HORIZONTAL DIALLING. Rule.--Observe which side of the triangle is given, and work by the specified case. When there is more than one draft in the operation, add the sums of the respective sides together for the answer. EXAMPLE I. Being required to put down a shaft 618 feet due east of an engine shaft at A, I am prevented from measuring in a direct line by intervening hills and wood: I therefore find it necessary, in order to avoid these obstructions, to go on an angle of 27° south of east from the shaft A. What distance must I proceed in this direction before I come at right angles with, or due south of, the eastern extremity of the given line, and how far must I then measure in a northerly direction to come exactly on the re quired spot. Or the question may stand thus:-Given the perpendicular 618 feet, angle 27°; the hypothenuse and base are required. It being required to find the distance between two shafts A and B, which are inaccessible to a direct measurement on account of a marsh or lake lying in the way: I consequently measure 352 feet on an angle of 63° south of west, from A to C; at this station (C) I can see the shaft B, which I find by observation bears 29° north of west, and the line from C to B measures 615 feet; how far are these shafts apart in a right line? Or the ques. tion may stand simply thus: Given angle 63°, hypothenuse 352 feet. Given angle 29°, hypothenuse 615 feet. The sum of the perpendiculars* are required. * As in this instance the perpendicular only is wanted, there is no ne ces sity for taking out the other side. VERTICAL DIALLING; OR, THE MENSURATION OF HEIGHTS. Rule.-Observe the given side and angle, and work by the respective cases as heretofore. From the bottom of a tower at B, I measured 200 feet in a direct line B A on an horizontal plane; I then took the angle A42° : required the height of the tower and staff B C. In operations of this nature the hypothenuse need not be regarded. |