292 



On an Ancient Magic Square, cut in a Temple at Gwalior. By Captain 



Shortreede. 



As every thing tending to throw any certain light on the antiquities 

 of India has an interest, I send you the following inscription of a Magic 

 Square, which I copied last year from an old temple in the hill fort 

 of Gwalior. It bears the date ^TW V*8° = a. d. 1483. 



The temple is on the northern side of the hill, and at one time it has 

 been a very magnificent edifice, though now it be sorely dilapidated. 



It has formerly suffered from the rude hands of the Musalmans, and 

 more lately it has been excavated under the site of the image to the 

 depth of twenty or twenty-five feet, in the vain hope of finding hidden 

 treasure. 



There is another and larger ancient temple in the fort, of a peculiar 

 form, which the Musalmans have converted into a Musjid. 



If I remember rightly, the Magic Square is cut on the inner side of 

 the northern wall, close to where the excavation has been made. I did 

 not measure the dimensions ; but the form is as follows : — 



\< 



«. 





V 





i 



\ 





^ 



•& 



\» 



The properties of the square are, that in 

 every way, whether vertically or horizontal- 

 ly, or diagonally, the sum of the numbers is 

 34 : the diagonals may be summed either in 

 one line as usual, or in two parallel lines; 

 containing together four numbers thus : — 



= 116 + 10 + 1+7 = 9+3 + 8 + 14 = 4 + 6 + 13 + 11=2 + 12 + 15+5 



It will be observed, that the places of the numbers 1, 2, 3, 4, form 

 a rhomboid, as do also 5, 6, 7, 8 ; 9, 10, 11, 12 ; 13, 14, 15, 16. It may 

 be remarked also, that the sum of every two alternate numbers taken 

 diagonally is 17 : and that all these properties will hold good if the 

 lines be transposed vertically or horizontally in the same order ; that is, 

 if the top line be brought to the bottom ; or if the left hand vertical line 

 be carried over to the right. 



