18] CORRECTIONS TO BE APPLIED TO THE PARALLAX OF THE MOON. 109 



The Moon's equatorial horizontal parallax, or, more strictly, the sine of 

 that quantity converted into seconds of arc is equal to 



3422"-32 + 186"'51 cos x+ 10"'17 cos 2 x + 0"'63 cos 3 x + 0"'04 cos 4 x 



- 0"'95 cos t + 28"'23 cos 2 1 + 0"'26 cos 4 t 



+ 34"'30 cos (2 t - x) + 0"'37 cos (4 t - 2 x) 



- 0"'40 cos z + 1"'92 cos (2 t - z) + l"'45 cos (2 1 - x - z) 

 + 1"'16 cos (x-z) - 0"71 cos (2 y-x) -0"'95 cos (x + z) 

 + 0"'0 1 cos (x - 1) - 0"'3 1 cos (2 x - 2 t) 



- 0"'3 1 cos (2 t + z) - 0"'23 cos (2 t - x + z) 



- 0"'l 1 cos (2 y - 2 t) + 0"'22 cos (2 t + x -z) - 0"'12 cos (3 x - 2 t) 

 + 0"'14 cos (t + z) + 3"'09 cos (2 t + x) + 0"-60 cos (4 t - x) 



- 0"'l 1 cos (t + x) + 0"'28 cos (2 t + 2 x) 



+ 0"'l 2 cos (2 x-z) - 0"'l cos (2 x + z) + 0"'09 cos (2 t - 2 z) 



- 0"'09 cos (2 y + x - 2 t) + 0"'05 cos (2 t - x - 2 z) 

 + 0"'06cos(4-x-z). 



Also, the correction to be applied to the equatorial horizontal parallax 

 found from Burckhardt's tables is 



l"-79 + 0"13 cos x + 0"'06 cos 2 x + 0"'14 cos 3 x + 0"'04 cos 4 x 

 + 0"'06 cos t + 0"'05 cos 2 t - 0"'29 cos 3 t + 0"'17 cos 4 t 



-0"'18 cos(2t-x) + 0"-0l cos(4:t-2x) 

 + 0"'05 cosz+0"-93cos(2-z) + l"-15 

 + 0"'07 cos (x-z) - I" '-50 cos (2 y - x) 



- 0"-05 cos (x - 1) + 0"-02 cos (2 x - 2 t) 

 -0"'90 cos(2 + z)-l"-l7cos(2- 



- //> 12 cos (2 y - 2 t) + 0"'12 cos (2 t + x -z) + 0"'10 cos (3 x - 2 t) 

 + 0"'14 cos (t + z) + 0"'09 cos (2 t - 2 z) - 0"'06 cos (2 y + x - 2 t) 

 + 0"'05 cos (2 t - x - 2 z) + 0"'07 cos (2 x + z - 2 t) 



- 0"'09 cos (2 t + x - 2 y). 



In both the above formulae, quantities less than 0"'05 have been neg- 

 lected, except where they can be included in the same table with larger 

 terms. 



When Burckhardt's parallax is known, it will be sufficient for ordinary 

 purposes to calculate the correction to be applied to it, taking into account 

 only the constant term, and the periodic terms depending on the arguments, 

 x, t, 2t-x, 2t-z, 2t + z, 2t-x-z, 2t-x + z, 2y-x, t + z. 



If extreme accuracy be required, the parallax should be calculated afresh 

 by means of the first of the above formula. 



