1373.] l*i [Chase. 



of a planet with a major axis equivalent to Mercury's modulus, and 

 eccentricity equivalent to the mean of the eccentricities of the other in- 

 terior planets, Mercury and Mars may have condensed simultaneously 

 from an intra-asteroidal ring, of a thickness corresponding to the differ- 

 ence between their rotation-moduli. /_* would then indicate the primary 

 nucleus of the first intra-asteroidal nebulous ring, or the mean distance 

 of Mars ; A 3 j the perihelion of Mars ; £^-, _*, _°, the moduli of rotation 

 of Mars, Venus, and Earth. 



PLANETARY RELATIONS TO THE SUN-SPOT PERIOD. 



By Pliny Earle Chase. 

 {Read befort the American Philosophical Society, March 1th, 1873.) 



Stockwell's discussion of Secular Variations has furnished an unex- 

 pected confirmation of my suggested accordance between Jupiter's mean 

 perihelion distance, the planetary centre of gyration, and the radius 

 vector of the disturbing force which occasions the mean sun-spot cycle of 

 11.07 ± years. 



In my previous paper (ante, xii, 410) I made the comparisons with the 

 present eccentricity of Jupiter. If we take the mean eccentricity (.04316 . 

 Jupiter's mean perihelion is in the precise orbit of the disturbing force. 

 provided the disturbance-period is 11.11 years. The factor of Jupiter's 

 variation from Bode's Law [(1.079)J] is also the factor of the perturba- 

 tion variation from the centre of planetary gyration 5.101 -=- 1.0257 = 

 4 973). 



Kirkwood has shown the approximate commensurability of the "Wolfian 

 cycle with 46 years of Mercury, 18 years of Venus, 11 of Earth, 6 of 

 Mars, and 1 of Jupiter. I have introduced these five periods in the fol- 

 lowing table, together with (6) jj of Saturn, (7) T 2 - of Uranus; (8) y 1 - of 

 Neptune ; (9) \ year of the mean centre of inertia of Jupiter's aphelion 

 and Saturn's perihelion ; (10) § do. Jupiter's perihelion and the aphelion 

 of Uranus: (11) f do. Saturn's aphelion and Uranus' perihelion; (13) 

 I do. Saturn's perihelion and Neptune's aphelion ; (13) yV do. Uranus' 

 aphelion and Neptune's perihelion. 



Approximations to the Wolfian Cycle. 



1. 4G years of Mercury 4046.63 



2. 18 " Venus \. 4044.60 



3. 11 " Earth 4017.86 



4. () " Mars .' 4121.86 



5. 1 " Jupiter 4332.5s 



6. |* " Saturn 4034.71 



7. " Uranus 4091.78 



8. J5 " Neptune 4008.45 



* Earth's radius vector, divided by % = Mercury's modulus of rotation. 



