210 ON THE THEORETICAL VALUE OF THE ACCELERATION, ETC. [26 



the ordinary lunar theory in the case of unvaried eccentricity are to be 

 substituted for v and r. 



Hence, the expressions for 8{T-} and S(P-\, which are employed 



\ a/ \ a) r J 



in the paper, are wholly incorrect, except in the case of the non-periodic 

 term, which gives rise to the principal term of the secular acceleration or 

 that found by Laplace. 



The remark made near the close of the paper, viz. that the magnitudes 

 of the quantities A, B, O, and therefore also that of the secular accelera- 

 tion are proportional to the inverse cube of the Sun's distance, or to the 

 cube of the Sun's parallax, can only be the result of inadvertence, as the 

 Astronomer Royal himself will be the first to acknowledge. 



In fact, the quantities A, B, C involve the factor -^ and this is equal 



* A 



to n'-, where n' is the Sun's mean motion and is known. The Sun's mass 

 cr is determined by means of the parallax from this equation ; or conversely, 

 if the Sun's mass be known the parallax is thereby determined. 



The values of A, B, C are approximately as follows 



where m denotes, as before, the ratio of the Sun's mean motion to that 

 of the Moon. 



