FORMULES DE LA MUTATION ANNUELLE. 



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+ (1— c ) )sin(3C;— 20 + r' + f )j 16 ï \ 



sin(2© — 2r'-t- f ) 

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(l + c,)sin(C:+20-r'- f )) i_ $ / 9e „_27 e „ iJ + 7 \ ( sin(2(T-2r'- + - ? ) j 

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î \ 2 /(-sin(2C-2Q- f )) 32 * |-sin(2©-2Q- f )j 2*1 2 12 / j+(i- C) ) s in(4(T-2r'H- ? )S 



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(l + c,)sin(4C-20- ? )) 1_ 

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(lH-c,)sin(2C+20 — 2r — ? )j 9 

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?)) 

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263 



9 s ( (l+c,)sin(2(;-20+2r- f ) 

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(l-+-c,)Lsin(2C;+20-2Q — f ) — sin(2(T— 2Q-+-2Q — ? )]|_9 < (| + C| )sin(2<T— 2r'_2Q + ? ) 



(1— c,)[sin(2C-4-20— 2Q-k ? )— sin(2Ç— 2Q+2Q + ? )]| 8*'" l | + (1— c,)sin(2<C— 2r'— 2Q— f ) 



A j (l + Cl )sin(4C-2Q_ ? )) 5 f (I + Cl )[sin(C-r'+ 2Q- ? )_sin(Ç-r -2Q + , 



/ (-+-('— fi)sin(4(T— 2Q + V )j 4 ' ( + (1 — c,)[sin ((T— I"+ 2Q + ? ) — sin (£— r'— 2Q — Wj 



(l + Cl )sin(C;— 8T'+f)j_ J_ se , t ( (l + c,)sin(2!C— 4r'+ ? )l 9 , s ( (c I + c 2 )sin(2(T— 2r'+ Q — ? )) 

 + (1— c,)sin(C— 5r'- ? )j 24 S,e j + (l— c,)sin(2C— 4r'—,)J 4 Le "j + ( Cl -c 2 )sin(2C— 2r'+ Q + ? )J 



(c 1 +c ï )sin(3C— 3r'H-Q — P ;) 17 g/ï ( (c 1 +c 2 )sin(4(T- 2T'-Q- ? )) J_ , ( ( e ,+ f2 ) s in((;-5r'+QH- ? )) 

 +-(r,— c 2 )sin(3<T— 5r'+Q+ ? )j + 2 " <l-(c 1 -c î ).sin(4C-2ï'-Q+ f )| 48 " ''( + (c,-f 2 )sin(C;-5r'-+-Q- f )| 

 Tome XLVII. 3 



