Chase.] 606 [jSTov. 4, 



- In the above equation, and elsewhere in the present note, Earth's mass 

 and semi-axis major are taken as the units of mass and distance. 



In studying the results of nebular "subsidence," let a represent the 

 locus of incipient belt-subsidence or secular aphelion ; y9, the locus of mean 

 belt subsidence or mean aphelion ; y, the semi-axis major ; ^, the mean 

 locus of belt-rupture or mean perihelion ; z, the locus of incipient belt- 

 rupture or secular perihelion ; subscript 0, 1, 2, 3, 4, 5, 6, 7, 8, Sun and the 

 principal planets in their order, Mercury, Venus, Earth, Mars, Jupiter, 

 Saturn, Uranus, Neptune ; m, mass. 



TO„ : TOj : : £5 : s„ : : 1047.879 : 1 (2) 



According to Stockwell (op. cit. p. 38), £5 = .9391726 ^-5. Therefore 

 y^ — 1047.879 £„ -- (5.202798 X -9391726) = 214.4513 £„ and ^5 = 

 1115.74 £(,. Mass being represented by the product of mean orbital ms, viva 

 by mean distance, we find, from (1) and (2), 



mo : ?W5 : : 1 X 1 : 60.7436 X 5.202798 : : 1 : 316.0366 (3) 



m„ -.m^:: (316.0366 X 1047.879 = 331668) : 1 (4) 



Earth's chief companion planet, Venus, shows the influence of incipient 

 subsidence-aggregation. 



m^ : m^ : : Y^ : 0-2 : ■■ 1 ■■ .77442 (5) 



m„ : m, : : (331668 -h- .77442 = 427630) : 1 (6) 



Jupiter's chief companion planet, Saturn, shows the combined influence 

 of modified belt-rupture and secular stability. 



^5 : ^6 : : p^y^ : [i-^y-^ : : 9.077645 X 9.538852 : 4.978245 X 



5.202798 : : 3.3432 : 1 (7) 



m„ : TOe : : (3.3432 X 1047.879 = 3503.22) : 1 (8) 



The outer planet of the dense belt. Mars, shows the influence of modi- 

 fied subsidence at the centre of nebular planetary inertia (Saturn), com- 

 bined with that of incipient subsidence at the centre of the belt (Earth). 

 m^ : m^ : : j3e : as ■■ : 10 : 1.0677352 : : 9.3657 : 1 (9) 



TO„ : ^4 : : (9.3657 X 331668 = 3101613) : 1 (10) 



The two outer planets of the system show the combined influence of 

 nodes of subsidence, rupture, and condensation. 



m, -.m,:: (ds — a,)ys : (d, -f a,)ys : : (29.73335 - 1.06774) X 



30.03386 : (29.73235 + 20.679233) : : 17.0776 : 1 (11) 

 m^:ms: : (331668 -^ 17.0776 =: 19392) : 1 (12) 



m^ : TO3 : : (;?, — £3) y^ : (/?, 4- S,) y^ : : (20.04418 — .93226) X 



19.18358 : (20.04418 + 4.97824) : : 14.6523 : 1 (13) 

 m„ : TO, : : (331668 ^ 14.6523 = 22602) : 1 (14) 



