INSTRUCTIONS. 57 



which, for example, is 45° for n— 4 and 30° if n= 6. The degree of ap- 

 proximation of this elimination increases rapidly with n. (For specifications 

 as to particular instruments see "Number of sets required and astronomical 

 azimuths" below.) The effect of this class of errors is always nil on an 

 angle equal to the angular distance between consecutive microscopes or a 

 multiple thereof. Other things, equal, therefore, we would expectthe measures 

 of such special angles to show less range than the measures of other angles. 



Besides the instrumental errors of the periodic class, there are also 

 accidental errors of graduation. These are in general small, however, in 

 the best modern circles and their effect is sufficiently eliminated by shifting 

 the circle in the manner explained under "Periodic errors" above. 



The effect of an error of collimation on the circle reading for any 

 direction varies as the secant of the altitude of the object observed. The 

 effect on an angle between two objects varies as the difference between the 

 secants of their altitudes. This effect is eliminated either by reversing the 

 telescope in its Ys, or by transmitting it without changing the pivots in the 

 Ys, the same number of measures being obtained in each of the two posi- 

 tions of the telescope. The latter method is the better one, especially in 

 determining azimuth, since it eliminates at the same time errors due to 

 inequality of pivots and inequality in height of the Ys. 



The effect of the error of inclination on the circle reading for any 

 direction varies as the tangent of the altitude of the object observed. If 

 the inclination is small, as it may always be by proper adjustment, its effect 

 will be negligible in most cases. But if the objects differ much in altitude, 

 as in azimuth work, the inclination of the axis must be carefully measured 

 with the striding level, so that the proper correction can be applied. The 

 following formula includes the corrections to the circle reading on any 

 object for collimation and inclination of telescope axis: 

 C sec li -\- b tan h ; 

 c — collimation in seconds of arc, 

 b = inclination "of axis in seconds of arc, ' 

 A — altitude of object observed. 



Parallax of wires occurs when they are not in the common focal plane 

 of the eyepiece and objective. It is detected by moving the eye to and 

 fro sidewise while looking 1 at the wires and imaere of the object observed. 



