1882.] "^'J^ [Chase. 



Other (Note 281), together with the various physical tendencies to division 

 in extreme and mean ratio (Notes 135, etc.), which make phyllotaxy a sim- 

 ple form of harmon^, seem likely to turn the scale largely on the side of 

 its present leaning, so as to make the fact of atomic phyllotaxy more and 

 more evident with each successive increase of precision in atomic measure- 

 ments. While the mean probability of the hydrogen unit, under the most 

 favorable aspect, is 1.93 times as great as that of any divisor taken at 

 random, the mean probability of the phyllotactic divisors, under the least 

 favorable aspect, is 1.845 times as great as that of hydrogen. If my di- 

 visors, like Gerber's, had been purely empirical, there would have been 

 more reason to think that they might lose credit with increased precision 

 of determination, but even then it would be strange if so large a relative 

 advantage were entirely overcome. The successive discoveries that Ger- 

 ber's divisors are approximately phyllotactic, that their significance is in- 

 creased by making them exactly phyllotactic, and that the most satisfac- 

 tory divisors which have yet been found stand in simple phyllotactic rela- 

 tions to the four fundamental organic elements, furnish no ground for ex- 

 pecting any future reversal or weakening of the harmonic indications 

 which I have already set forth. 



293. Photodynamie Precession. 

 To the many harmonic evidences of photodynamie action and reaction 

 between the chief centres of nucleation and of condensation, Sun and 

 Earth, may be added one which serves to illustrate and extend the princi- 

 ples that are involved in my first " photodynamie problem of three bodies" 

 fNote 254). If we suppose the photodynamie rotating influence on the 

 ^ethereal sphere, at the equatorial locus of Sun's modulus of light 

 (474028ro ; Note 263), to be such as would give planetary velocity at the 

 same locus, the time of rotation would be (474028-=-214.73)*=103721 years. 

 If nebular condensation wei'e to begin at that locus and proceed until the 

 primitive velocity of the locus would tend, through viscosity, to become 

 parabolic, the nucleal radius would be reduced to one-half and the time of 

 rotation to one-fourth of the primitive values. The period, or "great 

 year," which is thus indicated (25930.25 years), is virtually identical with 

 a complete revolution of the equinoxes, which Herschel estimates at 

 25,868 years ; Stockwell at 25,094 8 =h 281.2 years ;* Newcomb and Hol- 

 den "about 25,800 years." This accordance furnishes another reason for 

 believing, with Laplace, in the stability of the physical universe, rather 

 than in the ultimate stagnation which seems to be indicated by the ques- 

 tionable second law of thermodynamics. 



294. Harmonic Rotation of Earth and Moon. 



The improbability of Delaunay's hypothesis is further increased by har- 

 monies of rotation which involve the conjoint action of Sun, Earth and 

 Moon. 



* The differences from the mean value being due to secular inequalities. 



