TWEXTY-SIXTn AXXUAL MEETING. 



0.5 



' evo peparated; but, however the numbers of one quarter are shifted about, the 

 naj^ibers of all the other quarters are shifted about in a similar manner. 



L3t it be fully understood that, whether applying to lines, columns, pairs, 

 single numbers, couplets, or quaterniads, the first and second, also the third and 

 fourth, are adjacent; the second and third (though contiguous), also the first 

 and fourth (or those which are complementary to each other in any other posi- 

 tions), are 02:>posite; the first and third, also the second and fourth (or any oc- 

 curring with an intervening one), are alternate. Adjacent quarters are those 

 ou the same side of a square, whether vertical or horizontal; opposite quarters 

 are those diametrically opposite. 



General Rules. 

 The arrangement of numbers in a square is largely optional; yet the following 

 restrictions must be observed: 



1. Two odd numbers, and no more, must be placed in each line, each column, 

 and each central diagonal. 



2. The position of the odd and even numbers in the square must be deter- 

 mined beforehand according to a certain scheme to be agreed upon. • 



3. The number 1 must always be placed in the upper left-hand corner. 



4. The number 2 will be placed at the opposite end of a certain "coupling 

 line" to be seen in the predetermined scheme. 



5. The adjacent couplet ( 3 and 4 ) may have an arrangement the reverse or 

 crosswise of, or parallel to, the first couplet, in other columns and lines. ( The 

 best arrangement is when the four numbers of a quaterniad are so placed that 

 no two occupy the same line, column, or diagonal.) 



6. Regarding the quaterniad already laid as having a "dexter" (or sinister) 

 arrangement, the adjacent quaterniad (5, 6, 7, 8) must have a "sinister" (or 

 dexter ) arrangement, the couplets in reversed order, in the opposite half of the 

 square (whether horizontal, vertical, exterior or interior) as indicated by the 

 coupling lines of the scheme. 



7. The opposite quaterniads must have a similar arrangement, the coujjlets 

 in reversed order ( though some other order will answer to a degree ), in the oppo- 

 site quarters of the square. 



8. Thus arranged, numbers diametrically opposite will add together 17. This, 

 though best, is not strictly essential. • 



Now we will consider the scheme by which our square " No. 1 " is constructed : 



Scheme I (47 of Schedule). 



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The scheme has two forms — a regular (fig. 25) and an inverted (tig. 2G). 

 The original or primary square is constructed according to fig. 25. Seven of the 

 derived squares will be like fig. 25 ; eight of them like fig. 26. 



In the above figures (and in all other schemes) the lines connect couplets of 

 adjacent numVjers of the series; the second couplet of a quaterniad is to be in the 

 opposite half of the square. Thus, in the scheme above and our r.quare No. 1, 



