Ixxiv ASTRONOIMY, 



e. Relation of sidereal time to the right ascension and hour angle 



of a star. 



Tg = sidereal time at any place, 



= right ascension of the meridian of the place, 

 a = right ascension of a star, 

 / = the hour angle of the star at the time 7]. 



7] = a-)-/, /=7^ — a. 



4. Determination of Time. 



a. By meridian transits. 



A determination of time consists in finding the correction to the clock, chro- 

 nometer, or watch used to record time. If 7J denote the true time at any place 

 of an event, T the corresponding observed clock time, and AZ'the clock correc- 

 tion, 



T^ = r+ at: 



The simplest way to determine the clock correction is to observe the transit of 



a star, whose right ascension is known, across the meridian. In this case the 



true time Tq = a, the right ascension of the star ; and if 7"" is the observed clock 



time of the transit, 



AT= a— T. 



Meridian transits of stars may be observed by means of a theodolite or transit 

 instrument mounted so that its telescope describes the meridian when rotated 

 about its horizontal axis. The meridian transit instrument is specially designed 

 for this purpose, and affords the most precise method of determining time.* 



Since it is impossible to place the telescope of such an instrument exactly in 

 the meridian, it is essential in precise work to determine certain constants, which 

 define this defect of adjustment, along with the clock correction. These con- 

 stants are the azimuth of the telescope when in the horizon, the inclination of the 

 horizontal axis of the telescope, and the error of collimation of the telescope.f 



Let 



a = azimuth constant, 



d = inclination or level constant, 

 c = collimation constant. 



a is considered plus when the instrument points east of south ; /; is plus when 

 the west end of the rotation axis is the higher; and c is intrinsically plus when 

 the star observed crosses the thread (or threads) too soon from lack of collima- 

 tion. (The latter constant is generally referred to the clamp or circle on the 

 horizontal axis of the instrument.) 



* The best treatise on the theory and use of this instrument is to be found in Chauvenet's 

 Manual of Spherical and Practical Astronomy, which should be consulted by one desiring to go 

 into the details of the subject. 



t Other equivalent constants may be used, but those given are most commonly employed. 



