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To find the bearing and distance of NI.
As diff. of lat. of NI, 13.80 S.
Ar. Co. 8.86012
Hence IN bears, N. 60° 52′ E. dist. 28.35 ch.
2. Given the boundaries of a tract of land as follow;
viz. 1st. S. 35° W. 11.20 ch.
2nd. N. 45° W. 24.36
4th. S. 77° E. 16 ch.
ch. 3rd. N. 15° E. 10.80 ch. 5th. N. 87°1 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. divi
VARIATION OF THE COMPASS.
A meridian pointed out 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 pointed out by the needle, is called the variation of the compass.
The variation is named east or west, according as 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 the difference in compasses, causes many difficulties, and frequently inaccuracies, in
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 1° 41' 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 3rd, 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 in the morning of the following day.
Days 4mo (Ap.)|5mo(Ma.)|6mo. (Ju. )[7mo(July)|8mo. (Au.)19mo (Sep)
Days. 10mo(Oc) [11mo(No) 12mo(De)[1mo(Jan.)12 mo(Feb)[3mo(Mar)
To find the angle of bearing, or azimuth of the pole-star, when at its greatest elongation; subtract its declination from 90°, and the remainder will be the polar distance. Then,
Is to the secant of the latitude;
So is the sine of the polar distance,
To the sine of the azimuth.
The mean declination of the pole-star on the 1st of the first month (January) 1810, was 88° 17′ 28′′ N; and it increases 19′′.4 yearly; hence the mean declination may readily be obtained for any given time.
When great accuracy is required, the mean declinations must be corrected by allowing for aberration and nutation; but as these corrections are small, they are not necessary when our object is only to determine the varia
The following table exhibits the angle of bearing, or azimuth of the pole-star, when at its greatest elongation; calculated to the 1st of the first month (January) and of the seventh month (July), for each of the years contained in the first column, and for the different degrees of north latitude at the head of the table. In calculating it, the star's mean declination was corrected, by allowing for aberration and nutation.
Lat. 36. Lat. 38. Lat. 40. Lat. 42. | Lat. 44. Years. Months. Azimuth Azimuth Azimuth. Azimuth. Azimuth. 1 mo. 12°4' 54" 2°8′ 13" 2°11′ 54′′ 2°15′ 58′′ 2°20'28" 7 mo. 12 5 31 2 8 52 2 12 33 2 16 39 2 21 10
1 mo. 12 0 35
2 3 48 2
2 11 172 15 38