OP DIALING. 381 



we shall by Case 4. of KeilCs Oblique Spheric Trigo- * LECT, 

 Tiometry) find the base Z d, which is the sun's ^- ^ 

 distance from the zenith, or the complement of his alti- 

 tude. 



And (2.) As sine Z d: sine P d: sine dPZ; dZP, 

 or of its supplement D Z S, the azirnirthal distance from 

 the south. 



Or, the practical rule may be as follows. 



Write A for the sine of the sun's altitude, L and / for 

 the sine and co-sine of the latitude, D~and dfor the sine 

 and co-sine of the sun's declination, and Hfor the sine 

 of the horary distance from VI. 



Then the relation of H to A will have three 

 varieties. 



1. When the declination is toward the elevated pole, 

 and the hour of the day is between XII and VI ; it is 



A=L D+H I d, and H=^j^- 



2.. When the hour is after VI, it is A=L DHld, 



, TT LDA 



and H rr~ ' 

 la 



3. When the declination is toward the depressed pole, 



we have A=HldLD, and H=-L 



id 



Which theorems will be found useful, and expeditious 

 enough for solving those problems in geography and 

 dialing, which depend on the relation of the sun's alti- 

 tude to the hour of the day. 



EXAMPLE I. 



Suppose the latitude of the place to be 51J degrees 

 north ; the time five hours distant from XII, that is, an 

 hour after VI in the morning, or before VI in the even, 

 ing ; and the sun's declination 20 north. Required the 

 sun's altitude ? 



