You may recall, from a previous discussion, the distinction between precision and accuracy. A transit on which angles can be measured to the nearest 20 sec is more precise than one that can measure only to the nearest 1 min. However, this transit is not necessarily more accurate.

The inherent angular precision of a transit can be increased by the process of REPETITION. To illustrate this principle, suppose that with a 1-min transit you turn the angle between two lines in the field and read 4500. The inherent error in the transit is 1; therefore, the true size of this angle is somewhere between 445930 and 450030. For example, when using repetition, you leave the upper motion locked but release the lower motion. The horizontal limb will now rotate with the telescope, holding the reading of 4500. You plunge the telescope, train again on the initial line of the angle, and again turn the angle. You have now doubled the angle. The A vernier should read approximately 9000.

For this second reading, the inherent error in the transit is still 1 min, but the angle indicated

Figure 13-15.-Notes for the angle around a station, repeated six times.

on the A vernier is about twice the size of the actual angle measured. The effect of this is to halve the total possible error. This error was originally plus or minus 30 sec. Now, the error is plus or minus only 15 sec.

If you measure this angle a total of six times, the total possible error will be reduced to one-sixth of 30 see, or plus or minus 5 sec. In theory, you could go on repeating the angle and increasing the precision indefinitely. In actual practice, because of lost motion in the instrument and accidental errors, it is not necessary to repeat the angle more than six times.

The observation may be taken alternately with the telescope plunged before each subsequent observation. But a much simpler way is to take the first half of the observations with the telescope in the normal position, the other half, in an inverted position. In the example given above, the first three readings may be taken when the telescope is in its normal position; the last three when it is in its reversed position. To avoid the effect of tripod twist, after each repetition, rotate the instrument on its lower motion in the same direction that it was turned during the measurement; that is, the direction of movement should always be either clockwise or counterclockwise. Measuring angles by repetition eliminates certain possible instrumental errors, such as those caused by eccentricity and by nonadjustment of the horizontal axis.

Figure 13-15 shows field notes for the angle around a station, repeated six times. The angle BAC was measured six times, and the angle closing the horizon around station A was also measured six times. The first measurement is not a true repeat, but it is counted as one in the column headed "No. Rep." (number of repetitions).

With the transit first trained on B and the zeros matched, the plate reading was 0000. This is recorded beside B in the column headed "Plate Reading." The upper motion clamp was then released, the telescope was trained on C, and a plate reading of 8245 was obtained. This reading is recorded next to the figure 1" (for "1st repetition") in the column headed "No. Rep." The measurement of angle BAC was then repeated five more times. After the final measurement, the plate reading was 13628. This plate reading is recorded as the sixth repetition.

Now to get the mean angle, it is obvious that you need to divide some number, or figure, by the total number of repetitions. The question is, what figure? To determine this, you first multiply the initial measurement by the total number of repetitions. In this case, this would be as follows:

Next, you determine the largest multiple of 360 that can be subtracted from the above product. Obviously, the only multiple of 360 that can be subtracted from 49630 is 360. This multiple is then added to the final measurement to obtain the figure that is to be divided by the total number of repetitions. In this example,

Enter this in the column headed "Mean Angle." The following computation shows that you should use the same method to obtain the mean closing angle.

In the example shown above, the sum of the mean angle (824440) and the mean closing angle (2771520) equals 3600000. This reflects perfect closure. In actual practice, perfect angle closure would be unlikely.

It is often necessary to extend a straight line marked by two points on the ground. One of the methods discussed below may be used depending on whether or not there are obstacles in the line ahead, and, if so, whether the obstacles are small or large.