Chase.] ^^b [April 21, 



186. ForesJmdowings. 



The greatest superiority of Sj over S.^, as well as of the phyllotactic and ap- 

 proximately phyllotactic divisors over the hydrogen divisor, is found in the 

 di- and tetratomic group. The aggregate probability of hydrogen influence 

 on atomicity is more than 9,900,000,000,000 times as great as that of S,, or 

 more than 37, 800, 000, 000, 000, 000 times as great as that of Sj, or more than 

 243,700,000,000,000,000,000 times the probability of accidental coincidence. 

 Each of these numbers should be multiplied by 5592.6 to give the proba- 

 bility of the phyllotactic divisors. The lowest surd probability in either 

 group is that of Sj in the di- and tetratomic group, which is only 1.446 : 1, 

 or a little more than 13 : 9. Even this ratio, however, is satisfactory as 

 indicative of incipient action, and suggestive of researches in the "nascent 

 state," the "fourth state of matter," or in some other approximation to 

 the {Ethereal condition. The artiad and metallic elements seem also to offer 

 fields for important future discovery in regard to modifications of phyllo- 

 tactic tendency by condensation or combination. 



187. Hydrogen Shares the Phyllotactic Probabilities. 



In the foregoing notes I have treated hydrogen as outside the phyllotac- 

 tic group, in order to find the probability of the hypotheses of Dalton and 

 Prout as compared with other reasonable hypotheses . As a member of the 

 phyllotactic group, and the most general of the phyllotactic divisors, it 

 shares all the probabilities of the group. Therefore, if there is any value 

 in mathematical tests, the views of Berzelius, Turner, Marignac, Stas and 

 CUarke, as to the importance of the hydrogen atom, should be accepted, 

 rather than those of Thomas Thomson and Dumas. 



188. Inertia and Elasticity. 



Tlius the evidences are multiplying, in every direction, of the importance 

 of giving great heed to the blended sway of inertia and elasticity, in all 

 physical researches. The moment of inertia is of especial importance, 

 inasmuch as material particles, in an elastic medium, become the seats of 

 living forces which enable us to apply the laws of composition and reso- 

 lution of forces, to composition and resolution of motions. The principles 

 which I applied successfully, in 1863, to barometric estimates of the Sun's 

 mass and distance, have been abundantly exemplified in every field in 

 which I have sought for evidences of their influence, and now tliey are 

 found at the very threshold of material structure, where cohesive and 

 chemical attractions first show themselves. 



189. Phyllotaxy of Central Force. 



I have already spoken of the appearance of the phyllotactic numbers 1, 

 2, 3, 5 and. 8, in crystallization, and especially in the mimicrj' of frost- 

 pictures. The simplest phenomena of central force introduce the first 

 three phyllotactic powers ; Kepler's third law gives the phyllotactic frac- 



