SECTION III., 1882. tora Trans. Roy. Soc. CANADA. 
Note on the Bishop’s Move at Chess. 
By J. B. CHERRIMAN, M. A. 
(Presented May 25, 1882.) 
In the Traité des applications de l'analyse mathématique au jeu des échecs, by Jaenisch, it 
has escaped the notice of the author that the number of squares commanded by a Bishop 
in any given position on the ordinary board can be expressed by a simple formula, as 
follows :— 
The origin being a corner of the board, let (a, b) be the co-ordinates of the square on 
which the Bishop stands; then the number of squares commanded is given by 
14 — (a+b—9)—(a— b). 
This results without difficulty from the solution in positive integers, with the proper 
limitations, of the indeterminate equation 
x—a= À (y—b) 
which expresses the Bishop’s march. 
