Section 7. THEODOLITE SURVEYS. The adjustments and corrections in angular observation that may be required in using the theodolite are explained in Chapter I. As surveys in which the theodolite is used may be of any extent, large or small, and may be either for general or special purposes, they can only conveniently be classified under the heads of Triangulation surveys, and and combinations of the two; purely traverse surveys being more generally confined to special and engineering purposes, on works of communication. Triangulation surveys, as ordinarily conducted for topographical purposes of large or of moderate extent, are based on the same principles, operations, and modes of procedure as are now, or were originally adopted in the Great Trigonometrical surveys of large countries. These latter are beyond the scope of this work, but the operations employed in them will be referred to, not for exact imitation, but for the guidance they afford in carrying out corresponding operations with less precision on the same principles. The principal points in which such topographical surveys differ in operation from Great Trigonometrical surveys are the following. Ist. Astronomical observations of latitude and longitude are very frequently dispensed with. 2nd. The spheroidal form of the earth's surface is either entirely neglected, all triangles being treated as plane, or in extreme cases the very simple method of Legendre is adopted for treating large triangles as plane after applying a correction to the angles observed. 3rd. The country is completely covered by a network of triangulation, instead of divided into parallelograms by meridional and latitudinal series of triangles. 4th. The angular observations are made with small portable theodolites, having plates with graduated arcs of 4, 5, or 6 inches, and in exceptional cases 8 inches in diameter, which read to 20, 10, or 5 seconds, instead of with immense theodolites reading to hundredths of a second. 5th. The measurement of base lines is carried out with the simple surveyor's chain, and perhaps repeated a few times without using the troughs, trestles, straining weights, screw-marking-points and compensating bars adopted in the Great Trigonometrical survey. 6th. The whole scale of operation and the amount of accuracy required are smaller, the appliances more portable, the work more rapid, and the number of men employed less. The preliminary considerations before starting the actual surveying are: Ist. The extent of country to be surveyed and its nature: whether hilly, flat or cramped, or intersected by rivers, covered with buildings, wood, forest, or marsh, or any obstacles that may impede work in certain parts of it. 2nd. The scale on which the survey is to be delineated or represented; and the limiting error in measurement that becomes inappreciable on the final plan. 3rd. The amount of detail required: such as whether every field and hedgerow is to be shown on the plan, or whether every building, or only every block of buildings, or every frontage, or limit of holdings is to be shown. 4th. Any information that may bear on the special objects for which the survey may be made. 5th. The amount of time available, and the number of assistants, men, instruments, and appliances. Selection of Base Lines and Principal Stations.-These matters having been considered, the first operation is to examine the tract of land, country or town, with the view of choosing suitable positions for measuring a base line, and, if necessary, also bases of verification, and of arranging the distribution of the principal station-points over the whole tract. All such positions may then be roughly marked on the ground, and recorded with distinguishing letters or numbers in a rough sketch in the field-book. The conditions most favourable for a base line are an open flat extent of country, unimpeded by obstacles of any sort or long grass or vegetation; the ground moderately soft and capable of holding the iron pins or skewers used with measuring chains, or at least capable of being marked without chiselling at each chain length. The length required for a base line must be suited to the triangulation dependent on it; if the survey is extensive the sides of the main triangles are as long as possible in accordance with the powers of the theodolitetelescopes used, and as the form of triangle most suited to survey purposes is equilateral, the length of base line is then more governed by the two practical circumstances of the conditions of the ground and the powers of the instruments than by other considerations. The extremities of the base line should, when marked, be clearly visible from the country around, and hence an elevated plateau is an advantageous position for a base line of an extensive survey; but it is not by any means indispensable that the two extremities should be visible from each other; if circumstances are favorable in other respects, intermediate points in the base line may be ranged with extreme care to make up for the defect. Should it happen that the ground does not offer facilities for the direct measurement of a sufficiently long base, as may happen when other conditions are favorable, the greater portion of the base should be measured, and the length of an additional piece carefully obtained by calculation by any of the methods of prolonging bases hereafter described in the paragraph on measurement of base lines. The choice of station-points for the main triangulation, or principal network of triangles to be spread over the tract of country will necessarily be in accordance with the size of the triangles determined as most suitable to the conditions and extent of the tract, or the maximum and minimum limits laid down for the sides of these triangles; the position of the points should be so arranged that the signal flag at each one may be visible from the neighbouring points of observation, and thus admit of the observation of all three angles of every triangle; rather elevated points on open ground are hence to be preferred. If a spire or tower is made one of the main triangulation points, and happens to answer the purposes of a signal point only without affording facilities for setting up an instrument and taking angles from it, a satellite station of observation at a very short distance from the former must be used, and the angles observed there reduced by calculation to the point observed. (See formula in general collection.) This, however, should be avoided whenever possible. Two satellite. stations or two inaccessible points are inadmissible in any one triangle. The triangles adopted in main trian gulation should not have any angles less than 30° or greater than 120°, and are preferable when nearly equilateral. The demarcation of the survey points has been already treated on in section vi., Chapter I., pp. 67-69; but in this special branch, the marking of points for extensive main triangulation, it is necessary to mention that much loss of time may ensue from inability to find points badly marked, or from signals being removed or altered in position by the action of the wind; also, that however desirable it may be to have such triangulation as large and comprehensive as practicable, it is a considerable disadvantage to have to wait for very clear weather in order to discern very distant signal poles. In the Great Trigonometrical survey of a country it is worth while to wait months for an opportunity of observing on a very distant point, but in ordinary operations that is not the case, hence these practical disadvantages require attention. Next as regards very distant stations: the elevated signal point to be seen from a long distance has to be elevated in accordance with available means, and the corresponding point of observation on the ground or position of the instrument must be plumbed down; but at the same time, to afford the necessary amount of convenience, the height of the signal point, which is generally the point where the lower edge or sometimes the upper edge of the bunting joins the pole, should never be less than one foot per mile of the extreme distance of observation above the level of the lowest observing station in the immediate neighbourhood; it is, of course, better to elevate it more. When the signal pole is not fixed to branches of a tree or to other ready struc |