73 



D = apparent distance. 



d zz true distance. 



A — difference of apparent altitudes. 



a = diiference of true altitudes. 



p = horizontal parallax ) ^ _^ 



r = refraction of star or) 



p' = horizontal parallax) f^^^^^ 



?■' = refraction ) 



1. By Spherical Trigonometry 



cosA-cosD _ co.a-cc.d ^ ^^ ^^^^^ quantities being equal to 



cos H cos n' cos A cos n' ^ i o i 



the versed sine of the angle, contained by the two verticals 

 passing through the sun or star, and the moon. 



Hence cos d =■ cos a — '^°^ J^°^ ii> (cos A — cos D) 



cos rl cos H' ^ ' 



2. There are two convenient ways of computing the latter 



term. 1. Forming a table for the whole quantity ^^* ^"^"^^ ^, 



^2. Developing this quantity, and then forming tables for the 

 terms of its expansion. The former is adopted in the 

 method of Mr. Dunthorne, and its improvement, and in fact 

 in that of Mr. Mendoza ; the latter in the method here pro- 

 posed. 



3. Mi'. Dunthorne finds the natural number answerihs to 

 the Log. c°3 {/"os fl ,+ Log. (cos A — cos D)* which number sub- 

 tracted 



* Mr. Vince, in his Treatise on practical Astronomy, p. 55, instead of computing 

 Log. (cos A— cos D) uses Log. sin (^^) + Log. sin (^~) + Log. 2. This is rather 

 more convenient than Mr. Dunthorne's method, as we avoid finding the Logarithm of 

 a number, but this advantage is somewhat lessened by it being necessary to form the 

 arguments— t and — ^ 



