494 Mr. H. Holt on a Method of Calculating 



or collecting the coefficients of cos c x t, and putting their sum = 0, 



(c 1 2 + P + 3)F 1 + 2c 1 G 1 +p=(). ... (A) 



Again, substitute the assumed values of p and v in the equa- 

 tion (12), rejecting, as before, the squares and product of Fj 

 and G v 



dt) 

 /3 2 =l + 2F,cosc 1 /, 2-^-;2 + 2c 1 G 1 cosc,*, 



... 2 P *~ =2 + (4F, + 2c 1 G I )cos^, 



•'• i[ 2p * d iii =^1+^ sin c ^ 



Hence equation (12) becomes 



— c 1 (4F 1 + 2c 1 G 1 )sinc 1 # + 3A;sinc 1 ^=0, 

 consequently 



-c 1 (4F 1 + 2c i G 1 )+3A;=0, or -4F 1 -2c 1 G 1 = -3 -. 



c i 

 Adding this last equation to the equation (A), we have 



( Cl 2 + iA_l)F__3*(j r+ I). 



Also 



c l 



If we substitute for c x and k in the above expressions their 

 numerical values as found by observation, viz. 



^ = 2-2^ = 1-8503974, k= -^ =005595, 



we shall find 



Cl 2 +p- 1=2-4267680, F 1= =--0071962, 



CjGj = -0 1 89279, Gj = + -0102291. 



The inequality in longitude is therefore -0102291 sin cj, or, 



reducing to seconds, = -f 2109"-90 sin c\t. 



The inequality in p is = — '0071962 cos c x t. If P' denote the 



P' 

 mean parallax (57' 4"), the true parallax = — ; and substituting 



for r its approximate value 1 — -0071962 cos c x t } we find the in- 

 equality in parallax = + 24"- 62 cos c Y t. 



It may be remarked that the coefficients of the variation as 

 above computed, are much more accurate than those found by 

 the usual methods in the first approximation. 



5. Annual Equation computed. — In the preceding article, the 



