Therefore d and h = ±dtanO, or kasin20.
The rod may however be held perpendicular to the optical axis. Where this is intended the staff is equipped with a device which allows the rodman to sight on the instrument. In this case if 1 be the length from the foot of the stave to its intersection with the produced optical axis—(the sighting point) then s=kacos0:_tsin0 and d= 0.
In the course of a normal tachymetric survey a very large number of points are generally fixed and the trigonometrical computation becomes irksome. There ate numerous tables de signed to facilitate this computation, and there are also special instrumental fittings for the same purpose. Some continental forms of tachymeter solve the triangle by scaled bars which actually form the triangle whose sides ate s, d and h. The Beaman arc is a fitting used often in America. This arc is fitted against the vertical arc of the tachymeter but is independent of it and can be set to any zero. It has two scales which help in the solution of cosh and of isin20. Some recent models give a direct reading of the horizontal and vertical components. It may be said, generally, that the tachymeter should not be used for distances of over 600 feet, that errors increase proportionally to the distance (except in the case of refraction which acts as the square of the distance) and that they may be expected to reach at least one part in four hundred.
Tachymetry is a medium scale method and is particularly suitable to engineering surveys, above or below ground. It is used perhaps more than any other for continental topographical surveys at scales of 20 25.1000 but is unsuitable alike for the 25 inch mapping of the United Kingdom or the small scale mapping of the Empire overseas. Used on the plane table the tachymeter is useful for traversing in difficult enclosed country or, where the control points can be seen, for measuring distances and heights to points that are immediately round the point of resection.
Telemetry.—The very marked effect of refraction upon the precision of tachymetry has led to the use of staves in the hori zontal position. The need for greater precision seems to have
been felt particularly desirable for the distance between the cameras used in ground photo surveying.
Subtense methods are much used in topographical and mili tary surveys. In such cases a theodolite is usually available and a subtense bar or base can be rapidly improvised. The bar or base is arranged horizontal so that the line between stations is per pendicular to it either at its centre point or at one end. The angle is measured by "repetition" on the slow motion screws of upper and lower plates. Thus, sighting on the left hand mark, the telescope is revolved with the top plate slow motion screw to point at the right hand mark. The bottom plate screw is then used to repoint on the left hand mark and the process continued until some ro to 20 readings have been made. The whole angle is then read and divided by the number of times the measurement has been made. The general equation is if the perpendicular is to centre point 2 2 or d=b cota if the perpendicular is to end point.
Where d is the horizontal distance, b is the length of bar or base, and a the subtended angle.
The subtense base may be of any convenient size. Sometimes signals have been erected as ends of a subtense base of as much as a quarter of a mile in length the distance between being taped. But subtense bars of special design, 10-20 ft. long, are the com monest form of base. The end marks are often discs with black lines on a white ground. For distances up to Soo yards using a 'o f oot subtense bar, with disc terminals, errors of the order of may be expected, but with proper precaution, good end marks, and sufficient repetition, a much higher order of precision may be obtained. The advantages of these subtense methods over tachy metry lie in their greater range and precision, in the ease with which the base can be improvised, in the freedom from either a special instrument or a special staff of rodmen, and in the direct measurement of the horizontal distance.