'The Transactions of the Bombay Geographical Society. From January 1863 to December 1864. (Edited by the Secretary.) Volume XVII.' [‎26] (189/524)

26
METHOD OF COMPUTING
Thus are obtained the numbers in Table I. computed for every 30' 0 f
declination with the latitude 18° 54'N.
It only remains to apply the small corrections required for variations
in the angular motion and in the difference of the horizontal parallax
and refraction—the latter, in this latitude, never amounting to more
than half a minute.
If p = any horizontal parallax,
t* = the refraction at the same time,
and S 7 — p — r ;
we have for the correction—
_ . --2G ) — ^ —0?04(§'— 26 f ) a .
Vcos (lTd) cos (l—d)
This is tabulated for S 7 —26 A == 1' in Table I. ;
And if A, the difference in minutes of the times of two successive
transits of the moon, or her mean motion from the sun in the intervening
lunar day, the correction will be—
+ 0?0402557 H (a—50?472),
and is tabulated with the arguments II and a in Table II.
For the correct time of the moon's transit at Bombay, we have
the longitude 4 h 51?3 E. or —of the circumference very nearly.
Hence if A and B be the times of two successive transits at Green
wich, A their difference, and A / 2 > A "2, the second differences opposite
A and B respectively, then T, the time of transit at Bombay, is given
by the expression—
T = B —*2022 ^ a H— A 2 2 ^ or B ^-very nearly,
or T = A + -7978 ( A _Aq_Al) + 24 ,
= A+*7978(a— T 1 QA2)4-24 / f
where A 2 = 1 (^'2 + A'2 ).
Hence, if from the first difference of the mean of the second
differences be subtracted (algebraically), and the result used as the
argument in the following table, the correction there found, when
added to the time of the Greenwich transit A, will give the time of the
moon s meridian passage at Bombay following, or next day.