The errors involved in determining a line's azimuth can be divided into two categories: (I) measuring horizontal angles from a line to the sun and (2) errors in determining the sun's azimuth. Except when pointing on the sun, errors in horizontal angles are similar to any other field angle.
Since, the observations are taken at the edges of the sun, a correction for semi-diameter is required. The correction (C) to be applied to the measured horizontal angles is:
C = ±
sec a
where a is the (correct) altitude of the sun and is the semi-diameter of the sun (can be obtained from star almanac).
The width of a theodolite cross hair is approximately 2 or 3 arc-sec. With practice, the sun's edge, particularly the trailing one, can be pointed to within this width. In many instances, pointing the sun may introduce a smaller error than pointing the backsight mark.
Total error in the sun's azimuth is a function of errors in obtaining UTI time, and scaling latitude and longitude. The magnitude these errors contribute to total error which is a function of the observer's latitude, declination of the sun, and time from local noon .
Since errors in scaling latitude and longitude are constant for all data sets of an observation, each computed azimuth of the sun contains a constant error. Errors in time affect azimuth in a similar manner. Consequently, increasing the number of data sets does not appreciably reduce the sun's azimuth error. The increase can, however, improve horizontal angle accuracy and therefore have a desirable effect.
After azimuths of the line have been computed, they are compared and, if found within acceptable limits, averaged. Azimuths computed with telescope direct and telescope reversed should be compared independently. Systematic instrument errors and use of an objective lens filter can cause a significant difference between the two. An equal number of direct and reverse azimuths should be averaged.
An alternate calculation procedure averages times and angles, or points on opposite edges of the sun and averages to eliminate semi-diameter corrections. Due to the sun traveling on an apparent curved path and its changing semi-diameter correction with altitude, this procedure usually introduces a significant error in azimuth. Also, it does not provide a good check on the final azimuth.