Q 



COMSTOCK — STUDIES IX ASTRONOMY 10 



four place logarithms the following approximate equiva- 

 lents of those equations: 



t = cr., — a, tan M = 



'■ 1 — a cos t 



a ^ sin n cosec p cos N = 



(18) 



1 — tt cos t 



T, = T., = cT, - JT-\- M-^- N 



When the sidereal times T^ and T. are known the zenith 

 distances and azimuths of the stars may be directly com- 

 puted from the fundamental formulte for the transforma- 

 tion of coordinates, but the following method will usually 

 be found more convenient : 



In the spherical triangle formed by the polar star, the 

 zenith and the pole, we represent the east hour angle of the 

 star by r and find 



cos z = sin (p sin (5j -f" cos q> cos 5^ cos r 



= cos ((5j — (p) — cos (p cos (5j 2 sin^ i r 

 and applying to this the development into series of 



cos X = cos y -\- h 

 find when terms of the order r^ are neglected 



z = H- <p H = 90" - Tt cos r (19) 



Similarly from the development of the azimuth into 

 series we find when the azimuth is reckoned from the 

 north, positive toward east, 



A^ = 7t sin r sec (p = Mq sec cp (20) 



Values of E and J/o with the argument V are tabulated 

 below. 



To determine the difference of azimuth of the stars, we 

 represent by p the length of an arc of a great circle join- 

 ing them, and from the isosceles spherical triangle formed 

 by the two stars and the zenith, find 



cos p = cos^z + sin^z cos {A^ — A^) 

 which is readily transposed into either 



sin \ (A^ — A-i) =3 sin | p cosec z 

 or 



sin i p (21) 



tan |(^ 3 — J. 1 ) = 



\ sin ( ^ — 2 ) **^ (^ "^ ^) 



