Neill. — Readings of Graduated Circles. 



313 



Before proceeding with the analysis we have to consider the two systems 

 of measuring angles. 



Graduated circles are usually numbered from 0° to 360°, the numbers 

 increasing in the clockwise direction, and azimuths or bearings are referred 

 to the north point as zero. The four cardinal points correspond to 



North, 0° | South, 180° 



East, 90° West, 270° 



This may be termed the practical method of angular measurement. 



In trigonometry the angles are referred to the east point as zero and 

 increase counter-clockwise. The four cardinal points are represented by 



North, 90° 

 East, 0° 



South, 270° 

 West, 180° 



If we call this the theoretical method of measuring angles, and if we 

 bring the two zero points to coincide, an angle is converted from one 

 system to the other in this instance by 



a, theoretical = 360° — a, practical. 



Applying this conversion formula to the value of E = 186° 55', we obtain 

 E (as an azimuth) = 360° --186° 55' = 173° 05', and the line of no eccen- 

 tricity intersects the graduated circle at the points 173° 05' and 353° 05'. 

 Hence the reading of the vernier A requires a correction of 



+ i"-3 sin (a -173° 05') 



Taking the observed values of B — A and applying the correction for the 

 angular distance between the two verniers, we obtain the errors due to 

 eccentricity and imperfect graduation. Then computing the amount of 

 eccentricity, the residuals represent the errors due to imperfect graduation 

 and accidental errors of reading. 



The following form is a convenient method of tabulating these results : — 



Form B. 



As a check on the results in column (4) the values of B 

 by the formula (8) — 



y = A + A x cos a + A 2 cos 2a + &c. 

 + B x sin a + B 2 sin 2a + &c. 



A can be analysed 



