2] RELATION TO THE MOTION OF THE NODE OF THE MOON'S ORBIT. 101 

 We will now consider the remaining terms consisting of four elements. 



First take the terms (30), 4231, involving two constituents of the 

 diagonal. 



These are of the form 



hence their sum 



Next take the terms (20) and (28), 3241 and 4213, which involve 

 the constituent 2 of the diagonal. 



These terms are equal, and their sum is 



2abc 



+P - 1 Y - <] [(7 +p + 1 Y- * J ] [(7 +i> + a) 8 - * 7 J ' 



Along with these consider (24), 2431, and (29), 4132, which involve 

 the constituent 3 of the diagonal. These are likewise equal, and their 

 sum is 



2abc 



Resolving these terms into partial fractions and effecting the summa- 

 tion, we find 



(20), (28), (24), ad (29)= -- 



Now take the terms (18), 2341, and (27), 4123, which involve 

 no constituent of the diagonal. These are equal, and their sum is 



2a 3 c 



Along with these take (19), -3142, and (22), -2413, which also 

 contain no constituent of the diagonal. These are also equal and their 

 sum is 



