1920 .] 
Astronomical Notes. 
217 
A Brief Method of Calculating Occupations of Stars by 
the Moon. 
By C. J. Westland, F.R.A.S. 
The tables given herewith for the calculation of occultations of stars 
by the Moon visible at Wellington have been computed by the formulae 
given for the purpose in the Nautical Almanac and also in most of the 
text-books on astronomy, viz., 
u = p cos <f>' sin h , 
v = p sin cos 8 —■ p cos c p' sin 8 cos h, 
in which u is the apparent displacement of the Moon by parallax to 
east of true place, expressed in same units as the occupation elements, 
v is the displacement of the same nature to north of true place, p is 
the radius of the Earth at place of observation, <p' is the geocentric 
latitude, 8 is the declination of the star, and h is the hour-angle of the 
star at time proposed. 
The values of v were calculated up to six hours from the meridian in 
both north and south declination, instead of making the semi-diurnal arc 
the limit. This was an assistance in checking the accuracy of the tables, 
and it has also been found convenient to retain them in this form. When 
it becomes necessary to work with an hour-angle greater than six hours, 
all that is required is to use the supplement of the hour-angle and take 
the column for same declination of contrary name as regards north and 
south, v is always negative, and u is negative when the moon is east of 
the meridian. 
To compute the circumstances of an occupation, find from the almanac 
what is the local hour-angle of the star at the date of true conjunction. 
If the star is east of the meridian the apparent conjunction will be seen 
before the true conjunction ; if west it will be delayed by the same interval 
of time ; and the fraction of an hour by which it is accelerated or retarded 
is given in the little table A. This is to be entered with hour-angle at 
date of true conjunction at the side, and the element x' at the top. 
It must be remembered that the apparent conjunction is not midway 
between the star’s disappearance and reappearance, unless the star is 
centrally occulted, but it usually happens fairly close to the midway time. 
Most occupations last about an hour, because the Moon’s mean motion is 
not much more than the mean value of her diameter. For this reason 
it is convenient to take for calculation two times an hour apart, with the 
time at which apparent conjunction takes place situated nearly midway 
between them. 
Required the circumstances of the occupation of 16 r Aquarii at Welling¬ 
ton on October 31, 1919. 
Greenwich hour-angle is — 9 h. 40 m. Applying longitude -j- 11 h. 39 m. 
to this, we have local hour-angle + 1 h. 59 m., and Table A interpolated 
shows that the apparent conjunction will be retarded 0‘98 hour. The 
best times for our purpose will be J hour and 1J hours after true 
conjunction, when the Greenwich times are 21 h. 0 m. and 22 h. 0 m. 
respectively, and the local hour-angles are -j- 2 h. 29 m. and + 3 h. 29 m. 
respectively. 
