Publisher's Synopsis
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1921 Excerpt: ...the wires entirely past it. In such cases, a fractional part of a revolution is used. Obviously, the longer the rod, and the closer it is to the observer, the less probability will there be of such a necessity. The use of full revolutions greatly facilitates the work as it is then only necessary to multiply the stadia intercept by a simple whole number such as 2, 3, etc., an operation which can be carried on mentally. The general relations of distance to elevation involve the trigonometric functions of a right triangle of which the horizontal distance is the base, the difference in elevation between the alidade and the point on the rod cut by the horizontal wire the perpendicular, and the inclined distance the hypotenuse. The base (correct horizontal distance) times the tangent of the angle (number of drum divisions) gives the value of the perpendicular. The hypotenuse (correct inclined distance) times the sine of the angle also gives the perpendicular. The determination of distance as one hundred times the stadia intercept on a vertical rod gives neither of these but the approximate inclined distance and, as shown in the discussion of Fig. 36, should be multiplied by one-half the sine of twice the angle to obtain the true value of the perpendicular. However, the error involved by the use of the tangent in place of the above function is, for angles up to 10 revolutions or about 6, much smaller than is commonly believed. The amount is shown by the accompanying table (p. 124). A very close correction can be made by decreasing the angular difference in elevation by a number of hundredths of one per cent, equal to the square of the number of revolutions of the drum. In comparing the accuracy of the gradienter screw with that of the vertical arc one should remem...
