OF ARTS AND SCIENCES. 



339 



and observed planets? Had it been quite small, it might have been 

 regarded as an excusable numerical error. Had it even amounted to 

 once or twice the radius of the earth's orbit, it might have been deemed 

 an error, although it would then have been a grievous one, and would 

 have seriously marred the beauty of the result. But as it is, it cannot 

 be assumed to be a mere error, without admitting that such an one 

 radically vitiates the whole theory. Whoever adopts this opinion, be 

 it the author of the theory himself, is bound to show where the error 

 is, and how far it extends. Such an opinion has never been advanced 

 by me, and I am not responsible for it. I admit, however, that I 

 have not fully investigated this point, but maintain that the profound 

 geometry of M. Leverrier is not to be set aside without proof, or even 

 argument. M. Leverrier found that the planet which would best 

 account for the disturbed motion of Uranus was at the mean dis- 

 tance 36 from the sun ; and that, by increasing or decreasing the 

 mean distance of the hypothetical disturber, the want of coincidence 

 between the observed and computed motions of Uranus increased until, 

 at the mean distances of 38 on the increase and 35 on the decrease, 

 the residual difierences between theory and observation became so 

 great as to be wholly inadmissible. He therefore came to the natural 

 conclusion, from such a result, that the mean distance of the required 

 planet from the sun could not be less than 35, or more than 38 ; and 

 he contented himself with this conclusion, without extending his in- 

 quiries to still smaller mean distances ; and any facts in regard to 

 these inner distances which are at variance with this result are cer- 

 tainly not to be included under his theory. I have confined my re- 

 marks to M. Leverrier's researches, but nothing in Mr. Adams's less 

 comprehensive investigations, in which there is no attempt to ascer- 

 tain the limits, is opposed to these conclusions. 



" It has been intimated, that too rigorous an agreement with obser- 

 vation was insisted upon in the original inquiries, and that the limits 

 might have been extended to include Neptune, by a more liberal con- 

 cession to other unknown planets, or to an error in the mass of Saturn. 

 The inspection of the preceding table completely refutes such a sug- 

 gestion, for it now appears that Neptune satisfies the observations of 

 Uranus more perfectly than the best planet of previous theory. If 

 Leverrier was, as I have supposed, correct in his former computa- 

 tions, he must have found by extending them, that, although the action 

 of his hypothetical planet agreed less perfectly with observation by the 



