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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 accuracy 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 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, 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 different 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

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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

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 = √AB2 – 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 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 meas

inches in diameter; and to eliminate as much as possible, every source of error, great numbers of operations are made on each station, the readings being made on different points of the arc. Usually from 40 to 60 observations are made for each angle-one measurement, with the telescope direct, and one with it reverted, constituting a complete observa tion. With these precautions, it has been found that the error in a primary triangle (where the sum of its three angles has been compared with 180°), has fallen much within 3 seconds. The error of 3 seconds has been adopted as the highest admissible limit of error.

17. Observations are also made at the principal stations upon the pole-star, and other stars near the pole, for the purpose of determining the angle, made by the sides of the triangle with the meridian. In minor surveys, and in a secondary triangulation, the operations are much less elaborate; still; every precaution is to be taken to insure the greatest attainable accuracy. As a general rule, all the angles of every triangle, should be measured, if possible.

18. To illustrate the manner of carrying on a minor triangulation, let us refer to the plan of the harbor [plate 6], in which AB is the measured base, C, D, E, &c., triangulation points, at which signals have been erected. Commence the triangulation at A, the west end of the base; and for convenience in plotting, it would be well to make the line, passing through the 0 point, and 180° parallel, in each position of the instrument, to the base AB. Having brought the 0 of the vernier to the 0 of the limb, clamp the vernier plate, and direct the upper telescope to the signal at B, and clamp the limb. observation as in the following table:

OBSERVATION AT STATION A.

Enter the

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Having recorded the reading of the first vernier, and the minutes and seconds of the second vernier, unclamp the vernier plate, and direct the telescope to the station at E, and record both verniers, as before. Again unclamp the vernier plate, and direct the telescope on the signal at G; and then read and record, as before.

Having determined the angles subtended by all the signals visible from A, let the theodolite be removed to B. Bring the 0 of the vernier I to 180° on the limb, and direct the telescope on the signal at A-the line (0°, 180°) will then be parallel to its first position, and the limb may be clamped. Read now the angles to the signals at A, E, C, &c., and record as before.

If the theodolite is now removed to the station E, the line (0°, 180°), may be made parallel to its first position, by adding 180° to the reading of the first vernier, from A to E, and then directing the telescope on the signal at A. The line (0°, 180°), will thus be made parallel to AB, and the reading may be made and recorded as before; and so on until all the stations have been visited, and the angles measured. From the field records, the angles BAE, EAG, ABE, EBG, &c., may be easily deduced, the whole may be plotted on paper, or the several sides may be computed trigonometrically. It may be observed that the line (0°, 180°), has been made parallel to the base line at each station; where great accuracy is required, this cannot be done, since a single reading is insufficient to give the angle. The angle is then determined, as directed in the previous article, or by means of the principle of repetition.

19. To illustrate this principle of repetition, suppose the 0 of the vernier to coincide with the 0 of the limb, and the telescope to be directed, from the station A, upon one of the objects, as the signal at B. Clamp the limb, and unclamping the vernier plate, direct the telescope on the second object, as the signal at E. If we now clamp the vernier plate, and unclamping the limb, direct the telescope on the signal at B, the line (0°, 180°), of the limb, will make

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