done as the second differences are constant, but which of course varies 

 with the latitude. 



EXAMPLE. 



Aldebaran was observed Jan. 15, .1824, 5\ 20'. 20" off the me- 

 ridian Bar. 30. 3. Ther. 40°. 



Appar. N. P.D. = 73°. 48'. 50" « = 6. 0345 



^. = 7. 1. 26 X = 6282 



•D — ?=66. 47 24 to~«=5, 4063 



NumberT.l.ssO. 2992 log. (»j— «) 1.73291 



Log. Bar. 1. 48144 tang. (D—Q 10. 36771 



1. 78064. Log. M. 2.10062 



Refract = 126". 07 



In taking out », it is necessary to know Z. D. to a few minutes, 

 and the quantities necessary for finding it, are already computed ; 

 but for those who do not like calculation, a celestial globe will give 

 it near enough. Within two hours of the meridian it is given by 

 this approximation : 



^ ■» ^ tang.(D— C) 



where a = comp. latitude and i = a — ^. 

 The cosine of the angle of position also, 



_ , tang, o . , 



COS. S = 1 — -s- — — sin. d. 



tang. (D—O 



The Refraction in P. D is negative when D is less than ^, and 

 this latter changes sign when the hour angle is greater than 90°. 

 The refraction in AR is by ("2) in space, 



sin. S u COS. S. tang. S 



« = u —. ^ — — 



' sm. D sin. D. 



R. tang. S R. tang. P. ^i n. ^ 



~ sin. D. ~ sin. D. sin. {-D— C) (4) 



