1 92 Method of correcting the DISTANCE 



file tables. Then to the arithmetical complement of the loga- 

 rithmic cofine of the moon's altitude, add the proportional lo- 

 garithm of the reduced horizontal parallax, the fum will be the 

 proportional logarithm of the parallax in altitude j from the 

 parallax in altitude fubtract the refraction in altitude, and the 

 remainder will be the difference between the apparent and true 

 altitude of the moon ; which call the corrected parallax. 



IF, at the time of obfervation, the moon and ftar are in the 

 fame vertical, which may fometimes happen in low latitudes, 

 no angles are to be found. They will be in the fame vertical, 

 and on the fame fide of the zenith, if the apparent diftance and 

 lefler altitude together are equal to the greater altitude. In 

 which cafe, the fum of the corrected parallax and ftar's refrac- 

 tion, added to the apparent diftance when the moon's altitude 

 is greateft, or fubtracted from it when the moon's altitude is 

 leaft, will give the true diftance. They will alfo be on the fame 

 vertical, but on oppofite fides of the zenith, if the apparent di- 

 ftance, added to the fum of the altitudes, is equal to 180. In 

 this cafe, the difference of the corrected parallax and ftar's re- 

 fraclion, fubtrafled from the apparent, will give the true di- 

 ftance ; except when the moon is fo near the zenith, that the 

 corrected parallax becomes lefs than the ftar's refraction, in 

 which cafe the difference muft be added to the apparent di- 

 ftance. 



IF the apparent altitudes are equal, the angles at the moon 

 and ftar will alfo be equal, and may both be found at once, by 

 adding the logarithmic tangent of the common altitude to the 

 logarithmic tangent of half the apparent diftance, the fum, 

 rejecting radius, will be the logarithmic cofine of each of the 

 angles at the moon and ftar, and each of them will be acute, 

 or lefs than 90. 



WHEN the altitudes are unequal, the angles may be found 

 by the following method ; 



To 



