of the Knight's March. 105 



4. The top and bottom numbers of the same vertical column 



the 2nd and 7th do. do. 



the 3rd and 6th do. do. 



the 4th and 5th do. do. 



added together, will produce the same amount, 65. 



Thus in column 16, the top No. 54 and the bottom No. 11 make 65 

 13, ... 2nd ... 44 ... 7th ... 21 ... 65 



15, ... 3rd ... 55 ... 6th ... 10 ... 65 



10, ... 4th ... 3 ... 5th ... 62 ... 65 



But the columns 9 and 11 are different from the others in this 

 respect, which arises from the peculiar movement of the knight 

 in these columns already alluded to. 

 In these columns — 



The top No. of the col. 9 and the bottom No. of the col. 11, 1+64 make 65 

 ...2nd ... 9 ... 7th ... 11,48-1-37 ... 65 



...3rd ... 9 ... 6th ... 11,31+34 ... 65 



... 4th ... 9 ... 5th ... 11, 50+15 ... 65 



orthetop ... 11 ... bottom ... 9,47+18 ... 65 



and so with the rest. 



5. It will be observed that every number in the figure is 

 in apposition in six different ways. For example, No. 54 is 



1st, in apposition in the same vertical column with! fi( . 



No. 11, making J 



2nd, in conjunction with No. 28 it is in apposition 1 , „„ 



with Nos. 1 and 47, making J 



3rd, in conjunction with No. 42 it is in apposition \ ,„ 



with Nos. 25 and 11, making J 



4th, in apposition with the numbers in the same sub-1 , „„ 



division 43, 6 and 27, making J 



5th, in apposition with Nos. 5, 28 and 43, forming a\ , „ 



horizontal column in division B, making J 



6th, in apposition with Nos. 27, 42 and 7, forming a'l . „ Q 



vertical column in the same division, making J 



6. The knight's march may be commenced at the square 

 marked 64, in fig. 1, and so backwards, until the 64th move 

 terminates on the square marked 1. This will produce fig. 2, 

 which answers to the first figure in all its peculiarities. 



It will be easily observed that the march can be commenced 

 from any of the corner or rooks' squares of the board ; from 

 any of the bishops' squares, or bishops' eighths ; or from either 

 of the rooks' thirds, or rooks' sixths. 



William Beverley. 

 9 Upper Terrace, Islington, 

 June 5, 1847. 



