PHYSICAL ASTRONOMY. 557 



In truth, at the moment when this was uttered, the new Planet haor 

 already been seen by Professor Challis ; for, as we have said, he had 

 seen it in the early part of August. He had included it in the net 

 which he had cast among the stars for this very purpose ; but employ- 

 ing a slow and cautious process, he had deferred for a time that ex- 

 amination of his capture which would have enabled him to detect the 

 object sought. As soon as he received M. Le Verrier's paper of 

 August 31 on September 29, he was so much impressed with the saga- 

 city and clearness of the limitations of the field of observation there 

 laid down, that he instantly changed his plan of observation, and 

 noted the planet, as an object having a visible disk, on the evening of 

 the same day. 



In this manner the theory of gravitation predicted and produced the 

 discovery. Thus to predict unknown facts found afterwards to be 

 true, is, as I have said, a confirmation of a theory which in impressive- 

 ness and value goes beyond any explanation of known facts. It is a 

 confirmation which has only occurred a few times in the history of 

 science ; and in the case only of the most refined and complete theo- 

 ries, such as those of Astronomy and Optics. The mathematical skill 

 which was requisite in order to arrive at such a discovery, may in some 

 measure be judged of by the account which we have had to give of 

 the previous mathematical progress of the theory of gravitation. It 

 there appeared that the lives of many of the most acute, clear-sighted, 

 and laborious of mankind, had been employed for generations in solv- 

 ing the problem, Given the planetary bodies, to find their mutual per- 

 turbations : but here we have the inverse problem — Given the pertur- 

 bations, to find the planets. 3 



The Minor Planets. 



The discovery of the Minor Planets which revolve between the or- 

 bits of Mars and Jupiter was not a consequence or confirmation of the 

 Newtonian theory. That theory gives no reason for the distance of 



3 This may be called the inverse problem with reference to the older aud more 

 familiar problem ; but we may remark that the usual phraseology of the Problem 

 of Central Forces differs from tins analogy. In Newton's Prineipia, the earlier 

 Sections, in which the motion is given to find the force, are spoken of as contain- 

 ing the Direct Problem of Central Forces : the Eighth Section of the First Book, 

 where the Force is given to find the orbit, is spoken of as containing the Inverse 

 Problem of Central Forces. 



