III

p9i,o = 9"^ TV "^ -i ''^'''^' ~ ~r "^ — sT" '

p =. . .4- 6"sinG'-4-2"sin(G' — 2D) + i "sin(G' -)- 2D).

Pygo = 5-/n, r^93,n = 57 m, pos.o = — w, ^95,0 =63m,

$93,-2 = ?- ' ni, "'",95.-2 = -y- "^1 P95 -2 = '^^5 ^95,-2 = '-^O '^.

$95,2 = l'n-i r^ri,-i = —m', p95,2 = o.r?i; X9s,2 =3m;

(> =. . .-M"sin(G'-4- G) + i"sin(G"+ G — 2D);

Ç9c,o = ri"'"' ^■'•'''" = ^7 '^) p9C,0 = — T ''^' '"'•" ="^'^1

2'' 'Jk'

= . . .+ 2"sin(G' — G).

a3o- CHAPITRE XXII.

Zq-: n = O. m.

■SoS,2

•Sgo.o

-Sflfl,— :

i^tl-.O

<Jo--i

<ïilS,-2

M 00,0 — ,-3 ''î, <^ioo,o = 9"^)

■2ioo,— 2= o./n, ajoo,— 2 — râ '^'

3 9 -5ioo,2 = r,ni\ <Tioo,2 = T.m.

139. Pour les inégalités qui dépendent des j3uissances supérieures de e', on a :

Çioi.o = gmî — i8m3,

Çl01,-2=- 17'^'

Çioi,2 = -T m»;

iQioi.o = —

■"Qini.— 2 = —

9 3 '77 > Q 9 54 Pioi.o =— -m^-l-gm'H r^ 'n^', ^^loi.o = — - m -1- - m^ H -

— nf

Pioi,-2= I7mî+^m3, A,oi,-2 = — ^ '«-— J^^«^^

3 33 pioi,2 = m3-4-7m*; Xjm.a = -m^;

V =. . . — 7"sin2G' — 8"sin(2G' — 2D), sinTTT = . . .-+- o", I co?(2G' — 2 D).

DÉTERMINATION DES INÉGALITÉS DU MOUVEMENT DE LA LUNE, ETC. aSi

$102,0 =— "i: "^+ Ti^"* ' ■ "^lo-^o ——7^"^ r'^'

255 QQ71 „ > 255 i5i3q

p = ... — i"sin(2G'-t- G) — 7"sin(2G'-(- G ^ 2D).

Pio3,o = --/n-h-^m^, Xio3,o =-— /w--^mî,

Pl03,-2= — T /W ) ^^103,— 2 = r '^ '

pio3,2 = zm T^W; ^103,2 = T rn r^w^;

p =: . . . — 3"sin(2G' — G) — i"sin(2G' — G — 2D) — 3"sin(2G' — G-4-2D).

Çl04,0 = — 18 m, 'î'1104,0 = T3 "^: PlOt.O = f^j ^104,0 — ijs" '^'

Çl(,l-2 = r-^1 ■'"101.,— 2 = r '^5 pl04,— 2 = — 215 m.^, Aio4,2= TT "*>

$10.,, 0 = o.m, 7)105,0 = ^ /«, Pi05,o = — 27m', Aio5,o = — ,-7 '^J

$10S,^— -7-W5 "^105,-2= ir '^' Plfl3-2= ~'"' ^l«5,-2= ^ '^'

i"sin(2G' — 2D).

$100,0= 18 m, ■'1100,0= — "J "*' Pi06,o = „ '^' ^100,0— — —5-

$106.2 = -5 w: TQioe.a = iJT'^' Pio«.« = -^ "î'; A,or„2 — ^"^!

■i'i2 CHAPITRE XXII.

rargument 2 G' — 2 G H- 2 D, auquel correspondent les ternies afleclés de l'indice 106,2, étant à très longue période, on a usé de l'équation (A') pour déterminer p 100,2 •

-5jo7,n = ni H m2 ai 07,0 = -.: m -^ m»,

5i 3 ion 5i 2321

■5i07 ,—2 = z >n -^ w2 : cJ|U7,— 2 = :: m m- :

..— i''sin(2G-+- n - 2D).

