88 



SCIENCE PROGRESS 



(/) Opposite parallel half-sides taken anywhere, e.g. 

 (14+ i + ii + 8), (1 + 15 + 8+ 10), (11 + 2+ 16 + 5), etc. 



(g) The four corner numbers of every square of 9 cells, 

 e.g. (14 + 15 + 2 + 3), (12 + 9 + 8 + 5), etc. It may 

 be noticed that the opposite corner numbers total 17, e.g. 

 (14 + 3), (15 + 2), (12 + 5)i (9 + 8), etc. Hence the 

 two diagonals of any 9-cell square are equal to one another. 



(h) Similar terminations of any Knight's move on 

 opposite sides of any central line of the square, e.g. 

 (14+ 13 + 4 + 3), (12+ 11 +6+5), (8+ 16+ 1 +9), etc. 



(i) The sum of the two central numbers in any line, 

 horizontal or vertical, and the two outer numbers of a 

 parallel line next-but-one to it, e.g. (1 + 15 + 2 + 16), 

 (12+ 13+ 5 +4), etc. 



In addition to these properties, it is found that the " graph " 

 produced by joining the consecutive numbers 1, 2, 3, etc., in 

 rotation (including the line, shown dotted, joining 16 and 1) 

 forms an absolutely symmetrical figure, thus : 



1 



The symmetry of the figure will be the more apparent if it be 

 turned over on its right-hand side. 



Now it is to be noted that both the Dudhai Square and that 

 reproduced below, which was discovered on the gate of the fort 

 of Gwalior, share all these properties. 



Gwalior Square. 



