76 



This quantity may with much convenience be put into 

 five small tables.* 



The first table may give sin l"" (p' sin H'— 114', 6) the 

 argument will be p' sin H' the parallax in altitude answering 

 to the complement of the moon's altitude. 



The second table will give ^ sin^ 1" {p' cos H — r')- and the 

 argument will be the correction of the moon's altitude. 



The third table gives sin I" S tan U -\- ^ r^ sin^ I'' and the 

 argument will be the height of the star. This table is only 

 to be used when a star is observed. 



Tlie fourth table is to be used when the sun is observed, 

 and gives sin 1" {j,a"H} + i r" sin- 1" and the argument is 

 the altitude of the sun. 



The fifth table gives sin 1" 5' tan H' and the argument is 

 the altitude of the moon. 



Let a, (3, 7, £, represent the quantities given by these tables 

 which are always positive, and then we have 

 cos d = cos a — (1 — a — (3 — y — f) (cos A — cos D) 



Or lastly, 

 V. sin d=v. sin D — v. sin A — (a+(3+y+£) (v. sin D — v. sin A) 

 + V. sin a. 



The computation of the above formula will be rendered 

 very plain and short, by a table of versed sines to 120°, -}- 

 which table, including the addition for seconds, will not 



contain 



* See the tables at the conclusion of this paper, in which all the numbers may be 

 taken out by inspection, and which have all single arguments. 



+ By using the difterence of the altitudes in the above formula, instead of the sum 

 the limit of this table is that of the distance. 



