1883.1 ^^^ [Chase, 



binations of this sum with phyllotactic powers of 2, 3, and 5 give the fol- 

 lowing mass-approximations : 



Computed. Phyllotactic. 



Sun --- Jupiter 1047.879 1050 = (2 + 5) (2x5) (3x5) 



Sun -- Saturn 3501,6 3500 = (2 + 5) (2x5)^ (5) 



Sun -- Uran. and Nep. 10433 10500 = (2 + 5) (2x5)^ (3x5) 



Sun -- Earth 8304G3 330750 = (2 + 5)^ (2x5) (3x5)-^(3) 



Sun ~- Venus 427240 428400 = (2 + 5) (23x5) (3^x5) (34) 



Sun ^ Mars 3093500 3094000= (2 + 5) (2x5)=' (13x34) 



Sun --- Mercury 4865751 4873050 — (2 -f 5)^ (3x5)' (13x34) 



The greatest deviation is less than j'^^ of one per cent. 



341. Centripetal Harmonies of Planetary Mass and Position. 



If we begin with the outer two-planet belt, we find evidence of the fol- 

 lowing successive influences : 



a- Rotary vis viva, (vip'^ -^2). (1). If we call the sum of the masses of 

 Neptune and Uranus to,„ = m, -\- m^, we find that its influence of rotary 

 perturbation introduces both the same and the diametrically opposite mean 

 perihelion longitudes of Saturn, provided that p^^^ andp^^^ represent, respec- 

 tively, the incipient loci of subsidence of Saturn and Uranus ; m^.^ (p'^ — 

 p'^^^) = Wg.7(5)-. (2). If we call the sum ot the masses of Jupiter and the 

 dense belt, m.^^ :=.m^-\- m^ -}- 7n^ -\- m„ -j- m^, we find that its mean influ- 

 ence of rotary perturbation is the same as that of Saturn ; tn^^^p^- = rn^^p^-. 



/J. Rotary momentum. The interior mass of the three primitive masses, 

 m^5j, was so divided that Sun's semi-diameter became the rupturing locus 

 for the principal centre of gravity of the system (c. g. of m^ and m,^. 

 Designating Jupiter's radius vector at secular perihelion by p , we find, 



y. Photic time-integral. Sun's mass and density are so harmoniou.sly 

 adjusted that the oscillations of solar rotation indicate the actions and re- 

 actions of a wave-velocity which is equivalent to the velocity of light 

 (Notes 17, etc.). 



^. Secondary time-integrals. The solar superficial gravitating accelera- 

 tion, which is determined by the photic time integral, determines in its 

 turn the velocity of circular-orbital oscillation (j/^') at all distances from 

 Sun's centre. The velocity at Sun's surface gives Jupiter's time-integral : 

 the velocity at the mean centre of gravity of the system gives Earth's time- 

 integral. 



£. The photic time-integral (^), the probability that Sun's density is har- 

 monically determined by the density of hydrogen, and the equality of 

 sethereal and solar mass which is implied by their equality of action and 

 reaction, give the proportion at Sun's surface, 



Modulus' : p^^ : : density of hydrogen : aethereal density. 



