the Coefficients of the Lunar Inequalities. 497 



each pair of the arguments c x t, c 2 t, and c 3 t, and the coefficients 

 of which will be functions of the products of each pair of the 

 coefficients F p G u F 2J , G 2 , F 3 , G 3 , and k. 



Referring to the above values of p and v, it will be seen that 

 the form of each of the inequalities of p is Fj cos erf ; and that of 

 the inequalities of v is G z sin erf; or if we employ the character 2 

 to signify summation, we may put 



p = 1 4. 2F 7 cos cit, v = t + € + 2,Gisincit.- 

 Assume also 



—3 = -3 (l+2B z cosc^), 2(v—v l )=c l t + XDismcit. 

 Pi a i 



8. Substituting these values in the differential equation (7), 

 omitting the products of three or more inequalities, we shall have 



dv 2 

 (1) Value of p-^: 



dv 



■jr = 1 + 2c?G Z COS Cit, 



dv 2 



•*. ^2=l+22QG z cos^-f2i^GzC w G m cos (ci±c m )t; 



dv 2 

 """ P dt 2==l + 2(Fj + 2cA)coscj* + 2(cjGjF m + i^G^ w G m )cos(^±c w )^. 



— -t£ =%cJFi cos erf. 



(3) rflko/-^: 



- -i = ~1 + 22F /C os^-2|F,F m cos (c^J*. 



r 



(4) Ffl&e of \m l . 



P_. 

 Pf 



m t __ m, 



73 — ^-3 (1 + 2Bj cos cjf) =£ -f-2£Bj cos c /; 



.-. ^m l -^ = ik + ^k(F l -i-B l ) C osc l L 

 Pt 

 Phil. Mag. S. 4. No. 219. %>p/. Vol. 32. 2 K 



