C 5® 7 ] 
the third, for which arc the fecond, found by the fir ft 
rule, may be taken, without any fenfible error. 
Then, if the zenith diftance of the Moon is greater 
than that of the ftar, take the fum of this arc, and 
half the diftance of the Moon and ftar ; but if the 
zenith diftance of the Moon is lefs than that of the ftar, 
take the difference of the faid arcs; the tangent of the 
fum or difference, which may be called the parallaCtic 
arch, added to the cofine of the Moon’s zenith diftance, 
and the logarithm of the Moon’s horizontal parallax 
in minutes, abating 20 from the index, is the logarithm 
of the number of minutes required, by which the 
apparent diftance of the Moon from the ftar is always 
augmented by parallax, unlefs the zenith diftance of 
the ftar be greater than that of the Moon, and, at the 
fame time, arc the third be greater than half the di- 
ftance of the Moon and ftar ; in which cafe, the ap- 
parent diftance of the Moon and ftar is diminifhed by 
the parallax : 
Therefore, the number of minutes found by this 
rule is always to be fubtraCted from the obferved di- 
ftance of the Moon and ftar, firft corrected for re- 
fraction, in order to find the true diftance, cleared 
from the effeCt of parallax likewifej except in the 
cafe fpecified, when the zenith diftance of the ftar is 
greater than that of the Moon, and arc the third is 
at the fame time greater than half the diftance of the 
Moon and ftar, when the correction is to be added. 
In computing thefe corrections, four places of figures, 
beftdes the index, will be fufficient. 
It remains to be found, by calculation, at what 
hour under a known meridian, the diftance of the 
Moon from the ftar will be the fame a?s refults from 
Vol. LII. 4D the 
