An Elementary Treatise On the Lunar Theory With a Brief Sketch of the History O

Hugh Godfray

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24. Our investigations will be carried only to the second order ; it will be sufficient therefore if, in the preceding, we neglect small quantities of the fourth and higher orders. Let p = E+ M, MGM' = tan~*s = moon's latitude, E'V the direction of the first point of Aries, SG = / = A ; LVE'S= & = longitude of sun, M' E' = r = i ; LTE'M' =6 = longitude of moon, = & = difference of longitude of sun and moon. EXPRESSIONS OF THE FORCES. 25 Now, 8M*=8M"+MM* = SG*+ GM n - ZSG. GM' cos SGM' + MM' 1 ...an*, . #^ 8 \ = r" (1 - 2 r- cos S#Jf + jf- J ; therefore -g--, . 1, |l 4 i_^ cos ((9 - 0') j ; for 0-0' or #'Jf' differs from >S^Jf' by less than 7', Art. (17), and f J is neglected, being of the fourth order. 1 1 ( ' ^ f-J- 7') . .. .. .. .. Parallel to G8; whence P= (j^ 4- ^' JfJ^ cozMGM'- ^ M'E' wf(0- u, m'r 3m r =- M'E' cos (0 - ff) sin (0 - 26 LUNAR THEORY.

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