104 Prof. Challis on certain Questions 



the premises of the question. jBh/o, vaiet consequentia. It 

 astonishes me that Mr. Adams did not perceive, that as the force 

 is not wholly central, and the integration is approximate, the 

 equation (E) is the legitimate antecedent of (C). ]3y multiplying 



the former by ^, integrating, and omitting the quantity of the 



third order which the last term gives rise to, the equation (C) is 



immediately obtained. In this method it is assumed that the 



dr 

 value of -1- contains a factor of the first order of small quantities, 



or, in other words, that the radius -vector oscillates in value to a 

 small extent about a mean value, which might easily be shown 

 to be a consequence of the supposition of a mean motion of the 

 ► radius-vector in longitude. My method of proving the equa- 

 tion (C) rests only on this latter supposition." 



From this argument Mr. Adams does not, as before, conclude 

 that the equation (C) is positively false, but that it is " unfitted 

 for giving accurate information respecting the moon's orbit.'' I 

 must be permitted to express my great surprise that Mr. Adams 

 could have written so unscientific a sentence as this. What has 

 a mathematician to consider but the truth of his equations ? If 

 they are false, they give no information ; if true, they necessarily 

 give accurate information when rightly interrogated. There is 

 no intermediate species of equations. My equation being proved 

 to be true, must form an essential part of the lunar theory. 

 True results may be obtained without it by pis aller processes, 

 but without it all that is true of the moon's orbit cannot be 

 known. It is clear to me that Mr. Adams is involved in a 

 dilemma by having committed himself to the opinion that there 

 was no merit whatever in my paper. He cannot now admit 

 that it contained an important equation which remained un- 

 discovered from the days of Newton, and being unable to resist 

 the evidence for the truth of the equation, he has recourse to the 

 strange expedient of endeavouring to throw discredit upon the 

 information it gives. 



The arguments relating to Theorem I. conclude with the 

 assertion that the equation (C) "would make the moon's apsidal 

 distances to be constant,'^ and a needless appeal to the Nautical 

 Almanac ; to which I reply, that the apsidal distances are not 

 made constant by deducing the value of the radius-vector to the 

 first order of small quantities from the equation (C), any more 

 than they are made constant by assiming this same value. 



We have now come to Theorem II. (p. 32). And here I can- 

 not understand why Mr. Adams is solicitous to remove a diffi- 

 culty which I found in extracting information from the equa- 

 tion (C), since he is of opinion that this equation is unfitted to 



