306 ON THE GENERAL VALUES OF THE OBLIQUITY OF THE ECLIPTIC. [41 



Also 



a { = i , and therefore a,- 1 = y- ; 

 k~g { k-g, 



a .. = _ ia t (a/ - 1 ) tan h - / cot h ; 



= - i "- - { + / - 2 ) tan h + ("' + ^') cot h } > 

 



- 2a i ~ / + 2a >} tan /; + 2 !'' ( a < ~ a >) cot Jl - 



( Jl Uj 



Also 



I . = - a t (a t - 1 ) tan h - a { cot h ; 



1.. = i(t? ( f - 1 )" tan" h + ^ f (/ + j - 1 ) + Ja/ cot 2 /i ; 



" ^ 2/1- - r/ - a {"' ^ (i ~ X ) 



^^ 



?>'> = -- - a't, tan h + A - - {a^ (a s - 1 ) + a,- (or .- 1 )} tan 2 A 

 &-& ( Ji- ( Jj 



/ + *; ~ o< ~ 5^- + 6} ; 



or the value of this last coefficient may be otherwise expressed thus 



Also the value of <a, the obliquity of the ecliptic, is thus expressed 

 in terms of the same quantities : 



w = h + 2 (,- 1) y f cos {(A grj) t + a &} 



[ - ia t . (a f - 1 ) 2 tan A - 1 (< - 1 ) 2 cot A] y? cos 2 {(& - g t ) t + a - &} 



> \ - i or r ; ( rt * 2 + / ~ 2 ) tan 7i - 



L * </<<& 



cot 



? (a/ + a/ a f a,-) tan ^ + ^ (* + cs,- 1 ) cot /i 



X yff) cos {(2i - g { - gj) t + 2a-/3 t - ft,} 



