FIG. 84. is the most trustworthy that has yet been devised,* but some topographers prefer to count the revolutions of the wheel directly, using an arrangemen which rings a bell at each revolution. The circumference of the wagon wheel having been measured, the number of feet traveled can be at once ascertained by multiplying the circumference of the wheel by the number of revolutions made by it. The most accurate method of getting this circumference is to divide some known distance on a road (a mile, for example), by the number of revolutions the wheel makes in passing over it. This practically compensates for the slip of the wheel on roads similar to that used. Distances may also be measured with the Gradienter, and with the Transit and Stadia, to be explained hereafter. *The works are contained in a solid metal case, with glass covering the face of the dial. On the outer rim of the dial are 100 divisions read by an index securely attached to an under wheel with 100 cogs and carried forward one space by every outward movement of the steel lever shown. A wheel (Fig 84a), with 99 divisions and 99 cogs upon it, revolves under the index and on top of the wheel with 100 cogs, and makes a complete revolution and one division for every complete revolution of the index. The Odometer is fastened to the axle, as shown, a cam on the hub giving the FIG. 84 a. outward motion to the steel lever. CHAPTER VI. EXPANSION OF A SURVEY. The base-line having been measured, the next step is the expansion, which consists in the selection of stations, erection of signals, and the measurement of angles, keeping in mind the principle to work from the whole to a part, from greater to less, and to enter on no small operations early in the work. THE SELECTION OF STATIONS.*- The Stations, which are *Upon the proper selection of stations, together with the site for the base-line, depends, in a great measure, the value of the subsequent work. For this, experience and judgment are necessary. The reconnoitering officer must, in locating stations, consider the effects of the resulting triangles; compare the relative cost of cutting out lines and building high stations; foresee and avoid any disturbing influences or obstructions, etc. He usually provides himself with a pocket sextant for measuring angles between stations, a pocket compass for determin FIG. 91. F16.92. Fig. 93. FIG. 94. to be the vertices of the triangles, to be observed to and from, must be so selected as to form strong figures, in order to reduce to a minimum the errors which will creep in. No triangle should have an angle of less than 30°, nor more than 120°. The stations should be located on commanding ground, if possible, so as to be intervisible. They should be selected, as far as consistent with accuracy, with reference to the needs of the topographers-i. e., so as to have at least two or more fall upon a single field sheet. D The triangulation may be extended by continually increasing the sides of the triangles as in Fig. 90, where AB is the measured base-line, C and D are observed upon giving a new base CD, from the ends of which E and F are observed upon giving a new base EF, and so on. F16. 90. The triangulation stations are first plotted on the sheet that is to contain the finished map, and are usually surrounded by a triangle, thus A, which is read triangulation station. For ing the direction of lines, an aneroid barometer for determining approximate elevations, a pair of field-glasses, and climbers or tackle for going up trees. Having located a station, it is temporarily marked by a flag on a pole. Having arrived near where a station would be desirable, the highest ground in the vicinity is ascended, and if there are trees, a house, tower, or other high object on it, one is climbed, and with the fieldglasses a search is made for other stations. If no trees or other objects are available, ladders may be used, being held up by ropes. In cases where the triangulation takes the form of narrow belts of figures, simple triangles or quadrilaterals are the most desirable. The least expensive and most rapidly executed would be as in Fig. 91. If the greatest attainable accuracy is desired, then Fig. 92 would be used. If the greatest area is to be covered for a given degree of accuracy and cost, then Figs. 93 or 94 would be used. The reasons for using the above figures in different cases will be found in Appendix No. 15, Coast Survey Report of 1876. "filling in" the details, the area is divided into small tracts embracing 2, 3, or more triangulation points, which are transferred to the field sheets, and all information in regard to them given to the one in charge of the details. The plotting of the triangulation points consists in locating them to scale on the paper in their true relative positions.* THE SIGNALS.-These should be high, conspicuous, and so made that the instrument can be placed precisely under them, at the same time being of the simplest and least expensive form that will serve the purpose. A pyramid of three or four timbers surmounted by a staff may be used in many cases, or a stout post set in the ground on the side of which a staff is held for observing upon and removed when using the instrument there. When necessary to raise the instrument above the ground to overlook surrounding obstacles, structures for supporting the instrument should be combined with the signals. These should consist of an interior structure for the support of the instrument and an outer structure with a platform for the observer. The two should be separate to avoid jarring the instrument. To the signal staff is usually attached some kind of a target to make it more conspicuous, as red and white flags if seen against the ground, and red and green if seen against the sky. *The method employed depends on the extent of the earth's surface to be represented, the purpose of the survey, and the accuracy required. For very large areas on a single sheet, such as the U. S. Coast, Lake, and Geodetic Surveys include, the earth's sphericity must be considered and the polyconic projection of meridians and parallels be used. Points are plotted from computed latitudes and longitudes. For areas of not more than 100 square miles, in which the effect of the earth's sphericity is so mall that it may be neglected, the rectangular projection of meridians and parallels may be used, and points plotted from polar coördin1 ́es (azimuth and distance) or from rectangular coördinates (latitude and departure). Of these the latter is better, as each point is independently located and cumulative errors are avoided. |