174 



SECULAR VARIATIONS OF THE ELEMENTS OF 



We also have 













P = 21° 



6' 



26".8 



/? 4 =106° 



14' 



18".0 



ft=132 



4Q 



56.2 



&= 20 



31 



24.6 



/3 2 =292 



49 



53.2 



ft=133 



56 



10.8 



/3 3 =251 



45 



8.6 



/? 7 =306 



19 



21.2 



Precession on 

 fixed Ecliptic 



(559) 

 of 1850. 



Equations (550-553) reduced to numbers become 

 ^=50".438239i+8915".6+ 5800".35 sin (/<+/3 ) " 



— 3581".52 sin (U+fc) 

 + 5583".09 sin (f 2 t+(3 2 ) 

 +20438".28 sin (/,«+&) > 

 + 13294".37sin(/ 4 *+/3 4 ) 

 + 646".98 sin (/ 6 «+ft) 

 + 834".76 sin (/„<+&) 



— 3217".97 sin (/ T <+&) J 



El =23° 17' 16".57-2445".33 cos (ft+p )+1499".78 cos (.fr+fr) ] 0bl - uit of 

 -2189".55 cos (/ 2 *+/3 2 )-7950".46 cos (/,<+&) I ^j* 

 —5722".14 cos (/,*+&)— 277". 79 cos (/ 6 <+/3 B ) | fixed Ecliptic 

 -355".257 cos (/ 8 *+0 6 )+1158".Ol cos (/,<+&) J of 1850. 



4'=50".438239*+8915".6+696".462 sin (ft+P ) ' 

 — 552".463 sin (/^+/?i) 

 +2250".29 sin (/,<+&) 

 +8708".52 sin (/«<+&) 

 +10".0558 sin (/ 6 *+&) 

 +57U02 sin(/ 6 <+/3 6 ) 

 — 1910".92 sin (/ 7 <+/3 T ) 



Precession on 

 (561) 



apparent Ecliptic. 



e=23 17' 16".57-248".520cos(/H-/3)+ 196".017cos (fJ+PJ 



-755".057 cos (/ 2 *+&) -2901". 75 3 cos (/,*+&) 



— 3".644 cos (/ 6 H-A>)— 20".539 cos (/,*+&) 



+ 595". 433 cos (/,*+&) 



Obliquity of 



(562) 

 apparent 

 Ecliptic, 



If we take the differentials of equations (561) and (562), we shall get 



i^=50".438239+0".152998 cos (/*+/?)— 0".117438 cos (/ 1 <+/3 1 ) 



+0".360530 cos (/ 2 *+/? 2 )+l".352281 cos. (fJ+P,) k. (563) 

 -f 0".0024267 cos (/ 5 «+ 1 S 6 )+0".013156 cos (/,*+&) 

 — 0".227011cos(/;H-/3 7 ) 



* == +0".054595 sin (p *+/?)— 0".041668 sin («M+&) 



+0".120965 sin(</ 2 <+/3 2 )+0".450592 sm(^+^ 3 ) 



+0".0008794 sin (^+/3 6 )+0".004732 sin (&*+&) 



— 0".0707357 sin (fl^+ft) 



(564) 



