TWEXTY-SEVENTH ANNUAL MEETING. 



107 



Os is excessive and not a fair average. Os may contain an undiscovered ele- 

 ment (Til VII) of still higher atomic weight and specific gravity. The curves, 

 however, are calculated on an increase of 33% per cent, for the culminating 

 point, thus: K VIII, 9.09; Rb VIII, 12.12; Cs VIII, 16.16; and Au VIII, 21.55. 

 This places Co 1 per cent, below and Ir 1 per cent, above the culmination. Ac- 

 cording to this calculation, if there were an element at Th VIII its specific 

 gravity would be 28.73; but, according to those that already exist, as Co, Rh, 

 and Ir, in which the rate of increase is SiVz per cent., the specific gravity 

 would be 29.25. In the case of the twin metals, Ni, Pd, and Pt, standing with 

 Co, Rh, and Ir, at the culmination of the curves, the variation is so slight it 

 need not be taken into account. 



The average rate of increase in specific gravity of the several successive 

 members of each of the accrescent octaves, while not uniform, is approxi- 

 mately 36 per cent. The decrease in specific gravity of the several succes- 

 sive members of the decrescent octaves averages 13% per cent., or, computing 

 backward and upward from the lowest element in each octave, the increase 

 is 15 per cent. 



There are eight groups in the accrescent octaves and seven in the decres- 

 cent, fifteen in all. The rate of increase in specific gravity in the several 

 elements of each group in the accrescent octaves is strictly 33% per cent. 

 The members of the Thorium octave are an exception; the increase is only 

 15 per cent. The increase of specific gravity in the several elements of each 

 group in the decrescent octaves is 28 per cent. The Thorium hecdecade is no 

 exception; there are no known elements in the decrescent octave of the 

 Thorium hecdecadal series. Hence there is no decrescent octave; and the 

 term hecdecade is simply used in this case for convenience and comparison. 



Harmonies of the Hecdecades. 



The atomic weights, while not strictly a uniform arithmetical series, are 

 nevertheless harmonic to a degree. Like the tones in music, there are whole 

 steps and half steps, major steps and minor steps, as already shown, and 

 occasionally doublets or twins. Perhaps when all the elements in nature 

 have been discovered, there will be a "chromatic" series in each octave. That 

 these atomic weights are harmonic is readily shown by placing them in the 

 form of a square, thus: 



Potassium Hecdecade. 238.9 



238.2 



238. 



233.6 



239.0 



237.7 



237.5 



239.7 



234.3 236.5 



