1S4 PHILOSOPHICAL TRANSACTIONS. [aNNO I764. 



A Rule. To compute the contraction or augmentation of the apparent distance 

 of the moon from a star, on account of the moons parallax; the zenith dis- 

 tances of the moon and star, and their distance from each other being given 

 nearly. 



Add together the tangents of half the sum, and half the difference of the ze 

 nith distances of the moon and star, and the co-tangent of half the distance of 

 the moon from the star ; the sum, abating 20 from the index, is the tangent of 

 an arch, which call a. Then, if the zenith distance of the moon be greater than 

 that of the star, take the sum of the arch a, just found, and half the distance of 

 the moon from the star; but if the zenith distance of the moon be less than that 

 of the star, take the difference of the vsaid arch a and half the distance of the 

 moon from the star; and the sum or difference call b. To the tangent of b, 

 thus found, add the cosine of the moon's zenith distance, and the logarithm of 

 the moon's horizontal parallax, expressed in minutes and decimals; the sum, 

 abating* 20 from the index, is the logarithm of the effect of parallax, tending 

 always to augment the apparent distance of the moon from tlie star; except the 

 zenith distance of the moon be less than that of the star, and at the same time 

 the arch a be greater than half the distance of the iB^oon from the star, in which 

 case the effect of parallax diminishes the apparent distance of the moon from 



the star. 



Remarks on the use of the two foregoing rules. 



It has been remarked, after the rule for refraction above, that if the altitudes 

 of the moon or star are under 10°, the zenith distances must be first lessened 

 by 3 times the refractions corresponding to their respective altitudes, before the 

 effect of refraction be computed. But in order to compute the effect of parallax 

 from the 2d rule, the observed distance of the moon from the star must be first 

 corrected by adding the effect of refraction to it, found by rule the first: as must 

 the observed altitudes of the moon and star be also corrected by taking from them 

 their respective refraction in altitude, and the corrected arches thus found may 

 be made use of in computing the parallax. Only, if the altitudes of the moon 

 and star are both 10° or more, part of the calculation of rule the 2d may be 

 saved, and arch the 2d, found by rule the first, taken for arch a in the 2d rule 

 without any sensible error. In this case it will be most convenient to observe 

 the following order of computation, instead of that before prescribed to be used 

 when the altitudes are under 10°. 



1st. Making use of the apparent altitudes of the moon and star uncorrected, 

 compute arches the 1st and 2d by the directions contained in the rule of refrac- 

 tion. 2dly, Taking arch the 2d for arch a in the rule of parallax, compute the 

 effect of parallax according to rule the 2d. 3dly, With arches the 1st and 2d 

 compute the effect of refraction by rule the 1st. 4thly, and lastly, Applying 