'l08,-2 = :fn-\ /»2 ; a, 08,-2 = — -^, '" H T /'î* ;

•2lOO,0 = 9'"? ^lOfl.O = — 18 /?l,

-S109,— -2 = fn, aïoîi,— r) = — 5im;

^110,2 = 7- ^«, <T|in,2 = — 9'n;

•^111.0 — 7'^) '^in.o =

. -Si 11 ,— 2 = — -7 »î, 1^1 1 1 ,—i ■- r '«,

-Zll2,-2 = -Zr "^> "^112,-2= T-

-Sii2,2 = x/n; <Tn2,2 = — —,'n.

DÉTERMINATION DES INÉGALITÉS DU MOUVEMENT DE LA LUNE, ETC. v>33

Çiii.o = ^/«, "^114,0 = — ^ »i, piii.o = o.m, Xiii,o = -^'W,

?lllv2 = ^"î, Tllll,2 = -m, pi|i,2 = -^ /«^ >>lH,-2 = '/n;

çii.5,0 = o.rn, TQiiô.o = 77^"' Pii5,o = -'•7"'^, ^n.i.o = r^ "^

Çii.",,-2= -T ''î, r)l,.^i,.= ., "», puô,— 2= o./;?., A,|.i 2= -r '«,

Çii;,/2 = ^"î; "nus, -2 = ^'«; Pus, 2 = o.rn; Ans,, = -^ '« ;

la détermination de p, , ,2 a demandé les mômes soins que celle de p(o«,a-

Çiic.o = — 10 ni^ -+- 20 m^,

ÇiiG,2 = 5m^-+---m'; TQiir,,2 = r '" "^ ''* ;

Piifi.o = i .ni^ — 2 m-,

Piih,2=— 5/«- ^/«-'i >>nc,,2 = -m-— — — m^j

V = . . . — 2"?in2 D.

;i 17,— 2 = rj '^— —r '" ' 'Il 17.-2 = :: m -+- -^ /n--'

;ii7,î =— ::i7/"S •^117,2 = 5- /«s

pii7,o ==~~"*') ^117,0 = o (par convention ),

ni —in^-, A|,7— >= —m-\-

Pii7,2 = ^ni"-; Aii7,2 = r"»^;

t' = . . . -f- 2 " si n ( G — 2 D ).

i34 CHAPITRE XXII.

Çll8,-2= —m, r,,,8,-2= —r"^t pll8-2= 75'"*, X,,8,— 2= -TT'";

Çii9,2 =— '- m; 7)119,2 =— ^w; pii'.i,2 = — 75m; Xi,9,2 == ô»''"'

Aiic= ^m»— ^m^, rt/j/i,ç£,ei, = /i / — | m^ -t- m'Jj e, si, = — aS ;

Zi2oo =— i.m2, 1^120,0 = o (par convention),

i5 ^oq , i") 169

2120,-'»= — »iH r'"' 0^120,-2= -r'« -1- -rp /«^

^120,2 = r'«^; ^120,2 =— rr"^ )

s =...-+-i"sin(H — iD).

^121,-2= ^5 ni, ai2i,2= 3o m, i5 £5

/<ii9 = cm, nh\ ,.,£', £L,£,e, = — i".

Çi22,-2= -j w, •niL>n,--2= .-r'", Pi23,-2 = i5m2,

Çl-25,0 = '^"^' ■^'-•''" == ~ .r^ '" "^ .7^ '"'

pi25,o =— —^ m2 + — m-\ X,25,n ="-7^ "^ ^ .7^ '"*'

DÉTERMINATION DES INÉGALITÉS DU MOUVEMENT DE LA LUNE, ETC. 235 845 ^ - 9295 ,

pi2r,,o = — "Y^ /'î» ^i2c,o — — -y-T ''*)

pi2G,— 2= —rrn\ Ai2„2 = :r m ;

Çl2-,0 = -T-^ m, '1127,0 = r^ '"'

Çl2-,2 = -:'«; ^12-, 2 = ;"ï;

pl27,0 = ^T^ "i, >-l2-,0 = r^ "*7

Pl,- ., = — /7Z ; ^127 > = — — /« ;

= ni,

■Pr3'"'