78 STATEMENT AND EXPOSITION OF 



Thus — making use of the veritable distances as stated in Table (B), expressed 

 approximately, we shall find : — 



Jupiter^s distance — Mercury's distance 4.81 1.98 

 Asteroid distance — Mercunfs distance ~ 2 AZ~ 1 



But 



Saturn's distance — Mercury's distance 9.15 _ 1.90 ; 

 Jupiter's distance — Mercury's distance 4.81 1^' 



The same process would fail notoriously in the case of the next whole-planet 

 (U), Avere that yet to be found. But Uranus being an exterior half-planet, the 

 ratio of its distance to that of Saturn is .rl instead of r ; and so the double interval 

 for Uranus is tolerably well preserved in comparison with that of Saturn. 



But as the ratio of Neptune's distance to that of the exterior half-planet Uranus 

 (though on a larger scale than that immediately preceding, in the order here pur- 

 sued) is only rl, the subtraction of only Mercury's distance from each of the others, 

 leaves the interval for the greater in a ratio to that for the less of not more than 

 i-^±; and so, the representative number when it ought to be 301 appears in the 

 series of numbers illustrating the " law" as 388. 



The latest application of " Bode's Law" would seem to be that of Maxwell 

 Hall, Esq. ; an abstract of whose communication is given in the Monthly Notices of 

 the Royal Astronomical Society, vol. xxxiv, No. 7 (May, 1874), under the title of 

 '■'■The Solar and Planetary Systems." 



The author states " Bode's Law" as follows : " In the solar and planetary sys- 

 tems the mean distances of the planets do not greatly differ in value from the terms 

 of the series : 



4X, l?i, io;i, 16;i, 28;i, 52'a, l()0;i, 196;., 388a, etc., 



where /L has different values in different systems. But there may be more than 

 one, or there may be no planet or satellite near any of the above theoretical dis- 

 tances."^ And he then proceeds to determine 2. in miles for the planetary system, 

 and for the Jovian, Saturnian, and Uranian satellite-systems respectively. 



" Some of the numerical coincidences are very close ; thus in the Uranian system, 

 taking the distances to be 7;., lOX, 16X, and 28X, the first three satellites give 

 ;t = 17600, and 17100, and 17600 miles respectively (but the fourth satellite gives 

 X = 13400 miles). "^ 



" He then states a second proposition : ' Twice the unit of length in any system 



' Accordingly in the statement of the " Law" as not unfrequently made, which represents the suc- 

 cessive distances by the numbers 4, 4+1x3, 4+2x3, 4 + 2=X 3, etc., Saturn's representative 

 number exhibits a conspicuous failure. For instead of the true number 95, the distance is repre- 

 sented by 100; the veritable distance— as has, in effect, been stated — being too small to conform to 

 " Bode's I;aw." 



[The representative numbers 4, 1, 10, etc., appear in Mr. Hall's series, quoted in this Article.'] 



' Especially in this connexion, see Note to (1). 



^ What has already been stated in the way of exposition of the application of this (so-called) law 

 in the planetary system, and an inspection of our Table (E) in (21), with its two ratios in accord- 

 ance with veritable laws, will at once show the reason for this discrepancy. See also Note to (7). 



