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This is, however, no check upon the field work, as all the interior angles, right or wrong, will always come to twice as many right angles (-4) as the figure has sides, provided the work be correctly calculated.

The only check is the following, depending upon the axiom, that the whole northing or southing of a line, of any bearing, is equal to the sum of the northings or southings of any number of lines of the same bearing, when the sum of the several distances is equal to the one distance of the whole line. Resolve, then, all the bearings and distances into their corresponding northings and southings, and eastings and westings (either by construction, or by finding their respective sines and cosines to the given angles, and the given distances), then, because it is not possible to go from any place to the east without coming back the same distance to the west, nor to the north without coming back to the south the same distance, to get to the place of beginning, add all the northings together, and southings; eastings together, and westings: the sum of the northings should equal that of the southings; and the eastings, that of the westings.

There is an allowable error of one link to every three chains in the sum total of the distances.

CHAP. III.

Surveying with the Circumferentor.

The mode of surveying with this instrument is very simple and expeditious.

It matters not whether it is a road, pond, field, or wood, to survey; the same plan of taking the bearings and distances of the several sides must be adopted.

The chain and three flags only are required. Set your instrument at the first station, and a flag at the second, take the bearing of the second, and measure to it, taking such offsets upon the line as may be necessary; put the bearing in the centre column, and the line and its offsets above; at the end of this, draw a line in the book, and setting your instrument at the second station, and a flag at the third, proceed exactly as before, going round the whole of the ground to be surveyed till you come back to the place of beginning.

The same kind of check may be adopted with this instrument as with the theodolite, by taking at several stations (as you go long) the bearings to any fixed point, as a church spire, &c.

The following is an example of the survey, by the circumferentor, of the wood, given in chain surveying.

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Explanatory Remarks.

Measure
Through

IN plotting from the Circumferentor Notes, place the Base Line, AB (see Plate No. 12), upon the paper in such a position as may best suit the shape and size of the plan, then, because it bears N. 19° E. at A, lay off the angle BAN., 19° A N., or AS will be the meridian line. 7.30 chains to B, and mark off its various offsets. B, draw a line parallel to A N.; and because the next line bears N. 77° 30′ W., at B, the end of the first line, lay off the angle N. BC=77° 30', and measure BC 4.63 chains. Through C, draw another line NCS., parallel to NAS. Then because the next bearing is S. 15° 10′ W., at C, lay off the angle SCD=15° 10′, and measure CD=3·10 chains. Through D, draw another line parallel to the meridian line, and as this bears to the north, make the angle NDE 89°, counting the degrees from the north end; had the bearing been S. 89° W., then the degrees would have been reckoned from the south, as in the case of the preceding line CD. Proceed thus till you come to the last line, IA, the bearing of which is N. 54° 50′ E. Through I, draw the meridian line, and lay off the angle 54° 50′, as with the other lines, and measure the distance 3:43. The line IA, is the closing line; and you should now come back to the place where you started from. Some little error, however, is unavoidable, where there are many lines.

Having plotted the wood, divide it into triangles, and calculate the area.

Area of Wood:

A. R. P.

4. 0. 37.

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