## 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.

## 2. Angle repetition

When measuring a horizontal angle with a repeating theodolite, it was traditional to advance the horizontal circle so different parts of it would be used for the measurements. This would help compensate for any circle irregularities (recall that a theodolite's circle is etched glass). The most common method was to bring the initial FS reading back to the BS to serve as the beginning of the next measurement, Figure D-5. The angular value accumulated with successive measurements. (a) First measurement (b) Second measurement (c) Third measurement Figure D-5 Repeating Measurement

An upper and lower horizontal lock and slow motion was needed to accomplish this. Each would be used at different points in the measurement to either hold the circle or allow it to rotate.

TSIs generally have only a single lock and slow motion for the horizontal circle. The circle itself is electronically encoded so zero can be anywhere the operator chooses. Because the display is digital, the operation can also freeze or hold the reading so it doesn't change as the TSI is rotated. Manipulation of the lock and holding the reading allows the angle to accumulate also on a TSI.

## 3. Example measurement and field notes Figure D-6 Example Angle Measurement

We will show the process of measuring an angle and recording the readings. In our example, the TSI will occupy point B and measure the angle right (clockwise) from A to C, Figure D-6.

There are various note formats which can be used depending on the project and other measurements being made. Running a traverse, for example, would use a format which incorporates distances as well as angles.

For this example, we will use a simple angle only format.

The procedure and notes are shown in Figure D-7.

 Set up the column headings. Direct and Reverse angle readings are recorded in columns. A D/R angle set flows across the page The TSI is set on point B and carefully sighted on point A. The angle is set to zero and recorded in the Dir column for point A.  The lock is released and TSI rotated in the direction of the angle to point C. In this case,the direction is to the right. Using the lock and slow motion, point C is accurately sighted. The angle reading is frozen, read, and recorded for point C in the Dir column.  The value of the angle is the difference between the FS and BS readings. It should be computed immediately after the FS reading is made. This is the direct angle.  The telescope is reversed about the HA so it points away from C. Then the horizontal lock is loosened and instrument rotated to the right back to point A. Using the lock and slow motion, point A is accurately sighted. The angle reading is released, read, and recorded for point A in the Dir column. The angle reading to point A should be the same as the previous one to C. If the reading was released before final sighting on point A then the initial BS value will differ from the final FS value. Whatever it is, record the horizontal angle reading displayed before turning to point C.  The lock is released and TSI rotated right to point C. Using the lock and slow motion, point C is accurately sighted. The angle reading is frozen, read, and recorded for point C in the Rev column.  The value of the reverse angle is the difference between the FS and BS readings. The direct and reverse angle should be close. Their difference should be primarily due to instrumental and pointing errors. The process would be repeated for the number of D/R sets required. Successive direct and reverse angle sets should be relatively consistent taking into account random errors. If all the angles are within acceptable limits, the final angle is computed as the average of all the D/R angles. Figure D-7 Angle Measurement Process and Notes

## 4. Notes clarity

Because it's easy to do on a TSI, it's tempting to zero the horizontal angle reading on each BS sighting, Figure D-8. Figure D-8 Resetting Angle

While this makes it easier to calculate the angle, it can be confusing to a third party. How were the measurements made?

As two complete D/R sets, or,

Two direct measurements first rotating back and forth between A and C, then two reverse measurements rotating back and forth between A and C?

Allowing the angle to accumulate without zeroing intermediate BS sightings makes it clear the order in which the measurements are made.

### b. Mistake

Inevitably, a mistake is made, either reading the instrument, sighting, or incorrectly locking/unlocking the angle display. This will show in the notes as an angle with an excessive D/R difference. Figure D-9 shows a mistaken reading and how to correctly deal with it. The large difference for the second D/R set is an indication of a mistake. Upon closer investigation, it looks like the mistake occurred on the second direct angle as the second reverse angle "fits" with the first D/R set. The initial inclination is to toss the second direct angle and keep the second reverse angle. However, accepting the reverse angle without a corresponding direct one doesn't compensate instrumental errors. The correct way to address the mistake is to reject the entire second D/R set... .. and measure a third D/R set. Figure D-9 Correcting An Angle Measurement Error

## 5. Measuring a deflection angle

A deflection angle is measured from the extension of the previous line to the next line, Figure D-10. It is either to the right (clockwise) or left (counter-clockwise). Figure D-10 Deflection Angle

The procedure for measuring a deflection angle is the same as for an angle right (or left) except for when the instrument is reversed. To measure the deflection angle at point B from Point A to point C, after the TSI is set up at point B:

Step (1) Sight point A with the TSI in the reverse position.

Step (2) Rotate the telescope about the HA until it is pointing away from point A along the extension of line AB.

Step (3) Zero the horizontal angle and record it.

Step (4) Release the horizontal circle lock and rotate to point C in the direction of the angle (left in this case).

Step (5) Using the horizontal lock and slow motion, sight accurately on point C.

Step (6) Freeze the angle reading and record it.

Step (7) Compute the deflection angle by subtracting the BS reading from the FS reading. This is the direct angle.

Step (8) Release the horizontal circle lock and rotate to point A.

Step (9) Using the horizontal lock and slow motion, sight accurately on point A.

Repeat steps (2)-(7) to measure the reverse deflection angle.

Hits: 13508