2] RELATION TO THE MOTION OF THE NODE OF THE MOON'S ORBIT. 89 



determinant for its diagonal, we may replace the unit which the diagonal 

 of this minor would contribute by any other element of the minor.] 



If (p) denote the term 



a- q? 



and (p, q) the product of two such terms, in which we suppose p^ 

 then the terms of the fourth order in the determinant will be given by 



Z(p,q)-$(p,p + l), 



and it is easy to see that this is 



We then find by separating into partial fractions the different expressions 

 that occur 



\ 





g + 2p-q 



flTlfl i I ) 1~t I "I ) > _ -i' 



W J - [(g + 2p _ 2)2 _ ^ [(g + 2p} , _ q ,j [(g + 2p + 2)2 _ ?2] 



i^ f^ i ,v J_ A 



[The method by which these expressions were obtained involved con- 

 siderable labour, probably the reason why the developments were carried 

 no further at this date ; for another method, see below.] 



Now substitute 



A. II. 12 



