THE AREA OF AN IRREGULAR FIELD.

Otago Witness, Issue 3100, 13 August 1913, Page 14

THE AREA OF AN IRREGULAR FIELD.

The area of an irregular figure, such as a field having a winding creek for a boundary, or any irregular shape, may be determined by the drain alone. The process involves "the reduction of the figure—whatever shape it may be—to triangle and four-sided figures, two sides of which are parallel and also at right angles to the third side. In order to follow the method clearly a diagram is—necessary, and a sketch should be made on a small scale somewhat similar in shape to the boundaries of the field on which to

register measurements. In the accompanying sketch it will be seen that ihe field is bounded on the north by a winding creek and on the east by a drain which follows the course of the lowest ground,,

and therefore is not straight

The heavy lines indicate the boundaries of the field, and the dotted lines the measurements necessary to calculate the area. It will also be noticed that the general shape of the field is rectangular, and that the most of it may be included in a four-sided figure similar to that which has previously been described. As much of the ground as possible is therefore in eluded in the first large section selected Adopting the lettering of the diagram: I a perpendicular is laid down by squai and straightedge at B and produced til. it cuts the creek at K, and a transverse line run from E touching the bend of the creek at F and intersecting the western boundary of the field nt G, the four-sided figure ABEG will be formed, having AG and BE at right angles to AB and parallel to each other. Last week it was shown that the area of that figure was AB into the mean of AG and BE. In. determining the area of the field poles would be erected at each corner of this figure, and each side measured by the chain. Assuming that these were the measurements indicated in the plan, the area of this figure would be 800 into 512 links, or 409.600 square links. It will be noticed that the line BE runs for portion of its length outside of the field, while the line EG runs inside of it. While measuring the line TIE an inset of 120 links was taken at 200 links from B at right angles to BE, so as to intersect point C, and the point at which the line BE crossed the ditch boundary was noted at 410 links from B. Two right-angled triangles, BCy and Cyx, were therefore formed, and the data obtained to calculate their areas, which would be deducted from the original area obtained, because they are outside of the field. Proceeding with the measurement of BE from the intersection of the crock an offset of 20 links is taken at the first bend, and another at the second bend. Two triangles and a trapezoid are thus formed, the area of which must be added to that cf ABEG. Similarly in measuring the line EG the offsets —which are usually stepped—form two triangles and a trapezoid before arriving at F, the remaining portion of the field FGZ would be obtained by another offset making two small right-angled triangles. The points at which the offsets are taken depend upon the irregularity of the boundary lines. A line drawn from the terminal point of one offset to that of the next should either cover the boundary line exactly, or give and take an equal quantity of land. An examination of the dotted lines marked in the sketch will show that there are seven triangles and two four-sided figures to be added to the area of ABEG, while two triangles are to come off it. We now proceed to calculate the area from the data registered in the plan.

Deduct insets from line BE—--2UO x DO 1 = 12/00 and 2 0 x 120 2 = 12, GOO 24,G00 „ D' avieg the area 404,673 iq. links As there arc 10 square chains, or 100,000 square links in an acre, the area of the field is 4.0A675 acres, or four acres and poles.

that of ABKG i- 8 0 into 1 li<; mean of 644 and S80 = 512, or 409,000 sq. links Offsets fit in UK JO X 80 O =3 400 „ „ ,, 100 x 22 5 = 2.250 .. ;; „ ,, 24 x 252 — 4,1 / o ,, it Offsets from EG 100 x 50 2 1,000 „ .. 100 x mean of 40 * to = 30 = 3,000 „ „ :;oo x jo 2 6.009 „ „ CO X o Cl Cl 2 3,300 „ „ 170 x 30 2 2,550 „ ,, 429,275 „ „