306 Dr. Roget on the Problem of the Knighfs Move at Chess. 



deemed to possess sufficient interest to induce those who are 

 curious in these matters to bestow pains in inventing expedi- 

 ents for impressing some particular circuit on the memory, so 

 as to enable the possessor of this clue to guide the knight 

 through the mazes of his devious route, without reference to 

 chart or compass. In a memoir, which has appeared in 

 Frazer's Magazine for the present month*, which I have 

 just now seen, a method is recommended for attaining this 

 object, which consists in designating each square in the board 

 by a different syllable, composed of certain consonants and 

 vowels, indicating the horizontal and vertical columns in 

 which it stands. The whole series of these 64 arbitrary syl- 

 lables, joined into 16 words, pointing out the sequence of the 

 squares in the circuit, but void of any other meaning, is re- 

 quired to be learned by heart ; by an effort similar, and not less 

 distressing than that by which we strive to gain possession of 

 the chronological epochs of the kings of England, when com- 

 mitting to memory the barbarous cacophonies of Grey's Me- 

 moria Technica. 



It does not seem to have occurred to any of those who have 

 hitherto favoured the world with the results of their specula- 

 tions, that the problem in question would be rendered more 

 general, and consequently more curious, by imposing, in ad- 

 dition to the unlimited assignment of any square for the com- 

 mencement of the moves, the further condition that they shall 

 terminate at any other given square of an opposite colour f . 

 A great many years ago, I contrived a method by which the 

 problem, in this new and extended form, may be resolved 

 with the greatest ease ; and the attention of the public ha- 

 ving now been again called to the subject by the last-mention- 

 ed paper, I have thought that the communication of my 

 method might not be unacceptable ; especially as it depends 

 on a principle which not only furnishes the means of con- 

 structing an incalculable number both of recurrent and of 

 non-recurrent circuits, but also admits of very general appli- 

 cation to the problem of the knight's move. It is founded on 

 the following considerations. 



Conceive the chess-board to be divided into four quarters by 

 a vertical and horizontal line, both passing through its centre, 



* Entitled " Chess without a Chess-board, by a Chess Player," p. 316. 



t That the initial and the terminal squares must, of necessity, be of 

 opposite colours, will be evident from the consideration that, as the total 

 number of squares, namely 64, is an even number, and as the kni^l^t's 

 moves are always alternately from white to black, and from black ♦•« white, 

 the terminal square must be one of a different colour fron^ '^'^^ at which 

 the moves commenced. 



