462 Mr. E. V. Neale on the Numerical Relations of 



scribed to you only a very small part, in fact only the foundation 

 of the edifice. If you have any doubts on the subject, I trust 

 that you will ascribe their existence to the imperfections and 

 shortcomings of my exposition, and not lay them to the account 

 of the theory itself. 



LXVI. On the Numerical Relations of the Distances between the 

 Planets and Sun. By Edward Vansittart Neale*. 



THE great difference between the actual distance of Nep- 

 tune from the Sun, and the distance at which it ought to 

 be found, according to what is commonly called Bode's law, has 

 naturally produced attempts to find some theory of the planetary 

 distances more nearly corresponding to the observed facts than 

 that suggested by Bode. Accordingly, at the last Meeting of the 

 British Association, Mr. E. S. Browne proposed a scheme ex- 

 pressed by the following Table of proportional distances : — 



Names. 



Mercury 

 Venus ... 

 Earth ... 

 Mars ... 

 Junof... 

 Jupiter 

 Saturn... 

 Uranus 

 Neptune 



Theoretical distances. 



Totals. 



Actual distances. 



4 



4 



3-87 



4+ 3 



7 



723 



7+ 4 



11 



]0 



11+ 7 



18 



15-24 



18+ 11 



29 



2670 



29+ 18+11 



58 



5202 



58+ 29+18 



105 



95-39 



105+ 58+29 



192 



191-82 



192+105+58 



355 



300-37 



If we compare these distances with the series derived from 

 Bode's law, of 4, 7, 10, 16, 28, 52, 100, 196, 388, or with the 

 corrected list of numbers constructed upon the principle sug- 

 gested by V. Wurm (see f Kosmos/ iii. p. 443), i. e. 3*87, 6*80, 

 9-73, 15-59, 27-31, 50*75, 9763, 191-39, 378-91, it will be ap- 

 parent that, with exception of the numbers falling to Neptune 

 and Uranus, these series approximate to the observed distances 

 more closely than that of Mr. Browne. Therefore his series 

 cannot be considered as any material improvement on its prede- 

 cessors, though escaping the objection raised to them by Gauss, 

 that the distance betwen Mercury and the Sun does not harmo- 

 nize with the succeeding parts of the series (see 'Kosmos/ p. 444). 

 Nevertheless Mr. Browne's system suggests a mode of investi- 

 gating the numerical relations subsisting between the distances 

 of the planets whence more satisfactory results are obtainable. 



In the series suggested by him, the group of planets beyond 

 the asteroids is distinguished from that within them by the cir- 



* Communicated by the Author. 



t Juno is taken as the representative of the asteroids, — their mean 

 centre being uncertain, since the total number is not known. 



