250 NOTE ON THE INEQUALITY IN THE MOON'S LATITUDE [29 



and he shews that if s 1 denotes the perturbation of the Moon's latitude with 

 respect to the variable ecliptic which is due to the motion of that plane. 



, _ ^'(2i + i"} k sin (v + iv + e) 



1 nen s t 2, ^ ^ ^-. ^ , 



2 



where v denotes the Moon's longitude; 



f 2ki Aki~ ~| / \ 



or S 1 = Z -= 2 + 7^ i sm (v + iv + e) 



Lfwr (fmfj 



very nearly, neglecting i~ compared with { except when it is divided by 

 an additional power of -m". 



Or, replacing iv by it 



s 1 sin z/2 L: , + , ,, cos (it + e) 



.. f 2A; 



+ cos vZ 5 j + 

 - 



4Ar 1 



O JTT, sm (it + e). 

 r)-J 



(fm 3 ) 



Now, Hansen's expression for the elevation of the variable above the 

 fixed ecliptic at any point whose longitude is X is of the form 



p cos X + q sin X, 

 where p and q are functions of t, expressed in series of powers of t. 



Comparing this with Laplace's expression for the same quantity, we have 



> = 2& sin (it + e), 



hence j- 2ki cos (it + e), 



and -Jjjj = 2&r sin (it + e) ; 



-* 



similarly q = 2& cos (it + e), 



da _, 7 . . , . 

 -fj = SAS sm (i< + e), 



