1877.] 4yy [Chase. 



pulses beyond the belt. For log. (sec. aph. ^ X sec. aph. c?) — 215437; 

 log. mean aph. cj^ = .215944 (23.) 



The mean velocity of the centripetal gravitating impulses in the principal 

 nucleal belt is equivalent to the same orbital velocity. For log. (sec. aph. 



k X mean ^)^ = .216362 (24.) 



There is, therefore, an equivalence between the mean exterior and the 

 mean nucleal gravitating impulses, beyond the Telluric belt. For log. 



(sec. per. ^ X sec. aph. ^T)* = .855866 ; log. (sec. aph. Ij X mean per. 



;^ )i = . 855450 (25. ) 



The orbital velocity varies as the one-half power of the rotating velocity. 



The mean orbital velocity due to nebular action in the Neptuno-Uranian 



belt, is equivalent to the rotating velocity at the locus of nebular rupture 



1 

 in the principal nucleal belt. For log. (mean per. tp x mean g)* = 



.689039 ; log. sec. per. 11 =.688982 (26.) 



The initial rupturing position of the centre of planetary mass (17) is de- 

 termined by the mean influence of the intra-asteroidal centres (6), the 

 supra-asteroidal centre (18), and the nebular centre of planetary inertia 



( Ij ). For log. (mean © X sec. per. § X mean 13)^ = .742338 ; log. sec. 

 per. H = .741881 (27. ) 



The same position is also a mean proportional between the centre of the 

 supra-asteroidal and the outer limit of the intra-asteroidal belt. For log. 



(sec. per. § X sec. aph. <^y — .743575 (28.) 



The nebula- rupturing position of the centre of planetary mass is at the 



centre of the initial planetary system. For sec. aph. tp (30.470) — sec. 



aph. ^ (20.679) = 2 X sec. per. 2/ (4.886) (29. ) 



The initial position of mean planetary inertia is determined by the mean 



positions of the rupturing loci of the two principal two-planet belts. For 



log. (§ X :^)^ = .999583 ; log. mean aph. Ij = 1.000003 (30.) 



The atmospheric limit (4) of the infra -asteroidal belt, is determined by 



positions of Sun, Jupiter, and Neptune. For log. (^ X W -^ O ^') = 



3.429079 ; log. (sec. aph. c? ^ O r)^ = 3.429048 (31.) 



The atmospheric limit of the initial position of the infra-asteroidal cen- 

 tre, is determined by positions of Sun, Jupiter, and Saturn. For log. 



(sec. per. 2/ X sec. per. Jj 2 -^ r) = 3.147264 ; log. (sec. aph. -r- O 



r)^ = 3.147491 (32.) 



The atmospheric limit of the initial tendency to infra-asteroidal rupture, 

 is determined by positions of Sun, Jupiter, and Earth. For log. (mean 



per. 2/ X ©^ -^ Qr) = 2.680693; log. (sec. aph. ^ -- ©r)^ = 



2.680615 (33. ) 



The atmospheric limit at the inner locus of infra-asteroidal rupture, is 



