POPULAR SCIENCE 

 Their respective " graphs " are as follows : 



89 



x \ *" X is 



* \ X X X / 





Dudhai Square. 



Gwalior Square. 



The contortions through which any perfect 34 square may 

 be put without any sacrifice of its supermagic properties are 

 somewhat extraordinary. For instance, taking any one primary 

 square, which we will assume to be that shown with the number 

 1 in its left-hand top cell, we can imagine it inscribed on a 

 cylinder with vertical axis, revolving to the left or right (say 

 the left in this instance), thus bringing each column in rotation 

 into the position occupied by the first column in the primary 

 square, thus : 



First Derivatives. 



We can then imagine each of these four squares in turn 

 similarly dealt with on a cylinder with horizontal axis, revolving 



