be surveyed at a future time, the old lines can always be

re-run.

123. It has been found, by observation, that heat and cold sensibly affect the magnetic needle, and that the same needle will, at the same place, indicate different lines at different hours of the day.

If the magnetic meridian be observed early in the morning, and again at different hours of the day, it will be found that the needle will continue to recede from the meridian as the day advances, until about the time of the highest temperature, when it will begin to return, and at evening will make the same line as in the morning. This change is called the diurnal variation, and varies, sometimes, during the summer season, from one-fifth to one-fourth of a degree.

124. A very near approximation to a true meridian, and consequently to the variation, may be had, by remembering that the pole-star very nearly reaches the true meridian, when it is in the same vertical plane with the star Alioth in the tail of the Great Bear, which lies nearest the four stars forming the quadrilateral.

The vertical position can be ascertained by means of a plumb-line. To see the spider's lines in the field of the telescope, at the same time with the star, a faint light should be placed near the object-glass. When the plumb-line, the star Alioth, and the north star, fall on the vertical spider's line, the horizontal limb is firmly clamped, and the telescope brought down to the horizon; a light, seen through a small aperture in a board, and held at some distance

by an assistant, is then moved according to signals, until it is

covered by the intersection of the spider's lines. A picket driven into the ground, under the light, serves to mark the meridian line for reference by day, when the angle formed by it and the magnetic meridian may be measured.

SECTION IV.

TRIANGULATION.

125. 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.

126. 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, attempt nothing more than a brief outline of the operations in a trigonometrical survey, in which the Plane-Table and Compass are used in connection with the Theodolite, and in which, the curvature of the earth is not considered. We shall then explain the methods of mapping, or plotting, such a survey. The example will be limited to the survey of the harbor, delineated in plate 6.

127. 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

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.

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 subdivided 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, plane-table, or some of the methods already explained.

128. 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.

129. 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. They may be formed by arranging stripes of white and red, according to

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.

130. The measurement of a base-line on which the accuracy of the entire survey depends, is one of the most difficult operations of surveying, and one, for the successful accomplishment of which, art and science have been strongly taxed. The selection of a proper site for a 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 triangulation, should be selected with reference to the base. The length of the base, should, in a measure, depend upon the magnitude of the survey.

THEODOLITE.

131. 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 required to conform, must determine the size and perfection of the instrument to be employed. The angles of the primary triangles of the United States Coast Survey are measured with theodolites, whose horizontal circles are 24 or 30 inches in diameter; and to eliminate, as much as possible, every source of error, great numbers of observations are made at each station, the readings being made on different points of the arc by different