ASTRONOMY. IxXV 



Also let 



<^ z= latitude of the place, 

 8 =: declination of star observed, 

 a = right ascension of star observed, 

 T^=. observed clock, time of star's transit, 

 A 7':=: the clock correction at an assumed epoch T^, 

 r = the rate of the clock, or other timepiece, 



^ = s^" y^ ~ ) — the u azimuth factor," 

 cos 6 



B = S^il^^) = the " level factor," 

 cos 6 



C= ^ = the " collimation factor." 



cos 



Then, when a, b, c are small (conveniently less than lo' each, and in ordinary 

 practice less than i' each), 



T-\- Ar+ Aa -\- Bb ■\- Cc -\- r {T - T,) = a. 



This is known as Mayer's formula for the computation of time from star transits. 

 The quantity Bb is generally observed directly with a striding level. Assuming 

 it to be known and combined with T, the above equation gives 



AT-^Aa-\-a-\-r(T-To) = a-T. (i) 



This equation involves four unknown quantities, AT, a, c, and r ; so that in 

 general it will be essential to observe at least four different stars in order to get 

 the objective quantity AT. Where great precision is not needed, the effect of the 

 rate, for short intervals of time, may be ignored, and the collimation c may be 

 rendered insignificant by adjustment. Then the equation (i) is simpUfied in 



Ar+ Aa = a— T (2) 



This shows that observations of two stars of different declinations will suffice to 

 give AT. Since the factor A is plus for stars south of the zenith (in north lati- 

 tude) and minus for stars north of the zenith, if stars be so chosen as to make the 

 two values of A equal numerically but of opposite signs, A Z" will result from the 

 mean of two equations of the form (2). With good instrumental adjustments 

 {b and c small), this simple sort of observation with a theodolite will give AT' to 

 the nearest second. 



A still better plan for approximate determination of time is to observe a pair of 

 north and south stars as above, and then reverse the telescope and observe an- 

 other pair similarly situated, since the remaining error of collimation will be partly 

 if not wholly eliminated. Indeed, a well selected and well observed set of four 

 stars will give the error of the timepiece used within a half second or less. This 

 method is especially available to geographers who may desire such an approxi- 

 mate value of the timepiece correction for use in determining azimuth. It will 

 suffice in the application of the method to set up the instrument (theodolite or tran- 

 sit) in the vertical plane of Polaris, which is always close enough to the meridian. 

 The determination will then proceed according to the following programme : — 



