ASTRONOMY. Ixxvii 



Having the hour angle the clock correction A 2" is given by 



A7'= a-\- t — 7] 



in which all terms must be expressed in the same unit ; /. c, in sidereal or in mean 

 time. 



The refraction J^ may be taken from Table 31. 



The most advantageous position of the star observed, so far as the effect of an 

 error in the measured quantity s, is concerned, is in the prime vertical, but stars 

 near the horizon should be avoided on account of uncertainties in refraction. 

 The least favorable position of the star is in the meridian. 



Compared with the preceding method the present method is inferior in preci- 

 sion, but it is often available when the other cannot be applied. 



c. By equal altitudes of a star. 



This method is an obvious extension of the preceding method, and has the 

 advantage of eliminating the effect of constant instrumental errors in the meas- 

 ured altitudes or zenith distances. Thus it is plain that the mean of the times 

 when a (fixed) star has the same altitude east and west of the meridian, whether 

 one can measure that altitude correctly or not, is the time of meridian transit. 



This method may, therefore, give a good approximation to the timepiece 

 correction when nothing better than an engineer's transit, whose telescope can 

 be clamped, is available. When the instrument has a vertical circle (or when a 

 sextant is used) a series of altitudes may be observed before meridian passage of 

 the star, and a similar series in the reverse order with equal altitudes respectively 

 after meridian passage. The half sums of the times of equal altitudes on the two 

 sides of the meridian will give a series of values for the time of meridian transit 

 from which the precision attained may be inferred. 



This method is frequently applied to the sun, observations being made before 

 and after noon. For the theory of the corrections essential in this case on 

 account of the changing position of the sun, on account of inequalities in the 

 observed altitudes, etc., the reader must be referred to special treatises on prac- 

 tical astronomy.* 



5. Determination of Latitude. 



a. By meridian altitudes. 



The readiest method of determining the latitude of a place is to measure the 

 meridian zenith distance or altitude of a known star. When precision is not re- 

 quired this process is a very simple one, since it is only essential to follow a (fixed) 

 star near the meridian until its altitude is greatest, or zenith distance least. Thus, 

 if the observed zenith distance is Zy, the true zenith distance z, and the refrac- 

 tion i?, 



z=zz,-^R- 



* The best work of this kind is Chauvenet's Manual of Spherical and Practical Astronomy- It 

 should be consulted by all persons desiring a knowledge of the details of practical astronomy. 



