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To find the latitude and departure of CI, and area of the

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Hence IN bears, N. 60° 52′ E. dist. 28.35 ch.

1.13988

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2. Given the boundaries of a tract of land as follow viz. 1st. S. 35° W. 11.20 ch. ; 2d. N. 45° W. 24.36 ch.; 3d. N. 15° E. 10.80 ch.; 4th. S. 77° E. 16 ch.; 5th. N. 874° E. 21.50 ch.; 6th. S. 60° E. 14.80 ch. ; 7th. South, 10.91 ch.; 8th. N. 85° W. 29.28 ch. to the place of beginning; to divide the tract into two equal parts by a line running from the first station and falling on one of the opposite sides; the bearing and distance of the division line are required. Ans. N. 7° 18′ E. 15.28 ch.

CHAPTER V.

VARIATION OF THE COMPASS.

A MERIDIAN indicated by the magnetic needle is not, in general, a true one; for the needle does not point truly to the north point of the horizon, but varies from it, in some places to the eastward, and in others to the westward.

The angle contained between the true meridian and that indicated by the needle, is called the variation of the

compass.

The variation is named east or west, according as the north end of the needle points to the eastward or westward of the true north.

As the variation is different in different places, so also, in the same place, it does not remain the same, but differs sensibly in the course of a few years. Hence, in running a line that was run a number of years previously, the bearing will be found different from what it was at that time; this, together with some difference in compasses, causes many difficulties, and frequently inaccuracies, in tracing old lines.

The easiest way to guard against those difficulties and inaccuracies would be to make and return the surveys according to the true, and not the magnetic bearings. In order to do this, it will be necessary to know the variation of the compass for the place in which the survey is made; and this may readily be found by first tracing a meridian line in the following manner.

To draw a true meridian line by means of the greatest elongation of the pole star.

The pole star is situated about 11° from the true pole, and therefore apparently revolves round it, in a small circle, once in about 23 h. 56 m. When at its greatest distance east or west from the true pole, it is said to be at its greatest east or west elongation. It is therefore evident that in the course of one apparent revolution it must be twice at its greatest elongation, once to the east and once to the west.

The following tables exhibit the times, nearly, of the greatest eastern elongations of the pole star for six months of the year, and of the greatest western elongations for the other six months. The other greatest elongations take place in the day time, and are therefore invisible. Some of those inserted in the tables are also invisible; because they occur, either before daylight is gone, in the evening, or after it has returned, in the morning. The most of those in the 3d, 4th, 9th, and 10th months are in this situation.

The time in the tables is reckoned from noon; and therefore when it is less than 12 hours, the greatest elongation takes place in the evening of the same day; but when it exceeds 12 hours, if 12 hours be subtracted from it, the remainder will be the time of greatest elongation

Eastern Elongation.

Days. 4 mo. (Ap.) 5 mo. (Ma.) 6 mo. (Ju.) 7 mo. (July) Smo.(Aug.) 9 mo. (Sep.)

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Days. 10 mo. (Oc.) 11 mo. (No.) 12 mo.(De.) 1 mo. (Ja.) 2 mo. (Feb.) 3 mo.(Mar.)

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In order to determine a true meridian, by the method here used, it is necessary to know the bearing of the pole star, called its azimuth, at the time of its greatest elongation. This depends on the latitude of the place, and the distance of the star from the pole. This distance is called the polar distance of the star. It is subject to a small annual diminution, which is called its annual precession. The polar distance of the star on the 1st. of the 1st. month (January) 1830, was 1° 35′ 51′′; and its annual precession is 19.3".

The polar distance may be found for any subsequent time by multiplying 19.3", by the interval between the 1st. of the year 1830, and the given time, and subtract

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