110 CORRECTIONS TO BE APPLIED TO THE PARALLAX OF THE MOON. [18 



These formulae, as well as my tables in the Supplement to the Nautical 

 Almanac for 1856, give the value of the sine of the parallax, converted 

 into seconds of arc, which is frequently more convenient for use than the 

 parallax itself. 



To find this latter quantity, we must add 



0"'16 + 0"-03 cosx. 



Plana's formula for the parallax, as given in the Introduction to the 

 Greenwich Lunar Eeductions, also requires several corrections, partly in con- 

 sequence of the developements not having been carried far enough, and 

 partly from errors in the numerical conversion of the analytical expression. 



The constant of parallax employed in the Lunar Reductions appears to 

 be Henderson's, or 342l"'8 ; and the computed quantity is taken to be 

 the parallax itself. 



The correction to be applied to the parallax thus found, in order to 

 make it agree with my determination, is given by the following formula : 



0"-68 - 0"'16 cos x- 0"'13 cos 2 x + 0"'03 cos 3 x+ 0"'04 cos 4 x 



- 0"'05 cos t + 0"'63 cos 2 t + 0"'16 cos 4 t 

 + 0"-40 'cos (2t-x) + 0"'07 cos (4t-2x) 



- 0"'28 cos (2 t-z)- l"-9 1 cos (2y-x) + 0"'29 cos (2 t + z) 

 + 0"'01 cos(x-t)-Q"-5l cos(2x-2t) 



+ 0"'09 cos (2 y - 2 t) + 0"'14 cos (t + z) + 0"'10 cos (4 t - x) 



- 0"'l 1 cos (t + x)- 0"'02 cos (2 t + 2 x) 



+ 0"'12 cos (2 x - z) - 0"'10 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-ce-z). 



As before, quantities less than 0"'05 have been neglected, except when 

 they unite with larger terms. 



In the American Nautical Almanac for 1855, recently published, Plana's 

 formula for the parallax appears to have been employed ; the constant, 

 however, being slightly altered. 



The following table, which Mr Farley has obligingly calculated at my 

 request, shows the corrections to be applied to the parallaxes given in that 

 work, in order to make them agree with those found from my tables. 



