30 A MANUAL OF TOPOGRAPHIC METHODS. 



CORRECTION FOR INEQUALITY OF PIVOTS. 



This correction can be made a part of the level correction. 



Let ^> = the inequality of pivots. 



B = inclination of axis given by level for clamp west. 



B'= inclination of axis given by level for clamp east. 



b =true inclination of axis for clamp west. 



h'= true inclination of axis for clamp east. 



,, B'-B 



then p = 



4 



6 = B + p for clamp west. • 



b'=W — p for clamp east. 



(Chauvenet, vol. n, p. 155.) 



CORRECTION FOR ERROR OF COLLIMATION. 



This correction, designated by c, is the departure of the mean of the 

 threads from the optical axis of the telescope. For stars at upper culmina- 

 tion with clamp west it is plus when the mean of the threads is east of the 

 axis, and minus when it is west of it, For stars at lower culmination the 

 reverse is the case. The value of e is one-half the difference between the 

 clock error indicated by stars observed before and after reversal of the 

 instrument, divided by the mean secant of the declinations of the stars. 

 This is slightly complicated with the azimuth, although the effect of that is 

 largely eliminated by the proper selection of stars. Consequently it is to 

 be obtained by approximations, in conjunction with the azimuth errors. 

 The correction to be applied to each star equals c sec S — cC, which is plus 

 for a star at upper culmination and minus for a star at lower culmination. 

 It is least for equatorial stars and increases with the secant of the declination. 



CORRECTION FOR DEVIATION IN AZIMUTH. 



This correction, designated by a, represents the error in the setting of the 

 instrument in the meridian. Its effect is zero at the zenith and increases toward 

 the horizon. Since the instrument is liable to be disturbed during the oper- 

 ation of reversal, it is necessary to determine the azimuth error, both before 

 and after reversal, separately. A comparison of the clock error, determined 

 from observations upon north and south stars, will furnish the data neces- 



