the Coefficients of the Lunar Inequalities. 501 



(2) If c t t denote any argument, and if Fj, B b and D* denote 



Inequalities 

 in p 



the coefficients of the corresponding inequalities in p, 



n 

 2(v — v t ) respectively, then there will arise the following : 



F„= -$J[i(M,-JP0+ Jm,] coscA ^ 



^-}|r*(Ni-?i) + .J.N,Tcw^ 



y L y -J 



Inequalities J c *\ ^ 



3> and 



>(B) 



in v 



6 -l(*1 N '- 31? 



sin c^, 



where 



c x =c } +ci, c y =c l — c b 4=4 + ^— 1, Ay = c y + P— 1, 

 Mz=B z + 2F, + D;, N,=B Z + 2F,-D,. 



(3) If e^ and e*,^ denote any pair of arguments, and if Fj, F TO , 

 G z , G m denote the coefficients of the corresponding inequalities 

 in p and v, then there will arise the following : 



Inequalities in p: F^= j [(|F z -f-^G ? )F m — %ciGic m G m ']cos cj, 



I 



Inequalities in v : G*= — — [(JFj + cjGj)F m + 2F J sin c^/, 



where 



11. With the aid of these formulas the inequalities of the 

 second order can be calculated with great facility. For this 

 purpose it is only necessary to put I and m = l, 2, and 3 succes- 

 sively, and to substitute for F x , G [} &c. their values, either those 

 already computed, or as determined by observation, viz. : — 



c,= +1-8503974, c 2 = -0748006, c 3 = -991548, 



c,G,= -0189279, c 2 G 2 = - -00028372, c 3 G 3 = -1088310, 



Bi= 0, B 2 = -050286, B 3 = 0, 



F 1= - -0071962, F 2 =+ -0001419, F 3 =- -054696, 



D 1= -0204762, D 2 =--059468, D 3 = +-2195174. 



12. Substituting these values in the formulas (B) of Art. 10, 

 we find the following : — 



(C) 



