188J.] ■^^* [Chase. 



IV. The influence of paraboloidal directrices and vertices, (^J), is mani- 

 fested in eacli of tlie primitive belts : 



iMars = .2894 Mercury s. p. .2974 



I Neptune = 5.0068 Jupiter m. p. 4.9782 



i Neptune = 10.01128 Saturn m. a. 10.00006 



Tlie paraboloidal vertex for tlie whole Neptunian belt is within the 



Jupiter belt. 



V. By introducing Laplace's limit of possible solar atmosphere* (L = 



36. 36ro), and the ratio, f ' -V of the fundamental velocity ( — \ to the 



_.„..„.id(, •■,-). .■•■"."»-■'- 



equation of solar and plauetarj^ harmonic action at the centre of prin- 



(1 year Sun's semi -diameter \^ r- 



1 dajT "^ Earth-T^mT^ZT^ajor; " 3- ^his 



gives Earth's semi -axis-major = 214.547'q. 



VI. The combined influence of centres of nucleatiou, (a), and of nebu- 

 losity, (/3), at the centre of condensation, fy"), leads to the following sim- 

 ple harmonic estimate of Sun's mass and distance. 



Earth's semi-axis major being 214.54?'o, the leverage of the paraboloidal 



directrix is (214.54 + I =) 214.87?',,, and the mean leverage of Jupiter is 



(5.202798 — 1) X 214.54?-o — 901.668283ro. Multiplying by the respective 



masses, we obtain, for the ratio of Sun's comparative disturbing force at 



1047.879 X 214.87 

 the directrix and at the centre of condensation, 1 v Q 01~rr8^8R ~ ^^ 



249.712. The superficial nodal force ^s) being | as great, we find, for the 



7o _ 249.712 

 ratio of Sun's to Eartli's superficial gravity, — q — = 27.716. If 



ffi " 



we designate superficial gravit}^ by g, volume by V, density by d, and 

 mass by m, it is evident that r cc {g ~- d); Foe (g -^ dy ; m cc {g^ -:- d-) ; 



do mo /2'7.nGY 



d cc (.9 -H r). Hence we readily get , =.25523; — = \"955^3/ ^^ 



327,897; -" = c,^^o =108.71; Earth's semi-axis major = 214. 54ro = 



214.54 X 108.71 X 3962.8 miles = 92,422,000 miles. 



VII. The solar modulus of light, (M = 688.83'-?v,), furnishes the third 



element of the parabolic projection which is indicated by the fundamental 



gt 

 equation v := « • "^^^^ three elements are all photodynamic, viz : 1. The 



gt 

 locus (?'o) of luminous action which makes ^ equivalent to the velocity of 



light ; 2. The locus (L) of orbital lialf-revolution wiiich is synchronous 

 with solar half-rotation, the synchronic time being determined by the 

 velocity of light ; 3. The locus (M) of radial luminous progression during 

 the same synchronic time of solar half-rotation ; M is also the altitude, in 



* MfC. I'el., Ill, i J7. 



