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random line, is small. But when this distance is considerable, it will be better to find the angle by trigonometry.
ON LOCAL ATTRACTION.
It is well known that iron or any ferruginous substance attracts the magnetic needle, and consequently, when near, will draw it aside from the position in which it would otherwise settle. And as the earth in many places contains, near its surface, substances of this kind, the needle will not unfrequently be attracted from its true direction. The surveyor ought therefore, at each station, to take a back view to the preceding one; and if he arrive at one at which the compass does not reverse truly, he may conclude, provided no error was committed in taking the bearing at the last station, that at the present one, the needle is affected by some local attraction. In such a case, he should first determine whether any error was committed at the last station, and if none is found, take the difference between the bearing from the last station and the reverse bearing, which will be the local variation of the needle at the present station. This variation must be applied according to its name, to the bearing of the following station.
If at the first and second stations of a survey the compass is found not to reverse truly, the surveyor will be at a loss to know which of them is affected by attraction. But by taking another station, either within or without the survey, and taking its bearing from each of those sta
tions, and the bearing of each of those from it, he may in general determine, at which of them the attraction exists.
Note. The area of the survey is not affected by the general variation, because it is the same at each station. But where local attraction exists and causes a variation in the position of the needle, as this variation will be different at different stations, it will, unless ascertained, and allowed on the corresponding bearings, materially affect the truth of the survey.
1. A circular fish-pond is to be dug in a garden, that shall take up just half an acre; what must be the length of the cord that strikes the circle? Ans. 27.75 yards.
2. Two sides of a triangle are 20 and 40 perches respectively; required the third side, so that the content may be just an acre.
Ans. Either 23.099 or 58.876 perches.
3. In 110 acres of statute measure, in which the pole is 5.5 yards, how many Cheshire acres, where the customary pole is 6 yards, and how many of Ireland where the pole in use is 7 yards?
Ans. 92A. 1R. 29P. Cheshire; 67A. 3R. 25P. Irish.
4. The ellipse in Grosvenor square, London, measures 840 links the longer way, and 612 the shorter, within the rails; now the wall being 14 inches thick, it is required to find what quantity of ground it encloses, and how much it stands upon.
Ans. It encloses 4 A. 0 R. 6 P. and stands on 1760 square feet.
5. Required the dimensions of an elliptical acre, with the greater and less diameters in the ratio of 3 to 2.
equal to the difference between the lengths of the longer side and the diagonal; hence the sides are required.
Ans. 21 and 28 chains.
18. The boundaries of a tract of land are as follow: 1st. N. 14° W. 15.20 ch. 2nd. N. 70°1 E. 20.43 ch. 3rd. S. 6o E. 22.79 ch. 4th. N. 86° W. 18 ch. to the place of beginning; within the tract there is a spring, the bearing and distance of which, from the 2nd corner, is S. 75° E. 7.90 ch. It is required to cut off 10 acres from the west side of this tract by a straight line running through the spring; what must be the distance of the division line from the 1st corner, measured on the fourth side? Ans. 4.6357 chains.
19. The boundaries of a quadrilateral tract of land are as follow: 1st. N. 35°1 E. 23 ch, 2nd. N. 7501-E. 30.50 ch. 3rd. S. 301 E. 46.49 ch. and 4th N. 66°1 W. 49.64 ch., to the place of beginning. This tract is to be divided into four equal parts by two straight lines, one of which is to run parallel to the 3rd side; required the distance of the parallel division line from the first corner, measured on the 4th side; also the bearing of the other division line and its distance from the same corner, measured on the 1st side.
Ans. Distance of the parallel division from the first corner 32.50 chains, the bearing of the other, S. 88° 22′ E. and its distance from the same corner 6 chains.