PART III. 12. MEASURES USED FOR SURVEYING PURPOSES OR FOR THE MEASUREMENT OF LAND. metrical In a trigonometrical survey like that of the Ordnance TrigonoSurvey Department of Great Britain (now a department surveys. of the Board of Agriculture), the object of the survey may be said to be to determine the position of various points on the earth's surface which are far apart one from the other, and consequently to measure the distance between such points, and our cadastral maps are the outcome of such surveying. Geodetical measurements, on the other hand, relate mainly to the mathematical determination of the general figure of the earth. For trigonometrical purposes there are measured "baselines," of from 3 to 10 miles in length, by means of standard bars, made of iron or steel, of the length of 10 feet or of 1 or more metres; and from such base lines there starts a system of triangulations by means of which the positions of the various points on the earth's surface are determined. An account of the Great Trigonometrical Survey of this country begun in 1783 has been given by General Sir H. James, R.E. (London, 1858); and accounts of other trigonometrical surveys abroad have also been published, as of the Survey of India by General J. T. Walker (Dehra Doon, 1870); "Base Centrale de la Triangulation Géodésique d'Espagne (Madrid, 1865); "The Geodetic Survey of the United States" (Washington, 1866-1894); Report on "The Geodetic Survey of South Africa," by Dr. Gill (Government Printers, Cape Town, 1896,), &c. The principal base line measured in Great Britain was originally that on Salisbury Plain, by General Mudge in 1794; and in Ireland that of Lough Foyle in 1827-8, by General Colby; and a plan of the principal triangles in England and Wales and part of Scotland, showing the connections with the base lines on Salisbury Plain and Lough Foyle, has been issued by the Ordnance Survey Department. The difference in the British measurement of the Salisbury Plain base (1849) from that obtained by calculation through a large number of triangles starting from the Lough Foyle base was not more than 0.2 feet. The most recent of direct trigonometrical measurements is perhaps that of South Africa, when a base line of 6,000 feet was measured in two sections by means of standard bars, the probable sum of errors of one section being stated to be only± 0.023 inch and of the other section± 0·016 inch. All the English measurements are referred to the Imperial yard, a copy of which is kept at the headquarters of the Ordnance Survey at Southampton, the normal temperature followed being that of the Imperial Yard, viz., 62° Fahrenheit. An important statement as to the progress of the Ordnance Survey to 31st December 1893, may be found in the recent Report of a Departmental Committee, which included Sir J. Dorrington, Bart., M.P.; Sir A. Geikie, F.R.S.; Lieut.General Cooke, C.B.; and Major D. A. Johnston, R.E., as Secretary. As the length of a metal bar (as a 10 ft. steel survey standard) depends on the temperature of the bar, and as trigonometrical measurements have to be made in different latitudes, and at various temperatures, it becomes necessary to allow for the expansion of a bar by heat. For such purpose the rate of expansion of a bar may be experimentally determined (for instance, it has been found that a 10 ft. steel bar expands 0·0007632 inch for a rise in temperature of 1° Fahrenheit, or its "coefficient" of linear expansion for 1° Fahrenheit would be represented by 0-00000636). Or the expansion of a bar may be allowed for mechanically, as in the English and Indian surveys, by the use of compensating bars. In European surveys the old French toise and the old Austrian klafter were formerly used; now, however, the most of European geodedic surveys are expressed in The earliest triangulations, as those of Picard in France in 1667, which were referred to the toise, are stated to have enabled Sir Isaac Newton to establish finally his doctrine of gravitation, as published in his Principia in 1687, when he showed that the earth must be in the form of an oblate spheroid, and that gravity must be less at the equator than at the poles, as was proved by subsequent measures with a toise standard in Peru in 1735. ment For field and office work a variety of survey units are Measureused with a corresponding diversity of scale. The maps of land. of our Ordnance Survey are set out in Imperial units as follows: or 126.720 inches to the mile. 2500 or 25.344 inches to the mile. Tos60 or 6 inches to the mile. 63360 or 1 inch to the mile.. The scale maps cover almost the whole of the towns and parishes, and the 6-inch maps the whole of the United Kingdom. Town maps are also published to the scale of 5 feet and 10 feet to the mile. (See Catalogue of Maps, issued by the Director-General, Ordnance Surveys, 1896.) For plotting land measurements surveyors use finely divided scales showing 20 chains to a quarter mile, and 2 chains to the inch, represented by 200 divisions to the inch. In the mensuration of plane surfaces the following table of measures is followed :— 100,000 square links = 1 acre. As one link equals 7.92, inches we may find the area of a rectangular piece of ground in the following manner: Suppose the length of the ground is 792 links and its breadth 385 links, find its area in acres, roods, and perches. 792 × 385 links = 304,920 square links; as 40 perches equal 1 rood and 4 roods equal 1 acre, cut off five figures from 304,920 square links and the result will be 3.04920 acres. Multiply the decimal 0.04920 by 4 and 40 and the result will be-Answer 3 acres, 0 roods, 7.872 perches. In the United States the Imperial units appear also to be followed in private practice, drawings being made of so many feet to the inch, and where a surveyor uses a Gunter's chain of 66 feet, he plots his work to so many chains to the inch. Engineers in using a 100 feet chain, and measuring rods divided into decimal parts of a foot, also generally reduce maps to the inch units. measuring ments. A measuring wheel (viameter) is used for measuring Portable approximately distances along roads, as cab distances, &c. land The wheel is rolled over the ground to be measured and instruthe motion is communicated to a series of toothed wheels so proportioned that the index wheel registers the revolutions of the measuring wheel. Of course unless a straight or given line is followed, this measuring wheel will give uncertain results. Various other forms of instruments are also used for such purposes known as odometers, distance indicators, way-measurers, &c. The pedometer is an instrument sometimes used for counting and recording the number of steps taken by a person carrying it. Other and more accurate instruments are also used in the survey of land, as telemeters for finding the distances of inaccessible objects; or for measuring and calculating the areas of plane surfaces, as planimeters. Of course in the measurement of "base-lines," for the determination of astronomical positions other well known instruments are used, as the theodolite, zenith sector or transit instrument, &c. In measuring lines on maps, whether curved or straight, without the use of a rule or linear scale, small instruments are sometimes used known as the diagrammeter, opisometer graphometer, &c. measure ments. Steel chains of 100 feet and of 66 feet divided into Chain links, were at one time used in the Ordnance Survey, and were stretched in wooden-trays between a drawing-post and a weight-post with a "pull" of 56 lbs. In India the earlier survey measurements of Colonel Lambton up to 1826 were made by a Ramsden 100 feet steel chain, of a form described in the Philosophical Transactions of the Royal Society. Chain measures are, of course, still commonly used in the Ordnance Survey, and chaining officers have the following instruction : “The chain and tape (when it has to be used) must be compared with the standard every morning on parade, and F |