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consult a little pamphlet on the subject, by Andrew Ellicott, A. M. from which the substance of the preceding method is extracted, and which contains others, suited to those times of the year in which this cannot be applied. It may nor be improper also to observe, that the second volume of the American Philosophical Transactions contains an essay by Robert Patterson, Professor of Mathematics in the University of Pennsylvania, in which is given a method for obtaining the variation to a sufficient degree of accuracy for any purposc in surveying, and which has this advantage, that the observation may be made at any season of the year, and at any time in the evening. There are also other methods beside those alluded to above, by which a meridian line may be traced or the variation of the compass determined; but as the most of them require expensive instruments for making the observation, it is thought unnecessary to notice them in this work.
To obtain the true bearings of a survey, from the the variation being given.
If the variation be east, add it to the north-easterly and south-westerly bearings, and subtract it from those that are north-westerly or south easterly; but if the variation be west, add it to the north-westerly and southeasterly bearings, and subtract it from those that are north-easterly or south-westerly: this being done, the true bearings are obtained.
To find the difference between the present variation, and that at a time when a tract of land was formerly surveyed, in order to trace or run out the original lines.
Go to any part of the premises, where any two adjacent corners are known; and if one can be seen from the
other, take their bearing; which compared with that of the same line in the former survey, shows their difference. But, if one corner cannot be seen from the other, run the line according to the given bearing, and measure 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,*
To the difference of variation required.
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 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 effected 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 dif ferent 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 4A. OR. 6P. 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.