Error from neglecting to read both stadia webs in horizontal distance AB A short table of the values of cos20 and sin. cos 0 is given at the end of the book; the interval of 20′ corresponds with that of the vertical circle divisions on most tacheometers. Observed Distance, Staff Collimation Level, and Instrument Collimation. Fig. 11, which is not to scale, shows how the foregoing principles are applied in ascertaining the difference of level and the distance between two points. In what follows, the value of K (CC), which is the product of the length on the staff subtended by the stadia lines and the stadia coefficient (100 or 200, according to the optical arrangement of the telescope), is called the "Observed Distance," the reduced level of the point on the staff intersected by the central line of sight is called the "Staff Collimation Level" to distinguish it from the R.L. of the same line of sight at the instrument, this being the "Instrument Collimation Level " or height of the horizontal axis of the telescope above datum. 616 In fig. 11 the height of the first station, A, is 1000.00 feet above datum. The 1:100 stadia wires give the observed distance looking from B to A as 100(15-60-9-44) feet. The angle ◊ read on the vertical arc is 8° 40′ (a fall from A to B). Therefore the horizontal distance AB is 616 cos2 0 = = = = = 616 × 0.977 601.83 feet, and the vertical interval y between instrument collimation level and staff collimation level, or the fall of the line of sight from A to B, is 616 sin. cos 0 616×0.14897 91.77 feet. By placing a levelling staff against the instrument, or by using a graduated tape as the string of the plumb-bob beneath the instrument, it is found that the height of the telescope axis above B, or, ment at B, is 4·70 feet. level of B can be found by that of A, as follows : R.L. of Station A briefly, the "height of instruWith these data the reduced addition and subtraction from Observing from B to C, the observed distance 100 × (15.53 -6.53) = 900, is obtained. 0, on vertical circle = +6° 20′ (a rise from B to C). Therefore horizontal distance The values of cos2 and sin and cos above need not be taken to a greater number of places than will suffice to give the answer correct to two places of decimals of a foot, even for station points. For ground levels, which are not change points, but which will be used in delineating the natural features of the ground, correctness to the nearest tenth of a foot will suffice. After a little practice in reducing actual field notes, no necessity will be found for writing down the figures in this manner, as the columns in the field book are specially arranged to facilitate the work of reduction (see p. 24). If at first any doubt be felt whether to add or subtract, a rudimentary sketch will always settle the point. CHAPTER V. THE FIELD WORK OF A CONTOUR SURVEY, Ar the end of the book are given all the field notes of an actual tacheometrical survey for the contour plan shown in Plate I. The present chapter deals with the field operations of this and other similar surveys; the office work occupies the succeeding Chapters VI and VII. Plate I follows the field notes and is so arranged that it can be pulled out to face any page of the text. It will be seen that from each station both the preceding and following stations were observed; this was done in order to obtain an independent check on the levels, without going over the ground a second time (see p. 37). Selecting and Marking Station Points. It is advisable in selecting instrument stations or traverse points for a survey (especially for one referred to the magnetic meridian, which varies) that the position of at least one or two points be such that they can at any time be found again, without using instruments other than a common measuring-tape, in case it be required to extend or modify the original survey at some future date. On large surveys it is usually practicable to mark at least a few points with masonry beacons; but in ordinary engineering work the |