Prof. Boole^s Account of the late John Walsh of Cork. 351 



Parallel Lines/^ (Folio.) A series of definitions, axioms, and 

 enunciations of propositions without proof annexed. 



The definitions are headed by the motto " Space is Space, 

 Time is Time, Truth is Truth,^^ and the first of the so-called 

 definitions is '' Space and Time are infinite, coeternal, and can- 

 not be increased or diminished." For the rest, the propositions 

 appear to be those of Euchd expressed in another form, the word 

 '' angular plane " being used for angle. 



" Memoir on the Calculus of Variations, showing its total 

 unreality." 



" The Principles of Geometry." This consists of two books ; 

 the first, on the " Measurement of Infinite Space," apparently 

 the same as the second manuscript, but with demonstrations ap- 

 pended ; the second on the *' Measurement of Bounded Space." 



A manuscript in a brown paper cover, apparently a note-book 

 containing a series of mathematical speculations on the " mea- 

 surement of infinite space," the solution of equations of the 

 higher orders, the trisection of an angle, physical astronomy, &c. 



In these, and in nearly all of Mr. Walsh's speculations which 

 I have taken the trouble to examine, one peculiarity of his mental 

 procedure is very observable. He takes up some known method 

 or formula of analysis, makes in it a slight and quite unimport- 

 ant change (for every theorem admits of some variety in the 

 mode of its expression), and views the result to which he is led 

 as an original discovery. Thus, in a page headed '' Cubic Equa- 

 tions," he writes the name of Cardan opposite to a well-known 

 algebraic solution, that of Walsh opposite to the same result put 

 under another and less convenient form, and below these he 

 gives a formula headed " For a complete Cubic by Walsh only." 

 It is related of the dramatic poet Wycherley, that in his old 

 age the functions of memory and of genius were so strangely 

 mingled and confused, that if verses were read to him in the 

 evening he would reproduce them the following morning with 

 all the effort of original composition, quite unconscious of the 

 source of his borrowed inspiration. Mr. Walsh committed 

 similar errors without the intervention of a sleep. 



What importance Mr. Walsh attached to his supposed disco- 

 veries will appear from the following extract which I make from 

 the M S . note-book above referred to. It is not a solitary example. 



'' Discovered the general solution of numerical equations of 

 the fifth degree at 114 Evergreen Street, at the Cross of Ever- 

 green, Cork, at nine o'clock in the forenoon of July 7th, 1844 ; 

 exactly twenty-two years after the invention of the Geometry of 

 Partial Equations, and the expulsion of the diff*erential calculus 

 from Mathematical Science." 



Besides Mr. Walsh's own papers, there remain a large number 



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