18S1.] 453 [Chase. 



monic teadeucies in larger masses. Taking the nearest integral values of 

 n for each of the intra-asteroidal planets, we may construct the following 

 comparative table : 



Computed Values. Authority. 



8093500 = Sun -4- Mars. Hall. 



331700 = Sun -- Earth. Chase. 



427240 = Sun -- Venus. Hill. 



4865751 = Sun h- Mercury. Encke. 



The actual values of m\, which would give the computed values of 

 mass, are .307, 2.862, 2.222, .204. There is an approximation to the inte- 

 gral values oin, in the cases of Earth and Venus, that of Earth having the 

 same probability as that of Saturn, 2.3. The probability for Venus is only 

 \ as great, or 1.15. The masses of Mercury and Mars are evidentlj- con- 

 trolled by some other law, which overrides that of the repetition of solar 

 radial nodes. 



52. Reciprocal Coefficients. 



T have pointed out* the reciprocity between the coefficients of the 

 stellar-solar abscissas which indicate rupturing loci for Saturn and Nep- 

 tune. This reciprocity is interesting, not only for indicating the inverse 

 rotation of two portions of a primitive nebula, but also for introducing the 

 harmonic ratio of mass, into the retrograde portion, which is shown in 

 Note 50. We accordingly have the two following proportions : 

 cCj : ^j : : wig : TWg : : 6 : 7. 

 Xg : ps : : 77ig : m^ : : 7 : 6. 



In these proportions, x represents the stellar-solar abscissa, or rupturing 

 locus ; p, semi-axis major ; m, mass ; subscript .,, g. 9, Saturn, Uranus, 

 Neptune. 



53. Total Planetary Mass. 



Notes 46, 48, 49 and 52 indicate the probability of some photodynamic 

 influence in determining the primitive ratio of solar {m^ to planetary 

 mass (»in). On examination we find 



I modulus : Sun's semi-diameter : : m^ : m^. 

 553767 : 1 : : 744. 155^ : 1^. 



The following table gives the computed masses of the several planets. 

 Sun's mass being represented by 10,000,000,000. 



Mercury, 2,055 Encke. 



Venus, 23,406 Hill. 



Earth, 30,148 Chase. 



Mars, 3,23.3 Hall. 



Jupiter, 9,543,087 Bessel. 



Saturn, 2,855,837 Bessel. 



Uranus, 442,478 Newcomb. 



Neptune, 515,996 Newcomb. 



Sum, 13,416,240= w„ -H 745.365. 



*Ante, p. 209. 



