TWENTY-SIXTH ANNUAL MEETING. 



73 



2d. Reversing after placing the first series, running twice around in the 

 contrary direction, then reversing again at the end of the third series. 



3d. Reversing once for all after placing the first two series. 



Four squares are here shown, illustrating the methods of making squares 

 of this kind: 



No. 8. 



One turn. 



Two turns. 



Three Turns. 



Endless Chain. 



These squares are very variable, but are not transposable except by inversion, 

 reversion, reinversion, and rotiversion. The number 1 may be placed anywhere; 

 but, if moved from its present position, the little harmony the squares here have 

 is broken. The four squares above are all "endless chains." 



U. S. Grant Harmonic Square. 



The following square, first published in the Topeka Daily Capital July 29, 

 1885, the day of General Grant's funeral, is shown here to illustrate one of the 

 practical applications to which harmonic forms may be applied. It contains all 

 the years of General Grant's life systematically arranged: 



