The accuracy of the determination of terrestrial refraction from reciprocal zenith angles

Abstract

To investigate the accuracy of the determination of terrestrial refraction from reciprocal zenith angles and astronomical latitudes and longitudes at both ends of a line a test net with lines from 4 km to 23 km was observed and three dimensionally adjusted. As the measurements of the zenith angles were repeated every hour 40 times in an average the adjusted values were taken as a substitute for the true values. It is shown, that the mean refraction coefficient k, which is changing from k = 0.10 at day up to k = 0.34 at night, and the corresponding refraction angle can be determined very accurately, if both angles are measured simultaneously. Observations with day light are better than observations in the night. For observations with day light the mean difference between the true refraction angle at the observation station and the mean refraction angle of the observed line was smaller than ± 1″ independent of the length of the line. That means that the mean deviation of the true effective refraction coefficient in the observation station and the mean refraction coefficient of the observed line was inverse proportional to the distance.