Figure 13-14.-Vertical angles and zenith distances.on the vertical limb by means of the verticalvernier.On a transit with a movable vertical vernier,the vernier is equipped with a control level. Thetelescope is centered on the point as describedabove, but the vernier bubble is centered beforethe angle is read.The ZENITH is an imaginary point overheadwhere the extension of the plumb line will intersectan assumed sphere on which the stars appearprojected. The equivalent point, directly belowthe zenith, is the NADIR. Use of the zenithpermits reading angles in a vertical plane withoutusing a plus or a minus. Theodolites have avertical scale reading zero when the telescope ispointed at the zenith instead of in a horizontalplane. With the telescope in a direct position andpointed straight up, the reading is 0°; on ahorizontal line, the reading is 90°; and straightdown, 180°. When measuring vertical angles withthe theodolites (fig. 13-14, view B), you shouldread the angle of elevation with values less than90°and the angle of depression with values greaterthan 90°. These angle measurements with thezenith as the zero value are called the ZENITHDISTANCES. DOUBLE ZENITH DISTANCESare observations made with the telescope directand reversed to eliminate errors caused by theinclination of the vertical axis and the collimationof the vertical circle.Zenith distance is used in measuring verticalangles involving trigonometric leveling (discussedin the next chapter) and in astronomicalobservations. (See Engineering Aid 1 & C,NAVEDTRA 10635-C.)Measuring Angles by RepetitionYou may recall, from a previous discussion,the distinction between precision and accuracy.A transit on which angles can be measured to thenearest 20 sec is more precise than one that canmeasure only to the nearest 1 min. However, thistransit is not necessarily more accurate.The inherent angular precision of a transit canbe increased by the process of REPETITION. Toillustrate this principle, suppose that with a 1-mintransit you turn the angle between two lines in thefield and read 45°00´. The inherent error in thetransit is 1´; therefore, the true size of this angleis somewhere between 44°59´30´´ and 45°00´30´´.For example, when using repetition, you leavethe upper motion locked but release the lowermotion. The horizontal limb will now rotate withthe telescope, holding the reading of 45°00´. Youplunge the telescope, train again on the initial lineof the angle, and again turn the angle. You havenow doubled the angle. The A vernier should readapproximately 90°00´.For this second reading, the inherent error inthe transit is still 1 min, but the angle indicated13-13
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