the nearest distance between the line so run, and the

corner; then,

As the length of the given line,

Is to the said distance

So is 57.3 degrees.*

e;

To the difference of variation required.

EXAMPLE.

Suppose it be required to run a line, which some years ago bore N. 45° E. dist. 20 ch. and in running this line by the given bearing, the corner is found 20 links to the left hand; what allowance must be made on each bearing to trace the old lines; and what is the present bearing, by the compass, of this particular line?

Consequently 34 minutes, or a little more than half a degree, is the allowance required; and the line in question bears N. 44° 26' E.

Note. The above rule is simple and sufficiently accurate when the distance between the sought corner and

* 57.3 is the radius (nearly) of a circle in such parts as the circumference

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 sight 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 station of a survey the compass is found not to reverse truly, the surveyor will be at 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

stations, 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.

CHAPTER VI.

MISCELLANEOUS QUESTIONS.

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. 92 A. 1 R. 29 P. Cheshire; 67 A. 3 R. 25 P. Irish.

4. The ellipse in Grosvenor square, London, measuręs 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. Ans. 17.481 by 11.654 perches.

6. The three sides of a triangular field, containing 6 A, 1 R. 12 P. are in the ratio of the three numbers, 9, 8, 6, respectively; required the sides.

Ans. 59.029, 52.47, and 39.353 perches.

7. In a pentangular field, beginning with the south side and measuring round towards the east, the first or south side is 27.35 ch., the second 31.15 ch., the third 23.70 ch., the fourth 29.25 ch., and the fifth 22.20 ch. also the diagonal from the first angle to the third is 38 ch., and that from the third to the 5th. 40.10 ch.; required the area of the field. Ans. 117 A. 2 R. 39 P.

.;

8. Required the dimensions of an oblong garden, containing three acres, and bounded by 104 perches of pale fence.* Ans. 40 P. by 12.

9. How many acres are contained in a square meadow, the diagonal of which is 20 perches longer than either of its sides? Ans. 14 A. 2 R. 11 P.

10. A gentleman has a garden 100 feet long and 80 broad, and a gravel walk is to be made of equal width half round it; what must be the width of the walk, so that may take up just one fourth of the ground. Ans. 11.8975 feet.

it

11. A person has a circular yard that is 150 feet in diameter, and wishes a walk of equal width made round it within the fence: required the width of the walk so that it may occupy a fifth part of the ground.

Ans. 7.918 feet.

* This question may be neatly constructed by 28, 6 Playfair's Geometry. It may not be improper also to observe, that the 2d question, and all those