70 



KANSAS ACADEMT OF SCIENCE. 

 No. 10. 



its center the center of the square, will add 74, or two-thirds of 111. Many 

 other squares similar to this may be constructed, and some of them exhibit 

 singular features, but none of them are of special merit. 



Enough has been shown now by which any one may construct all the 

 squares of 36 places that he may wish, and place any numbers in any desired 

 position. 



Square of Sight. 



These squares are laid according to any of the schemes for the square of 

 four, but not forgetting the square of two. They are very easy, and hundreds 

 of thousands of them may easily be produced. For, schemes that do not 

 readily work in a square of 4 do well in a square of 8, and none of them fail. 



There are three general methods of constructing a square of 8, namely: 



1st. To divide the square into sixteen sections, and arrange the square as 

 a quadruple square of sixteen places. 



2d. To arrange it in four separate squares of sixteen places each, side by 

 side. 



3d. To place one square in the center, two dimidiated squares, either 

 right-side out or inside out, on the four opposite sides, and one quartered 

 square at the four corners. 



There are many modes of arranging the series to fill the respective 

 squares, two of which are here shown: 



First Method. 

 Here are shown two squares constructed according to the first method. 

 They are laid according to the third arrangement of scheme I (see square No. 

 33), Square of Four, and the diagonal (No. 3) method of the Square of Two in 

 its four different aspects: 



No.l. 



No. 2. 



