CERTAIN HARMONIES OF THE SOLAR SYSTEM. 



11 



ail additional column expressing in every case the same difference in terms of the 

 quantity to be compared, which is a', the planet's own mean distance from the Sun, 

 or else d\ the distance from the Sun of the limit in question. 



Thus, for example, in the instance of Saturn, Law — Fact = 0.094 of the Earth's 

 mean distance; and that^ in the next column, is seen to be only 0.010 of Saturn's 

 own mean distance from the Sun. 



Completed Arrangement of the Planetary System, exhibiting the Correspondence of 



Law with Fact. 

 Table (B). 







Law. 



Fact. 



Law — Fact. 



iNAiiES AND Symbols. 



Earth's dial. 



a' or d' 



s 



(U) 

 h 



n 



(A) 



% 

 e 



(©?) 

 ? 



Aph. S 

 Per. ^ 



Neptune, "[ s ) 

 , ( Uranus, j '^* • • ■ ■ V r 



rt ] Limit (U), ) 



( Int. to Q, I r 

 Saturn, ^ 



r *" 



30.057264 



19.55718 



16.91431 



(14.64275) 



9.44511 



5.23391 



2.87831 



1.57096 

 0.99335 

 0.85101 

 0.72975 

 0.45758 

 0.39166 

 0.28573 



30.057332 

 { 19.18336 



((missing) 

 9.53885 



5.20280 



(2.82293) 



1.52369 

 (1.00000 



( O.V2333 

 0.46670 

 0.38710 

 0.30750 



— 0.000 + 

 + 0.374 + 



— "0V094 — 

 + 0.031 + 

 + 0.055 + 



+ 0.047 + 



— 0.007 — 



+ 0.006 + 



— 0.009 + 

 + 0.005 — 



— 0.022 — 



— 0.000 + 

 + 0.019 + 



— 0.010 — 

 + 0.006 



+ 0.020 — 



+ 0.031 



— 0.007 — 



+ 0.009 + 



— 0.020 — 

 + 0.012 — 

 -0.071 — 



Limit (A), i ' 



r ">' 

 Mars, 1 3 ) 



I Earth, ^"^^ 



r2^ Limit (©9), .... ) 



i ( Venus, (. ,. 



r } Aph. of Mercury, > 



( Mercury, I j,| 



Per. of Mercury, > 



The coincidences between Law and Fact, as compared with previous approxima- 

 tions, are now far more complete. The greatest actual difference is that in the 

 instance of Uranus, which, after all, on the large scale of that planet's orbit is less 

 than jJq th of the quantity to be measured.^ 



The distances of Mercury in aphelion and in perihelion as stated in the column of 

 Fact are themselves computed from Mercury's mean distance and the eccentricity 

 of his orbit, at tJie present date. With other values of the eccentricity, we would 

 have had as follows: — 



Eccentricity. 



Aph. Dist. 



L.— P 



Per. Dist. 



L.— F. 



Maximum'= 0.2317185 



0.47680 



— 0.019 + 



0.29740 



— 0.012 — 



Mean =0.1766064 



0.45546 



+ 0.002 + 



0.31873 



— 0.033 



Minimum" =0.1214943 



0.43413 



+ 0.023 + 



0.34007 



— 0.054 + 



' Why, after all, TJranus seems to have, as it were, fallen in from his appropriate position, may 

 be considered in another connexion ; not here, where only the relations themselves are permitted to 

 have place, without the introduction of any physical hypothesis to explain them, as was indeed inti- 

 mated in the first part of this Section. The same may be said of Mars. 



" The maximum and minimum values of the eccentricity here inserted, are those given by John N. 

 Stockwell, M.A., in Ms Memoir on the Secular Variations of the Elements of the Orbits of Eight 

 Prin-cipal Planets, Introduction, p. xi. — Smithsonian Contributions to Knowledge, vol. xviii. 



