STATEMENT AND EXPOSITION OF 



SECTION II. 



ON THE LAWS OF ARRANGEMENT OF THE DISTANCES, BOTH OF PLANETS AND THEIR 

 SATELLITES, FROM THEIR RESPECTIVE CENTRES OF ATTRACTION. 



(4) The object of tliis section is to indicate distinctly the ratios which prevail 

 among the planetary and satellite distances from their respective centres, and also 

 the laws which include the same; ivithout the introthiction in this same connexion 

 of any physical hypothesis on which those laws seem to he founded, or of which they 

 are the exponents. 



The hypothesis which seems to reconcile and explain those laws, as well as a 

 numher of other phenomena, Avill be considered in a subsequent section. 



(5) The first correspondence and arrangement of ratios that will be noticed, 

 may be thus stated; Beginning with the mean distance of Neptune as found in 

 Table (A) in (3), if of this we take |, and of that fractional product, again, |, etc., etc. ; 

 then, among the terms in the geometrical progression thus developed, in addition to 

 that pertaining to Neptune, we shall find those which respectively, in their order, 

 exhibit close approximations to the mean distances of the two great planets 

 Saturn and Jupiter; another having an appropriate position among the asteroids;* 

 with, again, others which respectively exhibit close approximations to the mean 

 distance of Mars, and that of Mercury iji aphelion ; all which can be distinctly 

 traced in the following tabular arrangement, in which the approximations are car- 

 ried to the third place of decimals inclusive; though the computations were extended 

 to the fifth place. In the third column, it will be remembered, every term after the 

 first, is I of that immediately preceding ; so that the ratio of every one to its next 

 succeeding term will be that of 9 to 5 = to -| = J-| = 1^ = 1.8 ; a statement which, 

 in certain comparisons, will be found to be more convenient than the other. 



In this arrangement the column under the title of Law exhibits the results in 

 accordance with the (approximate) law of succession of the terms as now explained; 

 in comparison, respectively, with the recorded distances found in the column of 

 Fact ; the terms in the column of Lata forming a series in geometrical progression, the 

 ratio being 1.8. 



\st Approximate Arrangement. 



Names and Symbol's. 



Law. 



Fact. 



Diffeience 

 L.— F. 



s 



(U) 



(Si) 

 \ 



4 

 (A) 



% 



© 



(©?) 



Aph. V_ 



Neptune, 

 f Uranus, 

 ■i Limit (U), 



Saturn, 



Jupiter, 



Limit (A), 



Mars, 

 ( Earth, 

 -I Limit (©?), 

 ( Yenns, 

 { Mercury, '^ 

 \ in [■ 

 i Aphelion, ) 



30.05733 



16.698 + 



"9.2V7— 

 5.154— 

 2.863+ 

 1.591— 



0.884— 

 0.491— 



30.05733 

 (19.183 + 



( (missing) 

 9.539— 

 5.203— 

 (to be supplied) 

 1.524 



( 1.000 



( O.V23+ 

 0.467- 



0.000 



—0.262 

 —0.049 



+ 0.067 

 + 0.024 



Of which more hereafter. 



