Dr. Roget on the Prohlem of the Knighfs Move at Chess. 307 
as shown in the central diagram in the group marked LEAP, 
Plate I. and let the squares in each quarter be considered as 
grouped together into four sets, designated severally by the 
letters L, E, A, P ; thus, 
L 
E 
A 
P 
A 
P 
L 
E 
E 
L 
P 
A 
A 
E 
L 
It is here to be observed, that each of these sets of squares, 
marked with the same letter, constitutes a recurrent circuit 
of four moves of the knight. 
The squares in the other three quarters being similarly 
designated, as shown in the central diagram already referred 
to, it will be found that the several sets in each admit of be- 
ing connected by knight’s moves with the corresponding sets, 
similarly designated in the adjacent quarters. This is shown 
in the corner diagrams, L, E, A and P, where the con- 
nexions among the squares of each set are marked by oblique 
lines joining their centres^. The sets, thus connected, con- 
stitute four separate systems, of 16 squares each; and it will 
also be found that these 16 squares are so disposed that the 
knight may, in each system, perform the circuit of all its 
squares, beginning from any one given square, and ending 
at any other of a different colour. A few trials will soon sa- 
tisfy the learner that, in every case, this may very easily be 
accomplished, and generally in a great variety of ways. 
It will next be perceived that the knight can always pass 
from any of the squares, (excepting those situated at the 
corners of the board) of one system denoted by a consonant, 
to those of a system denoted by a vowel, and contrariwise ; 
(as is shown by the diagonal lines in the four diagrams in- 
termediate to the former); but not from vowel to vowel, or 
from consonant to consonant. From the corner squares, the 
move can only be made to squares belonging to the same 
system. 
The solution of the proposed problem includes three cases : 
1. If the given initial and terminal squares belong, the one 
to a system denoted by a consonant, and the other to a sy- 
stem denoted by a vowel, then, following the order of the 
letters when arranged in a circle, thus : 
* The white squares have a circle, and the black a dot in their centres, 
X 2 
