18S2.] 417 [Chase. 



the second supra-Neptunian locus which I indicated in 1873, and which 

 Forbes found to represent a group of cometary aphelion distances (Note 

 32). 



262. Photo dynamic Modulus of Planetary Revolution. 



A mathematical friend, in whose judgment I place great confidence, ad- 

 mits the con'^usiveness of the evidence in favor of paraboloidal harmony 

 in rupturing planetary loci (Note 46, etc.), but he thinks that the approxi- 

 mation to the locus of Alpha Centauri may be accidental. I am well 

 aware of the difficulty, which every one naturallj^ finds, in believing that 

 the seemingly quiet undulations of light should have any influence on 

 the relative positions of stellar systems. The remembrance' that the vis 

 viva of action or reaction, for any given mass, varies as the square of oscil- 

 lating velocity, would show that if there is any physical influence which 

 controls interstellar arrangements, it should be the one which has the 

 greatest normal velocity. The parabolic energy which is manifested 

 within the solar system, both in approaching and in leaving the sun, must 

 be indefinitely extended, and the luminous undulations which it indicates 

 are equally extensive. The symmetry of the three-fold division in the 

 paraboloid, together with the fact that the uncertainty of stellar distance 

 is of the same order of magnitude as i^lanetary eccentricities, excludes any 

 probable attribution of the stellar accordance to accidental coincidence. 

 The foregoing note furnishes additional grounds tor accepting all the har- 

 monic' relations of the photodynamic paraboloid as efl[ective. Since L^ 

 OCr^ (Note 75), and L„ at t^ = tt^ l^^, at the gravitating modulus ttV^, the 

 photodynamic modulus would be rr^f'^, its logarithm being 6 X .4971499 -f 3 

 X 1.5606934= 7.6649796. This is only .0013506 less than the logarithm 

 for the locus of a Centauri, as deduced fi'om the corona line and the 

 British estimate of Sun's semi-diameter, indicating a difference of less than 

 ^'g of one per cent. It is, therefore, certain that the photodynamic mod- 

 ulus of Sun's gravitating modulus is in the neighborhood, if not in the ac- 

 tual locus, of the nearest known star. 



263. A Chain of Photodynamic Harmonies. 



If we designate the planetarj'- locus which corresponds to the corona 

 line (Note 45) by x; Jupiter's greatest eccentricity b}'- 2/ ; and the theo- 

 retical locus of a Centauri by z, the following connected equations can all 

 be deduced from simple and obvious forms of elastic rhythm : 



1. ?/ = 1 — (1048.875^-- .5.202798 n) = .06055 Note 8 



2. m„ = (2 X 3 X 4)* m^ = 331776 m^ " 23 



3. a; ^ TT^ w„ = 460.61 r„ "45 



4. z:x:: m-^ : m^ z — 461746300 r„ " 46 



5. 'y„=^27rr„»2--^ ly ear = . 0006265013 r„ " 75 



6. Vo = TT ®o (^0 ^ ^o)^' = .4313442 r„ " 75 



7. V„ = ?ir„-- 497.827 w == 214.735 " 75 



