--- 1-;1 f1 - *+f2 - * fl tan 0.

which 0 is the same), and the distance from 0 along OT will be proportional to the reading on the staff. Thus if the staff be suitably graduated, the distance from 0 can be immediately deduced from the reading. Also, as before, if the telescope be inclined at an angle a to the horizontal, the distance OT inferred from the number of graduations in ST must be multiplied by cos t a to give the horizontal distance of 0 from T, and the horizontal distance so obtained must be multiplied by tan a to obtain the vertical distance of T from O.

The inconvenience of the reduction work necessary to obtain the horizontal and vertical distances produced the Wagner-Feunel tacheometer, by which the distances can be read directly from the instrument. As is seen from fig. 7, three scales are provided, to measure the inclined distance, the horizontal distance, and the vertical distance respectively. All three are arranged in a plane parallel to the plane in which the telescope turns. The inclined scale is attached to the telescope exactly parallel to its line of collimation, and moves with it. The horizontal scale is fixed to the upper horizontal plate of the theodolite. The vertical scale is on the vertical edge of a right-angled triangle, which can be slid along on the top of the horizontal scale. The inclined scale carries a slide which is provided with two verniers. One of these is parallel to the inclined scale, and is for the purpose of setting off on the scale (in terms of the divisions on the scale) the inclined distance of the staff from the axis of rotation of the telescope. The other turns on a pivot whose centre is accurately in the edge of the inclined scale at the point where the zero division of the inclined vernier FIG. 7.

cuts the edge, and is for the purpose of reading the vertical scale; it can be turned on its pivot so as to be vertical whatever may be the inclination of the telescope. Moreover, since the distance from the centre of the pivot to the zero of the vernier is always constant and known, the vertical scale can be graduated so that the reading of the vernier gives the height (in terms of the division on the scale) of the staff above the axis of rotation of the telescope. The horizontal scale attached to the horizontal plate of the theodolite is read by means of a vernier carried by the triangle. To ascertain the horizontal and vertical distances of the point on the staff which is cut by the middle wire in the diaphragm of the telescope from the rotation axis of the telescope, the inclined distance of the point on the staff is read by means of the wires, as in Porro's tacheometer. This distance (in terms of the divisions) is then set off on the inclined scale by means of the inclined vernier, and the vertical scale on the triangle is moved up to the vertical vernier, which is adjusted to its edge. With proper graduation of the horizontal and vertical scales the horizontal and vertical distances can be at once read off on the scales. This method, however, requires that the staff be held so that its face is perpendicular to the line of sight, which is more troublesome than holding the staff vertical.

Authorities. - Brough on " Tacheometry," *Proc. Inst. C.E.,* vol. xci. Pierce on the " Use of the Plane Table," *ibid.* vol. xcii. Kennedy on the " Tacheometer," *ibid.* vol. xcix. Airy on the " Probable Errors of Surveying by Vertical Angles," *ibid.* vol. ci. Middleton on " Observations in Tacheometry," *ibid.* vol. cxvi. Young on " Surveying with the Omnimeter," *ibid.* vol. cxvii. J. Bridges Lee on " Photographic Surveying," *Trans. Soc. Engin.,* vol. for 1899. " The Ziegler-Hager Tacheograph," *Engineering,* vol. lxv. (W. Ay.)

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