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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 polestar, 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 crotchets 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
dictated 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 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 plumbline; 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. This azimuth will be west if
the first month (January), but east if within the like timę of the 1st of the seventh month (July). Then,
Is to the tangent of the azimuth;
So is the distance between the stakes in feet,
Lay off the number of feet contained in this fourth term from the northerly stake, and perpendicular to a line joining the two stakes; it must be laid off towards the west if the azimuth is east, but towards the east if the azimuth is west. Next remove the northerly stake, and set it up at the other extremity of the distance thus laid then a straight line joining the two stakes will be a true meridian line.
To obtain the variation, set up a compass in the place of the southerly stake, and direct the sights truly to the northerly one; the needle will then point out the variation, which will be east or west, according as the needle points to the east or west of the north point of the compass. The whole process is so simple, that an example is deemed
It has already been observed, that the greatest elongations of the pole-star are invisible during the greater part of the 3rd and 4th months, and also of the 9th and 10th; consequently a meridian line cannot be obtained by the preceding method, during those periods. But as the surveyor may generally choose his time for tracing a meridian line, and as, when this is done, he can at any time obtain the variation, it is thought unnecessary to introduce other methods. Those, however, who would wish to be acquainted with simple and accurate methods of
consult a pamphlet on the subject, by Andrew Elli cott, 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 not 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 purpose 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 magnetic ones, 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 south-easterly 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 adja
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