Chase.] ^yo [jan. 5 and Feb. 2, 



in the ratio of its initial-rupturing radius to Eartli's radius of rupture. For 

 log. {f, — \i sec. apb.) — 3.34C812 ; log. (2^,^ -- 200.307) — 4.391929 = 

 log. 24r..-)fi.36 ; 10759.22 dy. -^ 2465G.3G = 10 h. 14 m. 4 s (13.) 



The lolatiiig velocity of Mars, relatively to its orbital velocity, has been 

 accelerated Jiearly in the ratio of its nucleal-rupturing radius to Earth's 

 secular aphelion. For log. {,, = (^ sec. per.) = 2.449775 ; log. ( 2n* -=- 

 229.413) = 2.839962 — log.' 691.77 ; 686.98 dy. -- 691.77 = 23 h. 49 m. 

 49 s ( 14.) 



The rotating velocity of Venus, relatively to its orbital velocity, has been 

 accelerated in the ratio of its mean rupturing radius to Earth's mean peri- 

 helion. For log. f, = 2.191493 ; log.(2 ^ -- 207.583) = 2.366824 = log. 

 232.715 ; 224.7 dy. ^ 232.715 = 23 h. 13 m. 36 s (15.) 



The rotating velocity of Mercury, relatively to its orbital velocity, has 

 been accelerated in the ratio of its initial-rupturing radius to Sun's aggre- 

 gatins radius. For log. ( /> = 5 sec. aph.) — 1.990608 ; log. (2/>2 -- 219- 

 .0894) = 1.941019 = log. 87.422; 87.97 dy. --87.422 ::= 24 h. 9 m. 

 2 8 (16.) 



Jupiier'ssecular aphelion (5.519:3) is a mean proportional between Earth's 

 mean distance, and Neptune's secular aphelion (30.4696). See also, infra 

 (27) to (29) (17.) 



The secular perihelion of Uranus, or its locus of nebular rupture (17.688), 

 is at the centre of the supra-asleroidal belt. For Neptune's secular aphe- 

 lion (30.470) -f Jupiter's secular perihelion (4.886) = 35.356 ; 35.356--- 

 2 = 17.678 (18.) 



The secular perihelion of Uranus is also a mean proportional between 

 Saturn's secular aphelion (10.343) and Neptune's mean aphelion (30- 

 . 330 ) (19. ) 



The centres of the outer and inner planetary belts are so related that 

 the mean distances of Uranus (19.184) and Earth's secular perihelion (.932), 

 are at ajises of a major-axis which would be traversed by light undulations 

 in the lime of planetary revolution at Sun's surface. (19.184 -j- .932 = 20- 

 .116; 688.3 X 2^: h- 214.80 =: 20.128) (20.) 



The major-axis of the November meteoric orbit is also nearly equivalent 

 to the major-axis of these primeval light undulations. For the meteoric 



period = 33.25 yr. ; 2 X =33.25^ = 20.68 (21.) 



When Sun's surface of dissociation was at the extremitj' of Earth's mean 

 radius vector, the locus of complete association, or the vertex of the stellar- 

 solar paraboloid*, was at Mercury's present perihelion (.3187). 1 -=- - = 



.3184 (22.) 



The orbital velocity varies (3) as the one-fourth power of the gravitating 

 velocity. The orbital velocity at the mean aphelion of the intra-asteroidal 

 belt, is equivalent to the mean velocity of the centripetal gravitating im- 



•II). X, Illustrations. By nn Inadvertence it was stated that there are nine 

 abscissas between Neptuno and aCentaurl. There were nine in my original 

 paraboloid (I'roc. H. P. A., .Sept.20, 1872), but if the vertex is taken at the locus of 

 coraplete solar aggregation there are elglitcen. 



