TWENTY-SIXTH ANNUAL MEETING. 



57 



To show what kind of squares this last series of arrangements will make, a 

 few samples are here shown : 



No. 34. 

 28th Arr. 



No. 35. 

 lOtli Arr. 



No. 36. 

 64tli Arr. 



No. 37. 

 OGrli Arr. 



This makes 1,536 magic squares that may be constructed from that one 

 scheme, 288 of which squares are harmonic. 



Instructions.— To construct a primary square from one of the above trial 

 arrangements : 



1st. Draw a blank square of 16 places ; and note the places for the odd num- 

 bers, as in the scheme. 



2d. Apply the eight numbers of the trial arrangement selected, in their order, 

 to the upper ends of the coupling lines, or conceive them to be so applied. 



3d. Double each number of the trial arrangement, and place the products in 

 spaces corresponding to both ends of the respective arrows, first subtracting 1 

 from the number falling in a space noted for an odd number. 



Scheme II (No. 39 of Schedule). 



Scheme II (figs. 33 and 34) is the same as scheme I turned over on its direct 

 central diagonal as an axis. No. 1 still occupies the upper left-hand corner. The 

 upper line in scheme I becomes the left-hand column in scheme II. All the col- 



