TWEXTY-SIXTII ANNUAL MEETING. 

 This would appear to the eye as rhombs, thus: 



31 



These, by a simple readjustment of the units, become squares, thus: 



Thirdly. By subtracting from the tetrahedral series the second preceding- 

 term, thus: 



1 4 10 20 3,5 56 84 120 165 220 286 3(31 . . . 



Subtract 1 4 10 20 35 56 84 120 165 220 . . 



1 1 ~9 16 25 36 49 64 81 100 121 144 .. . 



Fourthli/. By subtracting from the hexahedral series the preceding term, 



thus: 



1 5 14 30 55 91 140 204 285 385 506 650 .... 



Subtract 1 5 14 30 55 91 140 204 285 385 506 .... 

 "O 1 4 9 16 25 36 49 64 81 100 121 144 .... 



Remembering that the units in the pyramidal series are the same as in the 

 hexahedral series, if we consider that the above series is a pyramidal series, the 

 apparent strangeness of the performance disappears. 



The square series seems to be indestructible by addition to it (or subtraction 

 from it) of alternate, quartate, sextate, octate, or any regular arithmetical series, 

 in which the common difference is 2 or any multiple of 2. 



