208 Prof. P. E. Chase on ^Ethereal Nodes. 



asteroidal belt. For log (sec. per. 6 x sec. aph. $ )* = 

 •743575 (28) 



The nebula-rupturing position of the centre of planetary 

 mass is at the centre of the initial planetary system. For 

 sec. aph. Y (30*470) — sec. aph. 6 (20'679) = 2x sec. per. % 

 (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. 

 h= 1-000003 (30) 



The atmospheric limit (4) of the infra-asteroidal belt is de- 

 termined by positions of Sun, Jupiter, and Neptune. For 

 log (v x yWOr) = 3-429079; log (sec. aph. $ H- Or)* = 

 3-429048 (31) 



The atmospheric limit of the initial position of the infra- 

 asteroidal centre is determined by positions of Sun, Jupiter, 

 and Saturn. For log (sec. per. ^ x sec. per. ^ *-*-©?*) = 

 3-147264; log (sec. aph.® -r- 0^=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. y. x ©)~* = 2-680693 ; log (sec. 

 aph. $ -•- ©0^=2-680615 (33) 



The atmospheric limit at the inner locus of infra-asteroidal 

 rupture is the nucleal rupturing-limit of Mars relatively to 

 Earth. For log (sec. per. $ -r- ©r)*=2'420721 = log 1*226 © 

 r. vec. ; (sec. per. s -•-©)*= 1*225 (34) 



The atmospheric limit at the central locus of infra-asteroidal 

 rupture is at Jupiter's mean aphelion. For log (sec. per. 

 © -i- r)t = 3*068927 ; log(mean aph. 2/. -r- ©r) = 3*066743. (35) 



The atmospheric limit at the rupturing-locus of Mars is near 

 the rupturing-limit of Saturn. For log (sec. per. <?-"-0r)' 3r 

 = 3*266367; log sec. per. h -HO?' = 3*273391 ; 3*273391- 

 3*266367 = -007024= log 1*0163. This indicates a similarity 

 of contraction at the centre (6) and at the outer limit of the 

 belt (36) 



The atmospheric limits of the Venus belt, as determined by 

 reference to the rupturing-position of Mercury, are in or near 

 the Earth belt. For log($ -*- sec. per. $)*-r- © r. vec. = 

 l-942238@-024175;log© = l-969540(S)-028463. . . (37) 



The atmospheric limits of the Earth belt, referred to the rup- 



