Lectures On the Lunar Theory

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Multiply the second by — 2n n — 2n' + p this will eliminate 6 21 , and gives , and add to the first ; 2(n-n')(n-p)+l^- n _ S £, + p (n-n')(n-p)(l + b )^ + + • 4 (to — to') (to - p) (1 + b ) + 4to to— 2?i'+p (n-p) 3to' 2 + 6to?i' 2 to — 2to'+p (1 + 6.)+ (to-2to'+p) 2 -4to 2 + 3/u, a 51 =0.
Lastly the equations obtained by equating the coefficients of e cos (2i|r + nt — ra-) and e sin (2\}r + nt — ot) to zero are -2(TO-TO')(TO-|)) + |4la 2 -4(M-«')(«-p)(l + &o)&2-3TO' 2 (H-6„) + (3to - 2to' -pf +
... 8 n a^ - 2to (3to - 2n'-p) b a = 0, and 4 (to - to') (to - p) (1 + 6 ) a 2 + 2 (to - to') (to - jj) 6 2 + 3n' 2 (1 + b ) - (3re - 2to' -pf bn + 2to (3to - 2to' - p) a w = 0.
Multiply the second by — , 2to 3to — 2n' — p this will eliminate 622, and gives and add to the first ; XL] EQUATION OF THE CENTRE AND THE EVECTION.
2(„ -n')(n -J>) + JS£- 8m 2 a 3 3n-2n'-p 4>n - 4(n - m')(ra -P)(l + &o) - 6wn' 2 ■ 3ri* - 3?i — 2«' — p 3ra - 2m' - p (»-n')(n-p)(l+& ) (n — rc')(?j-p) + (3w-2n'-p) 2 -4ii 2 + ^ 0^ = 0.


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