## 1. Reversion and angle measurement

If the HA is not perpendicular to the VA then a sighting error is introduced when the telescope is rotated in a vertical plane. We saw in Chapte B that reversing the geometry of the TSI causes the sighting error to change sides. We use this behavior to compensate the effect of that instrumental error: taking the average of the same angle read in direct and reverse positions cancels the error. The process is to measure a horizontal angle at the TSI from BS to FS is summarized below

Figure D-1
Angle Measurement Setup

### Step (1)

In the direct position, the HA inclination causes the angle to be measured from the right side of the vertical line through BS. This causes the horizontal angle to be too small.

Figure D-2
Direct Measurement

### Step (2)

In the reverse position, the HA inclination causes the angle to be measured from the left side of the vertical line through the BS. This causes the horizontal angle to be too large.

Figure D-3
Reverse Measurement

### Step (3)

Because the HA inclination is the same in both positions but in opposite directions, the correct horizontal angle is the average of the direct and reverse horizontal angles.

Figure D-4
Principle of Reversion

This is repeated as many times as necessary for the particular project. Angles should always be read in matched direct and reverse (D/R) sets to allow systematic instrument errors to compensate. There are situations when angles are read only in a single position, but those are limited to lower accuracy needs.