1885.J On Certain Errors in Lunar Observations. 581 
intervals of thiee hours for every day of the year; conse- 
quently we can compare our measured distance with the 
calculated distance given in the “ Nautical Almanac,” and 
by proportion find what the Greenwich time was when we 
measured and found our lunar distance. 
The practical method of making the observations is as 
follows : — 
1st. When three observers can be obtained, one observer 
measures the altitude of the Moon ; another, the altitude of 
the Sun, or a star ; the third measures the angular distance 
between the Sun and the Moon, or between a star and the 
Moon. 
2nd. When one observer only is available, he measures 
first the altitude of the body which changes its altitude 
more slowly, then the altitude of the other body, then the 
lunar distance, then the altitude of the body moving most 
quickly, lastly the altitude of the body moving most slowly. 
The times at which each altitude is taken, and the time at 
which the lunar distance is measured, and the change in 
altitude of the two bodies, can then be reduced to the time 
at which the lunar distance is mentioned, so that the same 
results are obtained by one observer as could be obtained by 
three, viz., the exact altitudes of the Moon and star at the 
instant at which the lunar distance was measured. 
The problem now before us is to obtain the exact distance 
of the Moon from the Sun or a star. The measured distance 
is not the true distance, because the star, in consequence of 
refraction, appears higher in the heavens than it is in reality. 
The Moon from the same cause appears higher, but the 
Moon in consequence of parallax appears lower than she is 
— consequently a correction is required to be made to the 
Moon’s measured altitudes for refraction and parallax, the 
first being a minus, the second a plus correction. 
There are several formulas for working out a Lunar, and 
obtaining the true lunar distance from the measured lunar 
and altitudes; but I always found that students understood 
the problem better if I treated it as a pure matter of spher- 
ical trigonometry,— consequently I adopted in instruction 
the following method : — 
Having obtained the altitude of the Moon and star, as 
mentioned, and the lunar distance, do not correct for parallax 
or refraction, but find the angle with the Zenith, formed by 
the Moon and Star, as follows : — viz., H M the altitude of 
the Moon as measured, consequently Z M the Zenith dis- 
tance of the Moon. 
0 S the measured altitude of the Star, consequently Z S 
