. 



5 Sfottiswoode. "Note on Differential Resolvents." Manchester 

 Memoirs, Vol. II., Third Series, November, 1862, pp. 227-232. 



"On Differential Resolvents." Quarterly Journal of Mathematics, Vol. 

 VI., 1864, pp. 262-266. 



c Russell. "Solutions of the Quartic Resolvent." Manchester Pro- 

 ceedings, Vol- II., 1862, p. 240. 



"Solution of the Differential Resolvent." Manchester Memoirs, Vol. II., 

 Third Series, March, 1863, pp. 296-301. 



7 Rawson. — "On a New Method of Determining the Differential Resol- 

 vents of Algebraical Equations." Proceedings of the London Mathematical 

 Society, Vol. IX., 1878, pp. 202-215. 



"On the First \ Resolvent of the Quartic y 4 + *y 2 +x,y - ^a-= 0." Mes- 

 senger of Mathematics, Vol. XL, 1881, pp. 19-23. 



" On Differential Resolvents and Partial Differential Resolvents." Man- 

 chester Memoirs, Vol. VIII., Third Series, 1882, pp. 41-53. 



8 " Remarks on the Transcendental Solution of Algebraic Equations."' 

 Manchester Proceedings, Vol. II., Sessions 1S60-61 and 1S61-62, pp. 181- 

 186, 199-203, 237-241. 



" Notes on a Differential Equation." Quarterly Journal of Mathematics, 

 Vol. XVIII., 1SS1, pp. 41-46. 



