MR. LUBBOCK ON THE THEORY OF THE MOON. 133 



which is independent of m. In consequence of this term^ all the terms in my develop- 

 ment of R, of which the arguments are any combination of the quantity r + |^ are 

 incomplete. 



When the terms depending on y^^ and those depending on the square of the dis- 

 turbing force, are neglected, the inequalities of longitude are given by the equation 



d / — r2 — r V d X ^ ^• 

 I find from this equation in \ the term 



175 



32 



r405 15 2 1^^ 9I 1 



m&- — < -32 ^ ^ + T ^ ^ + ¥ ^ ^ f ¥' 



195 

 instead of -^ w^, according to M. Plana*. 



Xg contains the term — -^ rrP- ej- instead of t^ m^ e^^ for 



R . +|f^;cos(2r-y 



— nr ^^ ^/ ^^^ (2 r — I) 



r It) 



)55 



C 123 . 369 0") 2 ^^'^^ 



h |- -r^ - Gi"^ ;^/ =-"6r 



m^ e^. 



r\ 7? 



If the numerical coefficient of the corresponding term in the quantity — /*xr ^ ^j 

 be called H, then I find 



^22 = I 2 r22 + no + ni -f- -n + E22 + Bio + 4- E4 + -^ ^i} {2-2m + 3c) 



r2125 „ , 7 2 . '^3 9 21^ 21^ 2_i_ ^ 2 I ^'^-^ 2) ' 



= |t92^' + -2^ +T6w2-|--3-m2 + jgm2-f--gm2-|--m2+ ^-^^,^2 j _ 



779 o 

 = 792^- 



M. Plana has -^ m^, and for the numerical value of the coefficient converted into 



sexagesimal seconds 3"*309. M. Damoiseau has 1"'27 ; I obtain '77"- 

 I find 



r 7 o 33 m^ 3 ' 2_i_^-^1 ^ ^ ^2 



= I - ^m- - 32m2 - -2 - y^m2 - -7^2 + __ j - = - - w^. 



95 • 



M, Plana has — ^4^^ and for the numerical value of the coefficient converted mto 



sexagesimal seconds — -087. M. Damoiseau has — -19 ; I obtain — '073. 



* The figures are indistinct in the copy before me. 



