350 Prof. Boole's Account of the late Jolin Walsh of Cork, 



expense a large number of tracts, in which he endeavoured to 

 establish his views, and denounced in no measured tenns the 

 unjust and selfish opposition which he thought that he had met 

 with. Of a considerable number of these tracts, and also of the 

 original manuscripts of them, I have found copies among his 

 papers, and a brief account of them may be interesting. 



The printed tracts and papers are for the most part occupied 

 with the announcement of some discoveiy which was designed 

 to supersede the differential calculus in its application to pro- 

 blems respecting curves. The method in question consisted in 

 transferring the origin of coordinates to a point upon the curve, 

 developing the ordinate y in terms of the abscissa a?, and making 

 use of the coefficients of the expansion just in the same way as 

 the ordinary principles of the differential calculus would dii-ect 

 us to do. The titles of some of Mr. Walsh's papers will serve 

 to throw light on the particular objects which he had in view. 

 The equation of a curve transformed as above Mr. Walsh calls 

 its '' partial equation .'' 



" Memoir on the invention of Pai-tial Equations.'^ 



"The Theory of Partial Functions. Letter to the Right 

 Honourable Lord Brougham.^' 



" Memoir on the Theory of Partial Functions.'' 



" Irish Manufactures. A new method of Tangents." 



" An Introduction to the Geometry of the Sphere, Pyramid 

 and Solid Angles." 



'^ General Principles of the Theory of Sound." 



" The Normal Diameter in Curves." 



" The Problem of Double Tangency." 



" The Geometric Base." 



"Letters to S. F. Lacroix, the Editor of the Edinburgh Re*- 

 view. Rev. F. Sadleir, &c." 



" Dublin University. Notes on a Mathematical Controversy 

 between Dr. Lloyd the Provost, the Rev. Mr. Luby and Dr. 

 O'Brien, Fellows of the College, and Mr. Walsh, author of the 

 Geometric Base." 



" The Theoretic Solution of Algebraic Equations of the Higher 

 Orders." 



" Metalogia, &c." 



The mere list of titles above given, and it is far from being 

 complete, affords evidence of considerable industry, and Mr. 

 Walsh's unpublished papers confirm this testimony. The fol- 

 lowing is an account of the principal ones : — 



" llie Elements of Geometry, by John Walsh." (Folio.) This 

 merely contains a series of definitions and axioms, &c., beginning 

 with the " doctrine of ratio." 



" On the Measurement of Infinite Space, and the Theory of 



