TWENTY-SIXTU ANNUAL MEETING. 



79 



the outer circle is exactly three times the diameter in any direction. Each 

 of the quarters is equal to the diameter, and the sum of the inner circle is 

 the same. There is nothing remarkable about this. 



RHOMBS. 



In figure 63 is presented a harmonic rhomb or diagonal square, in which 



the full lines in any direction are always as many times the central number as 

 the number of places in the line. Black and white numbers may be added 

 separately or together in the central lines. 



STARS AND CIRCLES. 

 In figure 64 is presented a six pointed star, which is, so far, the most har- 

 monic in every respect of all forms presented. Lines, triangles, and circles, 

 whether taken at one side or through the middle, always add as many times 



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eauoV. 



the central number as the number of places taken. Everything that has 

 been said of tbe harmonic hexagon is equally true of this. 



There are only thirteen numbers in it; but, without changing the position 

 of the central number, which is the keystone upon which the entire star rests, 

 it is capable of 24 transpositions the same as the harmonic hexagon. As a 

 specimen of symmetry and perfect harmony, it excels all forms yet presented. 

 One of the transpositions is shown in figure 65. 



