TWUXTY-SIXTH ANNUAL MEETING. 

 Scheme IV ( No. 26 of Schedule). 



59 



-I - , -•' — - •- ■ 



^^ S/u 



^->.^y. 



'^is '^■ 



This scheme (figs. 37 and 38) is the same as scheme III turned over on its 

 direct central diagonal, and as scheme II, with the central columns transposed. 



The coupling arrows in this, as in scheme II, are to be numbered at their left- 

 hand end. The vertical columns of the trial arrangements apply to the respec- 

 tive halves of the square. 



One or two squares are given by way of comparison with those of scheme II. 



2d Arrangement. 

 No. 46. 



4th Arrangement. 

 No. 47. 



1 8 



7 2 



4 5 



6 3 



1 8 



6 3 

 4 5 



7 2 



All the arrangements shown for scheme I are equally applicable to the other 

 three. This makes for the four schemes 384 arrangements of 16 squares each; 

 or in all so far 6,144 squares, no two alike, of which 1,152 are perfectly harmonic, 

 384 of them to the highest degree. 



Other Schemes. 



But the foregoing schemes are not the only ones that can be made, though 

 they are more harmonic than others. I will now introduce several other schemes 

 and show at least one square made according to each by the first arrangement. 

 It should be said here that the same arrangements will not answer for all alike ; 

 but each set of schemes has its own peculiarities and requires its own series of 

 arrangements. 



( 17 6 4 ? 

 \ 823 5 J 



No. 48. 



Scheme V (fig. 39) is a variation of scheme I. 

 The variation consists in reversing the couplets of 

 the second and fourth quaterniads, which in the 

 scheme stand parallel with their complementary or 

 opposite couplets. (Square No. 48.) 



No. 49. 



Scheme VI (fig. 40) differs from scheme II exactly 

 as scheme V differs from scheme I anJ has the same 

 characteristics. (See square No. 49.) 



