274 
An easy Method of Predicting 
Sept. 
IX . — An easy method of Predicting Occultations and Eclipses . 
Put M = 
P = 
L = 
P = 
* = 
A = 
V = 
A = 
Calculate 
Tang, a = 
Sia A = 
Tang. V = 
From the moon’s 
tude* =/>, then 
AR of meridian at any proposed time. 
Moon's horary angle = moon's AR — M. 
Latitude (reduced) of the place. 
Moon’s true AR. 
Do. true north polar distance. 
Do. parallax in altitude. 
Star’s AR. 
Do. NPD. 
Angle of the vertical with declination circle. 
Moon’s true altitude. 
Cot. L. Cos. P. 
sin L. cos. ( A — n) 
cos. a 
Tang. P. sin a 
Sin (A ' — a 
true altitude and horizontal parallax, find the parallax in alti- 
x = * — ( 5 +?• sin. V) 
y = A — (A' + p- cos. V) 
We thus get the difference of apparent AR of the. moon and star (x), and of 
N. P. D. (y) for one instant of time, and if this has been judiciously chosen, these 
differences will, in general, without proceeding farther, show whetheror not the oc- 
cultation will take place. Now perforin a similar computation for an instant (say 
an hour) earlier or later than the preceding, as the first result will indicate, and you 
will have wherewith to construct a figure showing the time of beginning and end of 
the occultation, together with the place where the star will reappear from behind 
the moon’s disc ; which is indispensably necessary to enable an observer to seize 
the exact moment of this phenomenon. 
I subjoin an example, and shall select one in which no assistance (great as that 
undoubtedly is) is derived from the elements for the calculation of the principal oc- 
cultations given in the Greenwich Ephemeras. It will appeal", that without taking 
account of the second differences in calculating the moon’s AR and PD or cor- 
recting the place of the star for aberration and nutation, still the result will not ge- 
nerally err from the truth more than two or three minutes of time, and will always 
be sufficiently correct to prepare for observation, which is the sole object in view. 
The following is the calculation I made, in order to ascertain whether there would 
be an occultation of the star No. 651, of the Catalogue of the Astronomical Society 
of London, on the 8th April, 1829, at a place whose latitude reduced was about 
28°. 00' N. and estimated longitude = 5 h 08“ E. It appeared, that the conjunc- 
tion in AR would he at about 4 e. m. Greenwich time, and I made the first calcula- 
tion for 3 h 30“ Greenwich apparent time. 
©’s AR at 3 h 30“ Greenwich time =* I h 08“ 36’ 
Apparent time at the place of observation = 8 38 00 
M = 9 
46 
36 
5 = 5 
18 
21 
P = —67*03' 45"=— 4 
28 
15 
* The most simple formula for this perhaps is the following by DeLambre, from 
which I have calculated a table for my own use : but the common tables, having 
for argument the moon’s apparent altitude, may be made to answer the purpose, 
sin. rr sin. N sin. -w sin. 2 N . sin. 3 rr sin. 3 N . . . 
* = — n7F- + — + ** » 
sin. 2" 
sin. 3" 
