Accidental and Systematic Standard Deviations in Horizontal Angle Measurements

If measurements are made many times on each of many objects,we can obtain a precision index describing the consistency of the observed values on each object;and obtain an accuracy index from the conditions which the observations must satisfy.Assuming that the observations are random samples from normal distributions,we can estimate the"accidental standard deviation",a precision index,and the"systematic standard deviation",an accuracy index,of the observations using the technique of analysis of variance.This paper analyzes these two kinds of standard deviations of horizontal angle measurements in classical geodetic traversing and triangulation with theodolites.Experimental traverses were run with 1" theodolites and movable targets mounted on tripodes.The sides averaged 100m long.Systematic errors were found significant in F tests due to errors in centering the theodolites and targets.Accuracy was improved and systematic errors were made insignificant,when angles were measured in the following way.Each angle of the traverse is measured several times,each time with a different position of the horizontal circle,such as each time the circle is shifted 60°,The theodolites and the targets are recentered after each time the angle is measured and before the next measurement.A triangulation net of second order was analyzed,The sides averaged 8km long,The angles were measured by the method of directions using 15 positions of the horizontal circle with T3 theodolites,The result shows that the ratio of systematic and accidental standard deviations of measuring an angle is about 3.7:1.Possible ways of making systematic errors insignificant are discussed,The usual belief that if angles are measured by the method of directions the triangulation net should be adjusted by the direction method is groundless.