CHAPTER IV. CALCULATING THE CONTENT. (55) The CONTENT of a piece of ground is its superficial area, or the number of square feet, yards, acres, or miles which it contains. (56) Horizontal Measurement. All ground, however inclined or uneven its surface may be, should be measured horizontally, or as if brought down to a horizontal plane, so that the surface of a hill, thus measured, would give the same content as the level base on which it may be supposed to stand, or as the figure which would be formed on a level surface beneath it by dropping plumb lines from every point of it. This method of procedure is required for both Geometrical and Social reasons. A Fig. 25. B Fig. 26. A B F Geometrically, it is plain that this horizontal measurement is absolutely necessary for the purpose of obtaining a correct plat. In Fig. 25, let ABCD, and BCEF, be two square lots of ground, platted horizontally. Suppose the ground to slope in all directions from the point C, which is the summit of a hill. Then the lines BC, DC, measured on D the slope, are longer than if measured on a level, and the field ABCD, of Fig. 25, platted with these long lines, would take the shape ABGD in Fig. 26; and the field BCEF, of Fig. 25, would become BHEF of Fig. 26. The two adjoining fields would thus overlap each other; and the same difficulty would occur in every case of platting any two adjoining fields by the measurements made on the slope. D H Let us suppose another case, more simple than would ever occur in practice, that of a threesided field, of equal sides and composed of three portions each sloping down uniformly, (at the Fig. 27. Fig. 28. rate of one to one) from one point in the centre, as in Fig. 27. Each slope being accurately platted, the three could not come together, but would be separated as in Fig. 28. We have here taken the most simple cases, those of uniform slopes. But with the common irregularities of uneven ground, to measure its actual surface would not only be improper, but impossible. In the Social aspect of this question, the horizontal measurement is justified by the fact that no more houses can be built on a hill than could be built on its flat base; and that no more trees, corn, or other plants, which shoot up vertically, can grow on it; as is represented by the vertical lines in the Figure. Even if a side hill should produce more of certain creeping plants, the Fig. 29. increased difficulty in their cultivation might perhaps balance this. For this reason the surface of the soil thus measured is sometimes called the productive base of the ground. Again, a piece of land containing a hill and a hollow, if measured on the surface would give a larger content than it would after the hollow had been filled up by the hill, while it would yet really be of greater value than before. Horizontal measurement is called the "Method of Cultellation," and Superficial measurement, the "Method of Developement."† An act of the State of New-York prescribes that "The acre, for land measure, shall be measured horizontally." This question is more than two thousand years old, for Polybius writes, "Some even of those who are employed in the administration of states, or placed at the head of armies, imagine that unequal and hilly ground will contain more houses than a surface which is flat and level. This, however, is not the truth. For the houses being raised in a vertical line, form right angles, not with the de clivity of the ground, but with the flat surface which lies below, and upon which the hills themselves also stand." The former from Cultellum, a knife, as if the hills were sliced off; the latter to named because it strips off or unfolds, as it were, the surface. (57) Unit of Content. The Acre is the unit of land-measure ment. It contains 4 Roods. A Rood contains 40 Perches. A Perch is a square Rod; otherwise called a Perch, or Pole. A Rod is 5 yards, or 16 feet. Hence, 1 acre 4 Roods = 160 Perches = 4,840 square One square mile 5280 × 5280 feet 640 acres. = Since a chain is 66 feet long, a square chain contains 4356 square feet; and consequently ten square chains make one acre." In different parts of England, the acre varies greatly. The statute acre, as in the United States, contains 160 square perches of 16 feet, or 43,560 square feet. The acre of Devonshire and Somersetshire, contains 160 perches of 15 feet, or 36,000 square feet. The acre of Cornwall is 160 perches of 18 feet, or 51,810 square feet. The acre of Lancashire is 160 perches of 21 feet, or 70,560 square feet. The acre of Cheshire and Staffordshire, is 160 perches of 24 feet, or 92,160 square feet. The acre of Wiltshire is 120 perches of 16 feet, or 32,670 square feet. The acre in Scotland consists of 10 square chains, each of 74 feet, and therefore contains 54,760 square feet. The acre in Ireland is the same as the Lancashire. The chain is 84 feet long. The French units of land-measure are the Are 100 square Metres,=0.0247 acre, one fortieth of an acre, nearly; and the 2.47 acres, or nearly two and a half. Hectare 100 Ares Their old land-measures were the "Arpent of Paris," containing 36,800 square feet; and the "Arpent of Waters and Woods," containing 55,000 square feet. (58) When the content of a piece of land (obtained by any of the methods to be explained presently) is given in square links, as is customary, cut off four figures on the right, (i. e. divide by 10,000), to get it into square chains and decimal parts of a chain; cut off the right hand figure of the square chains, and the remaining figures will be Acres. Multiply the remainder by 4, and the figure, if any, outside of the new decimal point will be Roods. Let the young student beware of confounding 16 square chains with 10 chains square. The former make one acre; the latter space contains tea acres. Multiply the remainder by 40, and the outside figures will be Perches. The nearest round number is usually taken for the Perches; fractions less than a half perch being disregarded." (59) The following Table gives by mere inspection the Roods and Perches corresponding to the Decimal parts of an Acre. It explains itself. (65) Chain Correction. When a survey has been made, and the plat has been drawn, and the content calculated; and after *To reduce square yards to acres, instead of dividing by 4840, it is easier, and very nearly correct, to multiply by 2, cut off four figures, and add to this product one-third of one-tenth of itself. wards the chain is found to have been incorrect, too short or too long, the true content of the land, may be found by this proportion: As the square of the length of the standard given by the incorrect chain Is to the square of the true length of the standard So is the calculated content To the true content. Thus, suppose that the chain used had been so stretched that the standard distance measured by it appears to be only 99 links long; and that a square field had been measured by it, each side containing 10 of these long chains, and that it had been so platted. This plat, and therefore the content calculated from it, will be smaller than it should be, and the correct content will be found by the proportion 992: 1002 :: 100 sq. chains 102.03 square chains. If the chain had been stretched so as to be 101 true links long, as found by comparing it with a correct chain, the content would be given by this proportion: 1002 1012: 100 square chains : 102.01 square chains. In the former case, the elongation of the chain was 15 true links; and 1002 (101) :: 100 square chains 102.03 square chains. 2 (61) Boundary Lines. The lines which are to be considered as bounding the land to be surveyed, are often very uncertain, unless specified by the title deeds. If the boundary be a brook, the middle of it is usually the boundary line. On tide-waters, the land is usually considered to extend to low water mark. Where hedges and ditches are the boundaries of fields, as is almost universally the case in England, the dividing line is generally the top edge of the ditch farthest from the hedge, both hedge and ditch belonging to the field on the hedge side. This varies, however, with the customs of the locality. From three to six feet from the roots of the quickwood of the hedges are allowed for the ditches. |