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Booking format for two-set horizontal angle

Short answer

In the direction method, two sets with different zero settings (e.g., 0° and 90°) are recorded with FL and FR readings for each target. Mean direction = (FL + FR ± 180°)/2, and the mean of the two set angles gives the final result; example mean horizontal angle AOB = 62°24′45.0″.

Develop a booking format for recording 2 set horizontal angle with appropriate numerical example. Calculate the mean horizontal angle also.

In the direction method with two sets, the zero setting of the circle is changed between the sets (e.g. 0° for set 1 and 90° for set 2) so that different parts of the circle are used. Each set has face left and face right observations.

Booking format (angle AOB, 2 sets)

Inst. atSetSighted toFace L (D M S)Face R (D M S)Mean directionAngle for the set
OIA0°00′00″180°00′20″0°00′10.0″
B62°24′40″242°25′00″62°24′50.0″62°24′40.0″
IIA90°00′20″270°00′00″90°00′10.0″
B152°24′50″332°25′10″152°25′00.0″62°24′50.0″

Mean direction = [Face L + (Face R - 180°)] / 2.

Set I: A = (0°00′00″ + 0°00′20″)/2 = 0°00′10.0″, B = (62°24′40″ + 62°25′00″)/2 = 62°24′50.0″, angle = 62°24′40.0″.

Set II: A = (90°00′20″ + 90°00′00″)/2 = 90°00′10.0″, B = (152°24′50″ + 152°25′10″)/2 = 152°25′00.0″, angle = 62°24′50.0″.

Mean angle AOB=62°24′40.0″+62°24′50.0″2=62°24′45.0″\text{Mean angle AOB} = \frac{62°24′40.0″ + 62°24′50.0″}{2} = 62°24′45.0″

Answer: mean horizontal angle AOB = 62°24′45.0″. The two sets agree within 10 seconds, so the result is accepted.

✓ Answer checked by Claude Opus 5.5 (high effort)

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