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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 elonga
Days. 4 mo. (Ap.) 5mo.(May) 6 mo, (Ju.) 7mo. (July) 8mo.(Aug) 9 mo. (Sep.)
Days. 10mo.(Oc.)11mo.(No.) 12mo(Dec) 1 mo. (Jan.) 2mo.(Feb.)|3mo.(Mar)
To find the angle of bearing, or azimuth of the polestar, 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 declination 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.
mo. 1 2 0
mo. 1 2 1
2 6 29
2 6 38
2 10 7 2 14 8 2 18 34 210 45 2 14 47 2 19 15
2 9 38 2 13 38 2 18 4 2 10 16 2 14 17 2 18 44
2 9 11 2 13 10 2 17 34 9 49 2 13 49 2 18 15]
2 8 42 2 12 40 2 17 4) 9 20 2 13 19 2 17 44
8 15 2 12 12 2 16 35 8 53 2 12 51 2 17 15
7 47 2 11 44 2 16 51 8 27 2 12 24 2 16 47
Note. The azimuths in the foregoing table corresponding to the 1st of the first month (January) of each year, are easterly, and those corresponding to the 1st of the seventh month (July) are westerly.
In order to observe the greatest elongation of the pole star, it will be necessary to prepare the following simple apparatus.
Place two posts firmly in the ground, about three feet apart, and nearly east and west from each other; the height of the posts, which should be the same, may be about two or three feet; on those posts, place a thick board or plank, five or six inches wide, and nail it fast to each of them, taking care that it be level or nearly so; take a piece of board, a foot or eighteen inches long and four or five wide, and near the middle of it fasten a compass sight perpendicularly; this board is to slide on the horizontal one already mentioned.
Take a stiff pole 18 or 20 feet in length, and fix it in an inclined position, in such a manner that a plumb line suspended from the upper end, may be nearly north, and about ten feet distant, from the middle of the horizontal board; the elevation of the pole must be such that the pole-star, when viewed through the compass-sight placed on the horizontal board, may appear a few inches below its upper end; when in this position the lower end should" be fastened in the ground, and the pole should be supported by a couple of crotches placed near the middle. The plumb should weigh a pound or more, and should swing in a vessel of water, in order to prevent the line being agitated by the motion of the air.
The apparatus being prepared, proceed, about 15 or 20
dicated by the table, to make the observation as follows: Let an assistant hold a lighted candle near the plumb line, so as to illuminate it and render it distinctly visible; place the small board with the compass-sight attached to it, on the horizontal one, and move it east or west as the case may require, till the pole star, plumbline, and aperture in the compass-sight are all in a direct range. If the star should be deviating to the east, it will leave the plumb line to the west, and the contrary if deviating to the west; keep therefore shifting the sight, till the star appears stationary behind the plumb-line, which it will do for several minutes at the time of its greatest elongation, and will then recede from the line on the contrary side from which it did before it became stationary. The compass sight must not be moved after the star has attained its greatest elongation; but the aperture in it being then in a direct range with the plumb line and star, the board to which the sight is fixed, must be fastened to the one on which it slides, by a small tack passing through each end. This being done, let an assistant take a straight stake, with a small piece of lighted candle stuck on it, and go north to the distance of 30 or 40 perches; then looking through the compass-sight, direct him to set it up perpendicularly, and in such a situation that the candle stuck on the top may appear exactly behind the plumb line; when thus placed, let it be firmly fixed in the ground; next let another straight stake be set up in the same manner near the plumb.line; the remaining part of the work may then be left till morning.
Measure accurately the distance between the two stakes; and from the table of azimuths take out, for the given time and latitude, the azimuth of the pole-star when at its greatest elongation. Tuis azimuth will be west if the time is within two months, before or after the 1st of B b