366 Astronomical and 'Nautical Collections. 



Final correction 26 3 



Dr. Briukley makes the correction in this example 26' 6". 

 Dr. Maskelyne 26' 9". 



Demon.stration. 



This computation is an exact counterpart of the construction, 

 as will appear from a consideration of the figure, supposing a 

 diameter to be drawn parallel to the lunar chord, on which the 

 sum or difference (2) will be projected. The same demonstra- 

 tion will consequently serve for both methods. 



Since in every spherical triangle (ABC), cos. a rr cos. b cos. 

 c + sin. b sin. c cos. A, if we call the angle at the moon A and 

 consequently the zenith distance of the sun or star a, that of 

 the moon b, and the distance observed c ; since the effect of the 

 horizontal parallax p is first reduced by the altitude to p sin. b, 

 and then by the obliquity to p sin. 6 cos. A, we have for the 



multiplier of the horizontal parallax sin. b cos. A z: —r— 



^ sm. c 



cos. b cos. C 1 X /I o o\ 



— — : zz cos. a. cosec. c — cos. o cot. c (1,2,3). 



sm. c 



In the next place the direct effect of refraction is to be 



