Figure 13-15.-Notes for the angle around a station, repeated six times.on the A vernier is about twice the size of theactual angle measured. The effect of this is tohalve the total possible error. This error wasoriginally plus or minus 30 sec. Now, the erroris 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-sixthof 30 see, or plus or minus 5 sec. In theory, youcould go on repeating the angle and increasing theprecision indefinitely. In actual practice, becauseof lost motion in the instrument and accidentalerrors, it is not necessary to repeat the angle morethan six times.The observation may be taken alternately withthe telescope plunged before each subsequentobservation. But a much simpler way is to takethe first half of the observations with the telescopein the normal position, the other half, in aninverted position. In the example given above, thefirst three readings may be taken when thetelescope is in its normal position; the last threewhen it is in its reversed position. To avoid theeffect of tripod twist, after each repetition, rotatethe instrument on its lower motion in the samedirection that it was turned during the measure-ment; that is, the direction of movement shouldalways be either clockwise or counterclockwise.Measuring angles by repetition eliminatescertain possible instrumental errors, such as thosecaused by eccentricity and by nonadjustment ofthe horizontal axis.Figure 13-15 shows field notes for the anglearound a station, repeated six times. The angleBAC was measured six times, and the angleclosing the horizon around station A was alsomeasured six times. The first measurement is not atrue repeat, but it is counted as one in the columnheaded “No. Rep.” (number of repetitions).With the transit first trained on B and thezeros matched, the plate reading was 00°00´. Thisis recorded beside B in the column headed “PlateReading.” The upper motion clamp was thenreleased, the telescope was trained on C, and aplate reading of 82°45´ was obtained. This readingis recorded next to the figure ‘‘1” (for “1strepetition”) in the column headed “No. Rep.”The measurement of angle BAC was then repeatedfive more times. After the final measurement, theplate reading was 136°28´. This plate reading isrecorded as the sixth repetition.Now to get the mean angle, it is obvious thatyou need to divide some number, or figure, bythe total number of repetitions. The question is,what figure? To determine this, you first multiplythe initial measurement by the total number ofrepetitions. 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 besubtracted from 496°30´ is 360°. This multiple is13-14

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