33. When the plane of reference is so chosen that the points of the work fall on different sides of it, all the references on one side are called positive, and those on the other, negative. The curves having a negative reference are distinguished by placing the minus sign before the number; thus-( ).

34. In topographical surveys, great care should be taken to leave some permanent marks, with their levels written. on them in a durable manner. For example, if there are any rocks, let one or more of them be smoothed, and the vertical distance from the plane of reference marked thereon: or let the vertical distance of a point on some prominent building, be ascertained and marked permanently on the building. Such points should also be noted on the map, so that a person, although unacquainted with the ground, could by means of the map, go upon it, and trace out all the points, together with their differences of level.

35. Besides representing the contour of the ground, it is often necessary to make a map which shall indicate the cultivated field, the woodland, the marsh, and the winding river. For this, certain characters, or conventional signs, have been agreed upon, as the representatives of things, and when these are once fixed in the mind, they readily suggest the objects for which they stand. Those which are given in Plates 5 and 6, have been adopted by the Engineer Department, and are used in all plans and maps made by the United States Engineers.

It is very desirable that a uniform method of delineation should be adopted, and none would seem to be of higher authority than that established by the Topographi cal Bureau. It is, therefore, recommended, that the conventional signs given in Plates 5 and 6, be carefully

BOOK I V.

GEODESIC, TRIGONOMETRIC AND MARITIME

SURVEYING.

SECTION I.

GEODESIC AND TRIGONOMETRIC SURVEYING.

1. WHEN a large extent of territory, or a long line of sea-coast is to be surveyed, it becomes necessary to consider the curvature of the earth's surface; this branch of surveying is called Geodesic surveying.

2. Extensive geodesic operations prove that the earth is an oblate spheroid, the shortest diameter of which coincides with the terrestrial axis, and all of whose meridians, are equal ellipses. The meridian lines, however, differ so little from the circumferences of circles, that they may be taken for them, except when great accuracy is required. The earth, will, therefore, in the following pages, be regarded as a perfect sphere.

3. The operations necessary to the successful execution of a Geodesic Survey, require the minutest attention, and when performed, numerous corrections are to be applied to the measured lines and angles, on account of the various causes of error incident to such operations.

To investigate those causes of error, and to deduce rules for correcting the errors, in all cases, would far exceed the limits of an elementary treatise. We shall, therefore,

of a trigonometric survey, with the application of some of the more important corrections.

4. It may be observed that most of the operations described in this section, are equally applicable, whether we regard the area surveyed as plane or spherical: in either case, the basis of an accurate survey, is an extensive system of triangulation.

5. After having made a preliminary examination or reconnaissance of the territory to be surveyed, suitable stations are selected at the most prominent points, and these points are marked by staves or signals.

A base line is then measured. The length of the base will, in general, depend upon the magnitude of the survey, and each extremity is marked by a signal.

The next step is the triangulation. At each extremity of the base, the angles between the base, and the lines drawn to each of the visible signals, are carefully measured by means of a theodolite. The sides of the triangles thus obtained, serve as new bases upon which other triangles may be formed, and so on, until the entire area is covered by a net-work of triangles.

6. This system of triangles is called the primary system, and the operation of forming them is called the primary triangulation. Within the primary triangles, and depending upon them, a system of smaller triangles is formed in the same manner, called the secondary system; and if the extent or importance of the work should demand it, the secondary may be sub-divided into tertiary triangles.

Having completed the triangulation, the characteristics of the surface, such as roads, streams, villages, boundaries, &c., are filled in by means of the compass, plain table, or some of the methods already explained.

After the field work is completed, the triangles, when regarded as spherical, are reduced by applying the formula for spherical excess, hereafter explained, and other necessary corrections, and thus the whole work is plotted upon

PRELIMINARY RECONNOISSANCE AND ESTABLISHMENT OF

SIGNALS.

7. Before commencing a trigonometrical survey, an examination 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 manner 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 desirable 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.