of the Knight's March. 103 



These figures show the successive moves of the knight over 

 the chess-board, every square being numbered in the order 

 of the knight's march; so that the numbers in each vertical 

 and horizontal column, added together, shall be equal ; the 

 sum of the eight numbers in each column being =260. 



These figures also present many other peculiarities. 



1. The chess-board (see fig. 1) is divided into four equal 

 parts by the lines ab and cd. These parts are marked A, B, 

 C and D, and consist each of sixteen squares, — four squares 

 in height and four in width ; and if the columns of any of 

 these parts be added up, both vertically and horizontally, each 

 column will give the same addition, 130. 



e. g. the part marked C. 



2. The figure is divided into sixteen equal parts by the lines 

 ab, ef, gh, cd, ij, kl : each of these parts consists of four squares; 

 and if the four numbers in the four squares which compose 

 any one of these parts be added together, they will make 130. 



e.g. 



or 



^=130 



= 130 



3. The figure is divided, by the vertical line ab, and the ho- 

 rizontal column 1 is also divided by the same line, into two 

 equal parts. Each part consists of four squares, in two of 

 which the numbers are even, and in the others odd. Take 

 the even numbers in the left division of the column, and the 

 odd numbers in the right division, and add them [together, 

 thus : 



