306 Dr. Roget on the Problem of the Knight^ s 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 
vow'els, 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 knight’s 
moves are always alternately from white to black, and from black to white, 
the terminal square must be one of a different colour from that at which 
the moves commenced. 
