Permanent Contraction of the Planetary Orbits. 99 



labours I have described, had not adopted Bode's law of 

 distances, they would never have arrived at the elements of 

 the orbit,"* or, in other words, would never have discovered 

 Neptune. 



The parallelism of the discovery of new planets through 

 the law of the multiple proportions of the planetary 

 distances, and the discovery of new elements through the 

 law of the multiple proportions of the atomic weights, as 

 shown in my former papers, will not fail to be evident to 

 all investigators in natural science. 



Notwithstanding the brilliant results which followed 

 the application of the law of the multiple proportions of the 

 radii vectores of the planetary orbits, the admission made 

 of the truth of the law was only wrested from Airy by the 

 irresistible logic of facts ; for, in the same review, he states 

 that, " it is a law for which no physical theory of the rudest 

 kind has ever been suggested, and the assumption of the 

 law was only an aid to calculation that did not compel the 

 computer to confine himself to the condition assigned by it, 

 as instanced in the ultimate change of mean distance made 

 by Adams and Leverrier, who used the law to give the 

 first approximation of the mean distance." 



Sir John Herschel also says of Bode's law that "no 

 account a priori, or from theory, was to be given of this 

 singular progression, which is not, like Kepler's laws, 

 strictly exact in numerical verification." While admitting 

 the value of Bode's law as a useful auxiliary to serve as a 

 stepping stone in the path to discovery, Herschel repudiates 

 it as a fundamental truth because of its discordance with 

 the distance of Neptune. In his forensic ardour to dis- 

 credit the law, he has made this discrepancy appear twice 

 as great as it really is, since he compares the orbit of Neptune 

 with the orbits of Uranus and Mercury instead of Bode's 



* Proc. Roy. Astronomical Society, Nov. 13, 1846. — Phil. Mag. [3], 

 Vol. XXL, p. 537. 



