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



The outer atmospheric limit of the Jupiter belt, referred to 

 Earth's rupturing-locus, is at the mean aphelion of Saturn. 

 For log (sec. aph. ^ -=- sec. per. ©)«"= -999328 ; log mean aph. 

 h =1*000003 (49) 



The mean atmospheric limit of the Saturn belt, referred to 

 Earth's mean locus, is near the mean aphelion of Uranus. 

 Forlog(h-r-e)* = 1-305995; log mean aph. 6 = 1*301989. (50) 



The atmospheric limit at Jupiter's mean aphelion, referred 

 to the rupturing-locus of Mars, is at Saturn's rupturing-locus. 

 For log (mean aph. V -f- sec. per. c?) 3" = '940244; log sec. per. 

 h =-941236 (51) 



The mean atmospheric limit of the Uranus belt, referred to 

 Jupiter's rupturing-locus, is at Neptune's mean aphelion. 

 For log ($ -f- sec. per. V-)%= 1*480913; log mean aph. x \> = 

 1-481951 (52) 



The same limit (52), referred to Jupiter's mean perihelion, 

 is at Neptune's mean locus. For log (§ -f- mean per. V-)^ — 

 1-478215; log ^ = 1-477611 (53) 



The same limit, referred to Jupiter's mean position, is at 

 Neptune's rupturing-locus. For log ($-5- "4)^ == 1*471828 ; 

 log sec. per. ¥ =1-471268. (54) 



The important influence of Earth's position at a centre of 

 early nucleal condensation is also shown by the simplicity of 

 relations between Earth's radius vector and the secular epicy- 

 clical undulations of the supra-asteroidal planets. 



Earth and Sun are convertible points of suspension for a 

 linear pendulum equivalent to the secular excursion of Uranus. 

 For 3 -f- 38*365 = '0782 ; the maximum eccentricity of Uranus 

 is -0780. See (20), (21). (55) 



The excursion of Saturn is nearly equivalent to the atmo- 

 spheric limit of a nucleus which has Earth's thermal radius 

 (1-4232*= 1-601). For 1*601 -f- 19*078 = *0839 ; the maximum 

 eccentricity of Saturn is *0843 (56) 



The excursion of Jupiter is equivalent to the mean radius of 

 rotating inertia at Earth's orbit (\/ T 4 = *6325). For *6325 

 -f- 10*406 = '06078, Jupiter's maximum eccentricity being 

 •06083 (57) 



The excursion of Neptune is in the inverse ratio of its own 

 coefficient (^), and in the direct ratio of the coefficient of 

 Uranus (|), in the abscissas of the solar aggregating-parabo- 

 loid. For j-j- 60*074 = *0146 ; Neptune's maximum eccentri- 

 city is *0145 (58) 



