I 



BY K, M. JOHNSTON, F.L.S. 129 



9. Months in Year or 12 = Angles on 4 faces 4X3: 



also equal to base of a-^ 

 simple pyramid of even 

 numbers whose aggre- 

 gate represents 364: alsoj 

 the seventh of the aggre- 

 gate of a simple pyramid 

 of odd having 7 for its 

 base. 



10. Lunar Months in year orl3'^ nearly (lo""'') = 



^ 7X4 



Square Pyuamid of Mixed Odd and Even Numbbes, 

 Having fok a Base (7 x 2)^ or 14^ = 196. 



Perhaps this forms the most interesting of all the com- 

 binations. Its natural proportions and naturally related 

 numbers are most suggestive. 



The following combinations are most striking : — 



1. If we take either the exposed cubes on the margin of each 



layer, or the total faces of distinct cubes in the four 

 sides, the aggregate comes exactly to 365, or the exact 

 number of days in the year ; and therefore the propor- 

 tional number of cubes on each triangular face is 91 j, 

 corresponding to days in the quarter of a year. 



2. If we now take the basal layer alone, we find the exposed 



number of cubes in the square to be 52, corresponding 

 to weeks in the year. 



3. If again we take the aggregate of all cubes in the pyramid, 



we find they amount to 1,015, and if this number be 

 multiplied by 36, or 4 times 9 (the latter number repre- 

 senting the number of verticle angles on faces of the 

 four wedges or prisms of which the pyramid is built, as 

 indicated by its diagonals), we obtain 36,540, or within 

 8 inches of the best actual measurements of its present 

 state, which has no doubt undergone some slight settle- 

 ment due to superincumbent pressure. 



4. A quarter of this gives 9,135 inches, or within 2 inches of 



the mean of the best actual measurements obtained by 

 competent investigators. 

 6. If we now take the square of its basal layer, 14 x 14, we 

 get 196, and it is remarkable that if this number be 

 multiplied successively by half the side, and by the 

 number of sides, i.e., 196 x 7 x 4, we get 5,488, or within 

 16 inches of the best estimates of the present height of 

 the Great Pyramid, any two of which differ far more 

 seriouslv with each other than this curious combination. 



