'The Transactions of the Bombay Geographical Society. From January 1863 to December 1864. (Edited by the Secretary.) Volume XVII.' [‎23] (186/524)

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Art. IV .—A Method of Computing the Times of the Moon's Rising,
Setting, and Southing .— By J. Burgess, Esq., F.E.I.S.
[Read before the Society, September 17th, 1863.]
Owing to the rapid variations of the moon’s declination, angular
motion, and parallax, the determination of the times of her rising and
setting is more complicated than the analogous problem for sunrise and
sunset. The usual method is tedious, owing to the necessity of re
peating the calculation after finding an approximate time ; but by
employing the mean values of the parallax and angular motion from the
sun, we may construct tables for any latitude, by which the operation
may be performed very expeditiously and with considerable accuracy,
even when the second correction is neglected. The corrections in such
a case will only be such as arise from variations from the mean values
of the elements, especially the angular motiorn
To form the tables :—*
LetNZPbethe meridian, Z the
zenith, P the pole, and MN
the arc described by the moon.
Then-
Let l — the latitude of the
place = PO.
d — the moon’s declination,
= PM —90° or 90°—PM.
H = the hour angle Z PM,
= 180°—MPO.
Then, in the spherical triangle MPO, right angled at O—
cos MPO = —cos ZPM = ;
Now PM = 90 o dt d,
Hence, cos H — —tan l tan d (1)
But the effect of refraction is to make the body appear elevated above
its true position, whilst that of parallax is to make it appear depressed