APPENDIX.
The Knight’s move over the chess board has engaged the attention of so many scientific men, that I cannot doubt that a collection of different solutions of the problem will prove acceptable to all admirers of chess.
The Knight’s path is of two kinds—terminable and interminable—it is interminable, whenever the last, or concluding, move of a series be made on a square, which lies within the Knight’s reach of that from which he originally set out—and terminable in every other instance.
Euler published a paper in the Memoirs of the Academy of Berlin, 1759, which contains a method of filling up all the squares, setting out from one of the corners. It also contains an endless or interminable route; and explains a principle by which these routes may be varied so as to end upon any square. Montmort, Demoivre, and Mairan, have severally given solutions of the same problem. These solutions will be found in the following collection.
Observing that the Automaton, under the direction of Mr. Maelzel, occasionally traversed half the board, I was induced to pursue the subject, and I found that the move might be performed on any parallelogram consisting of twelve squares and upwards, with the exception of fifteen and eighteen squares. The whole board admits of a great variety both in the terminable and interminable routes.
In describing the Knight’s path, I have preferred lines to figures; the former giving a clearer idea of the plan pursued, and affording a greater facility of comparing one route with another, than the latter.
DIRECTIONS FOR PLACING THE PLATES.
Plate 1 to face the Title.
Plates 2 to 5—Page 36.
—— 6 to 10 —— 38.