1S77.] 501 [Chase. 



The inner atmospheric limit of the Saturn belt, referred to tlie rupturing 

 limit of Venus, is at the secular aphelion of Uranus. For log. (sec. per 



k -=-sec. per. 9)^ = 1.312473; log. sec. aph. § =1.315531 (46.) 



The outer atmospheric limit of the Saturn belt, referred to the rupturing 

 position of Mars, is also at the secular aphelion of Uranus. For log. (sec. 



aph. \2 -f-sec. per. c?)^ == 1.313669 (47.) 



The inner atmospheric limit of the Jupiter belt, referred to Earth's rup- 

 turing position, is near Saturn's rupturing position. For log. (sec. per. 



11 ^ sec. per. ©)^ == .928798 ; log. sec. per I2 = . 941236 ; .941236 — 



.928796 = log 1.029 (48.) 



The outer atmospheric limit of the Jupiter belt, referred to Earth's rup- 

 turing position, is at the mean aphelion of Saturn. For log. (sec. aph. '21 



-f- sec. per. ©)* = .999328 ; log. mean aph. 1^ = 1.000003 (49.) 



The mean atmospheric limit of the Saturn belt, referred to Earth's mean 



4 

 position, is near the mean aphelion of Uranus. For log. (>i ^ 0)'= 



1.305995 ;log. mean aph. § =1.301989 (50.) 



The atmospheric limit at Jupiter's mean aphelion, referred to Ihe rup- 

 turing position of Mars, is at Saturn's rupturing position. For log. (mean 



aph. 2/ -4- sec. per. (j^)^ = .940244 ; log. sec. per I2 =.941236 (51.) 



The mean atmospheric limit of the Uranus belt, referred to Jupiter's rup- 

 turing position, is at Neptune's mean aphelion. For log. (§ -r- sec. per. 



;y)t = 1.480913; log. mean aph. ^ = 1.481951 (.52.) 



The same limit (52), referred to Jupiter's mean perihelion, is at Nep- 



4 

 tune's mean locus. For log. (§ h- mean per. 2/)* = 1.478215 ; log. ^^ = 



1 .477611 . . . . ■ (53. ) 



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

 turing position. ' For log. (§ -^ 11)^ = 1.471828; log. sec. per. ^J = 

 1 .471268 (54. ) 



The important influeuce of Earth's position at a centre of early nu- 

 cleal condensation, is also shown by the simplicity of relations between 

 Earth's radius vector and the secular epicyclical 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 h- 38.365 = .0783 ; 

 the maximum eccentricity of Uranus is .078^^ ; see (20) (21 ) (55.) 



The excursion of Saturn is nearly equivalent to the atmospheric limit of 



a nucleus which has Earth's thermal radius (1.4232^^ = 1.601). For 1.601 

 -^ 19.078 = .0839; the maxium eccentricity of Saturn is .0843 (56.) 



The excursion of Jupiter is equivalent to the mean radius of rotating 

 inertia at Earth's mean distance (i/.4 = .6-325). For .6325 ~ 10.406 =1 

 .06078 ; the maximum eccentricity of Jupiter is .06083 (57.) 



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



PROC. AMER. PHILOS. 80C. XVI. 99. 3K 



