FORMULES DE LA NUTATIOIS ANNUELLE. 



i9 



(l + c,)[sin(4C-i-0-r-2Q-j.)-8in(4C-0-*-r + 2Q- T )]) 11 



4 S,eim | + (l_ Cl )fsin(4C:+0-r-2Q + ? )-sin(4C:-0+r + 2Q+ ? )] 

 (1 + c,) [sin (© — r — 2Q h- y) -4- sin (© - r -+- 2Q — ? )] 



3 , 

 4 



.(l_c,)îsin(0 — r-2Q- ? )+sin(© — r-t-2Q + y)]j "'"lC* 26 " i 4£- 



32 



DD 



33 ( sin(4(T-20-2Q- ? )] 75 ,. ( (c,+c 2 ) sin(2<C-20+2r'-Q- î >)) 15 

 — .«„r»r< > e u« . . . , „ ,? — r 



e ei7»M 



(l+c,)sin(2(C-20-2Q-+-y) 

 + (l-c,)sin(2C-20-2Q- ? ) 



sin(4(C— 20 — 21"-+- y)) 

 sin(4£— 2© — 2r'— y)j 



(c,+c,) sin(C-©+r'+r-Q- j.) 



~32 S2 ' n, |-sin(4C-20-2Q+ ? )S le' U>i i+(c 1 -c î )sin(2<C-20+2r'-Q+ ? )) 4 ' i+Cc.-cOsin^-O+T'+r-Q+y)) 



_ i (c,-t-c 2 )[sin(2C+0-r-Q- f )-sin(2(C-0 + r-Q- f )]) 15 e , eiw | (c,+ c,)sin(C+0H-r'-r- Q-y)) 

 aeun j + ( C| _ C2 )[ s in(2C+0-r-Q + f )-sin(2C-0 + r-Q-t-y)]) 4 j + (c,-c,) sin (C+O + r'- r-Q+ f )] 



e ' im ( 5+ V W )i 



(c, + c,) sin (5<C- 2© + r'— Q — ?))_ 53 e , J (c, -+- c a ) sin (C- 2© — r' + Q + y) 

 - (c,— c s ) sin (3<C— 2© -h r'— Q -*- y)) 32 e " n j + ( Ct _ c,) s i n (C— 2© — r' + Q — y) 



( Cl +c s )[sin(3C— 20— r'+Q- f ) + sin(C— 2© + r'— Q + ? )]) 9 siSem j sin(20©— r— 2Q-y)j 

 .(c 1 -c,Usin(3f-2©-r'+Q + ? ) + sin(r-20-t-l'— Q-y)1i 4 2 |_ s in(200— r — 2Q-h p )Î/ 



45 „ j (c 1 +c,)[sin(2C-2© + Q-f)— sin(2©-2r'+R- ? )]j 9 gi , m j sin(2C~G 

 ~Ï6 e tm ( + (c,- Cî )[sin(2C;-20H-Q + ? )-sin(2©-2r'+QH- P )]i 4 2 (_ s i n (2C-e 



-0+T-2Q — y) 

 ©+r — 2Q-*- f ) 



9 



( Cl +c 2 )[sin((C+Q-r-r'-HQ- ? )-sin(C-©H-r-r'+Q-?)]) ^ < 

 4 (-j-(c,-c 2 )[sin(C;+0-r-r'+Q-+- f )-sin(C-Q+r-r'- ) -Q+ ? )]j 4 ' 



-e eim 



(l-t- Cl )sin(4C-0 + r-2Q-y) 

 :+(l-c 1 )sin(4C-Q + r-2Q + f ) 



(20) 



Suite. 



sin(2(C-+-© — r — 2r'-t- ? ) 



+ 45 S eVmi -MC-2Q-r'-2Q-y)-sin(3C-2Q^r'_ 2 Q_y)j_9 



+ Ï6 S2etm |_ s in( C ;H-2o-r'-2QH-y) + sin(3C-2Q + r'-2Q + y)j 2 (-sin(2(> 0-r-2r'— ,) 



- s 2 e"em 



sin(2(C— O-t-r — 2r'+y) 

 ■ sin (2<Ç— © -t- r — 2r'— y) 



9 , 

 -s s e em 

 4 



45 



( sin(C-*-2©-3r'-+- ,, 

 8 s ' e m i_sin(C-t-2©-3r'-y)| 16 



H 



sin(Ç— © + r — r'-Hy) — sin(C-+-© — r — r'+ ? )] 



• sin(C— © -t- r — r'— y) + sin(<C-*- © — r — r'— y)j 



59 



m -+- — m 

 i 5 



195 „ 3 , 



4 4 



sin(5C— 2© — r'-f-y)» 

 — sin (3(C— 2© — r'— y) | ' 





A celte expression il faut encore ajouter les termes qui proviennent de 

 Faction du Soleil; il est clair que, pour les obtenir, il suffit, dans l'expres- 

 sion précédente, de faire < = 0, m = 0, de remplacer C par © et de supprimer 

 les indices des quantités e' et r'. On obtient ainsi les termes suivants : 



1 +i eî+ y e *) sin ''- H * 1 ( 1 ~2 e, ' + "ï^ 



(1-H Cl )sin( 2 0- f )) S L .9, 

 -(1 — c,) sin (2©-+- y)) 2 \ 8 



sin(© — r -+-y) 

 -sin(© — r — y) 



2 ' V 8 e j|+(l_ Cl )sin(3Q-r+ ~ 



I 

 8 



(l+c,)sin(©+r- f )) 1 , (9+7 -j sin(2©-2r + y) 



. -s 2 e a (9-+-7e 2 h 

 (1— c,)sin(© + r + y)) 4 '(-8111(2© 



-2r+y)^ 

 -2r-y)( 





