244 



Kansas Academy of Science. 



tern as square No. 41, under scheme II, published on page 58 

 of volume XIV, Transactions Kansas Academy of Science 

 (1893-'94), and by an easy transposition of the fourth column 

 for the third, and the fourth line for the third, it becomes a 

 perfect square like No. 15 above. 



Scheme IV (fig. 20). — Coupling-arrows joining altemute 

 lines and adjacent columns. This is the same as scheme III, 

 with the second and fourth columns transposed. The numbers 

 in the trial arrangements are therefore to be applied to the 

 first and fourth columns. This puts 15 in the upper right-hand 

 corner. The six model squares here follow : 



First Aerangement, 



Second Arrangement. 



1 8 



7 2 



6 3 



4 5 



1 8 



7 2 



4 5 



6 3 



No. 19. 

 Fourth Arrangement. 



No. 20. 

 Fifth Arrangement. 



1 8 



6 3 

 4 5 



7 2 



1 8 



4 5 



7 2 



6 3 



No. 22. 



No. 23. 



Third Arrangement. 



1 8 



6 3 



7 2 

 4 5 



No. 21. 

 Sixth Arrangement. 



1 8 



4 5 



6 3 



7 2 



No. 24. 



Remark. — One of the most conspicuous objects in an old 

 copper engraving, entitled "Melancholia" and executed by Al- 



