Mécanique Céleste Vol.3

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in 142 566 THEORY OF THE MOON ; [Méc. Cél.
[5275] produces the term,* r53891 ^ \ 5^-g^" (l-2m).(3-2,.,).(10+19»»+8;».^) ^,o,,^^ } o /4.-4^.
^ ' 2a i 2—2m—c 4.(2c— 2+2m) ' '"^2-2»!$ * \-2CTf2n produces qu [5288/1] — -^■A'^e-'.cos.{4v—4mv—2cv) ; and this is the only term of [5288e], which is of sufficient importance to be noticed. The second term of [5273] is developed as in [4923r] ; and a little attention will show, that the only term of whi [4904], necessary to be noticed, is ./3^''e.cos. (2 «
... — 2}nv — cv), [5288i] corresponding, in [4923iy], to k^=A[''>e, f^2— 2m— c=l, nearly. Combining this with the terra fc'.cos.v' [4923u, 4885 line 2], which is nearly equal to — 2ê.cos. {2v — 2m V — cv) ; making k' = — 2e, y'=z2v — 2mv — cv; we get, for the second term of [4923a;], the expression, [5288fc] —^.ikk'.cos.Uv—4mv—2cv) = —.A['k^.cos.{'iv—4mv—2cv).
4«, 2ffl, This is equal to the term [5288/i], but has a different sign ; so that the two terms destroy each other, as in [5288'] ; therefore, the whole of this function may be neglected.


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