PRELIMINARY RECONNOISSANCE AND ESTABLISHMENT OF SIGNALS. 7. Before commencing a trigonometrical survey, “u ex amination of the entire territory should be made for the purpose of selecting a location for the base line, and proper points for stations; this examination should be more or less elaborate, according to the nature and extent of the survey. The proper distribution and combination of the triangles, so as to adapt them to the survey in hand, require great judgment and care, and but few rules can be given for the selection of trigonometrical points. Those points should, in general, be chosen in such a manner, that they may be distinctly visible from each other, and so that the triangles formed, by uniting them, may be as nearly as possible equilateral. It is easily seen, that a triangle which has an obtuse or a very acute angle, will experience a greater change of form for a given error, than one which is nearly equilateral; and since the accuracy of each triangle depends upon the preceding ones, it is further evident, that the introduction of a single ill-conditioned triangle, might vitiate the whole survey. Except in extreme cases, no angle, less than 30°, should be used, and even angles of 30° should not be admitted when the locality can be so chosen as to prevent it. The base is usually much shorter than the sides of the primary triangles; these sides, however, should be increased as rapidly as is consistent with the above remarks. 8. The accompanying diagram will illustrate the Lanner of increasing the sides without introducing ill-conditioned triangles. Having measured the base AB, and the requisite angles, the triangles ABC and ABD, may be determined, and the line DC computed; with DC as a base, the triangles DCE and DCF are formed, and thence EHF, and EGF, in which the sides are much greater than the In this manner the sides may be increased to any de sirable extent. An ordinary map of the country, or a sketch made with the pocket compass, will be of material assistance in making a proper distribution of the stations. 9. The stations are marked by signals, which may be constructed in a great variety of ways, depending upon the locality of the stations, and the lengths of the sides of the triangles. Sometimes a signal has to be raised above the level of the adjacent country, in which case it is constructed of timbers, and upon the apex, is placed a vertical staff, bearing a flag. The exact trigonometrical point is determined by a plumb-line, suspended from the apex of the signal. A temporary signal may be constructed with three, or four pieces of scantling framed and traced, as shown in the annexed figure, with a short pole projecting from the apex. The plumb determines the point B, which is the exact trigonometrical point over which the theodolite is to be placed. Where the sides of the triangles are not very great, a pole, planted vertically, and surmounted by a flag, will answer as a signal. In order to distinguish the different signals, the flags which they bear, should be different from each other. red, according to some pre-arranged plan, and the flags of the different stations should be entered in a book. For the purpose of future reference, the trigonometrical point, at each station, as B, should be indicated by a permanent mark. If the point falls upon a rock, a hole may be drilled to show the locality; or if not, a mark-stone may be sunk under the point, deep enough to be beyond the reach of accident. A record of the monument should be preserved, together with its reference to some of the permanent objects in the neighborhood. In order to render the signals visible from the distant stations, polished tin plates are sometimes attached to the signal-post, so as to reflect the sun towards the stations at certain hours of the day. The Drummond-light has also been used to show very distant stations. A light may also be produced that can be seen at a distance of 60 or 70 miles, by placing a ball of lime about a quarter of an inch in diameter, in the focus of a parabolic reflector, and heating it intensely by a stream of oxygen gas, directed by a blow-pipe, through a flame of alcohol. If obstacles, as trees, and under-brush intervene, vistas have to be opened along the lines, from station to station. MEASUREMENT OF A BASE LINE. 10. The measurement of a base line on which the ac curacy of the entire survey depends, is one of the most difficult operations of geodesic surveying, and one, for the successful accomplishment of which, art and science have been strongly taxed. The selection of a proper site for à base line, forms one of the first objects of the preliminary reconnaissance. It should, if possible, be fixed on an open plain. It must be so chosen, that the surrounding signals. may be distinctly seen from its extreme points; and hence, those signals which mark points of the adjacent triangula tion, should be selected with reference to the base. The length of the base, should, in a measure, depend upon the magnitude of the survey, though circumstances seldom 11. Different instruments have been used for measuring base lines, such as steel chains, glass, platinum and deal rods; and more recently, a combination of rods, of differ ent metals, so adjusted, that the apparatus maintains an invariable length at all temperatures. This last mentioned apparatus, has been much improved, and most successfully used by Prof. Bache, in the Survey of the United States Coast. 12. In minor surveys, where the base line does not much exceed 1000 or 2000 feet, sufficient accuracy may be attained by the use of wooden rods. To render the rods less susceptible of change, from moisture, they should be saturated with boiling oil, and covered with a thick coating of varnish. The ends of the rods should be protected by metallic caps, which prevent their wearing, and insure a more perfect contact. When the rods are prepared for use, they should be carefully compared with some standard measure, and from time to time this comparison should be repeated, in order to detect any minute change of length, should such change take place. 13. The following method of measuring a base line of 1000 or 2000 feet, may be rendered very accurate. Having decided upon the direction of the base, and measured it carefully, two or three times with a chain, let a theodolite be planted at one end of the line, and directed upon a flag, planted at the other. Then, by means of the vertical limb, let a row of pickets be driven along the base, taking care to plant them at a distance from each other, equal to the length of one of the deal rods. Then, plant in the place of each picket, a vertical post, 6 or 8 inches in diameter, and projecting a sufficient distance above the surface of the ground. If necessary, let the posts be steadied by heaping about them, earth or stones. Next, with the assistance of a spirit-level, let each post be sawed off, so as to bring their tops to the same horizontal 12 plane, and by means of the theodolite, let a line be marked on the top of each post, in the direction of the base. This line will determine the direction in which the rods are to be placed, and the contact of the ends must all be on this line. The contact of the rods should be made with great care, so as to avoid moving the rod already established; and this will be more readily done, when three rods are used. The measurement should be repeated two or three times. to guard against error. 14. If the nature of the ground does not admit of the posts being brought to a level, let them, by means of the theodolite, be brought into an oblique plane AB, and after B Ар having measured, as before, the line AB, determine accurately the difference of level between the points A and B, equal to BC: then, from the right-angled triangle ABC, we should find the horizontal distance AC = √AB - BC2. . 15. In very extensive surveys, the base should be several miles in length, and the apparatus for measurement, as well as the operations on the field, become more complicated. For a full description of a very perfect base apparatus, and the method of using it, the reader is referred to Prof. Bache's pamphlet, on the subject—the details of the description would exceed our limits. TRIANGULATION. 16. The theodolite is generally used for measuring the angles of a trigonometric survey. The extent of the survey, and the standard of accuracy to which the results are re quired to conform, must determine the size and perfection of the instrument to be employed. The angles of the pri mary triangles of the United States Coast Survey, are meas |