ELEMENTS OF SURVEYING. CHAPTER I Definitions and Introductory Remarks. €8. Surveying, in its most extensive signification, comprises all the operations necessary for finding. 1st. The area or content of any portion of the surface of the earth; 2d. The lengths and directions of the bounding lines; and 3d. The accurate delineation of the whole on paper. 69. The earth being spherical, its surface is curved, and every line traced on its surface is also curved. If large portions of the surface are to be measured, such as states and territories, the curvature must be taken into account; and very material errors will arise if it be neglected. When the curvature is considered, the method of measurement and computation is called Geodesic Surveying. The radius of the earth, however, being large, the curvature of its surface is small, and when the measurement is limited to small portions of the surface, the error becomes insensible, if we consider the surface a plane. This method of measurement and computation, is called Plane Surveying, and is the only kind that will be treated of in these Elements. 70. If at any point of the surface of the earth, a plane be drawn perpendicular to the radius passing through this point, such plane is tangent to the surface, and is called a horizontal plane. All planes parallel to such a plane, are also called horizontal planes. 71. A plane which is perpendicular to a horizontal plane le called a vertical plane. 72. All lines of a horizontal plane, and all lines which are parallel to it, are called horizontal lines. 73. Lines which are perpendicular to a horizontal plane, are called vertical lines; and all lines which are inclined to it, are called oblique lines. Thus, AB and DC are horizontal lines; BC and AD are vertical lines; and AC and BD are oblique lines. D A 74. The horizontal distance between two points, is the horizontal line intercepted between the two vertical lines passing through those points. Thus, DC or AB is the horizontal distance between the two points A and C, or the points B and D. 75. A horizontal angle is one whose sides are horizontal; its plane is also horizontal. A horizontal angle may also be defined to be, the angle included between two vertical plunes passing through the angular point, and the two objects which subtend the angle. 76. A vertical angle is one, the plane of whose sides is vertical. 77. An angle of elevation, is a vertical angle having one of its sides horizontal, and the inclined side above the horizontal side. Thus, in the last figure, BAC is the angle of elevation from A to C. 78. An angle of depression, is a vertical angle having one of its sides horizontal, and the inclined side under the horizontal side. Thus, DCA is the angle of depression from C to A. 79. An oblique angle is one, the plane of whose sides is oblique to the horizontal plane. 80. All lines, which can be the object of measurement. must belong to one of the classes above named, viz.:. 1st. Horizontal lines: 2d. Vertical lines: d. Oblique lines. ll the angles may also be divided into three classes, viz.: 2d. Vertical angles; which may be again divided into angles of elevation and angles of depression: and 3d. Oblique angles. CHAPTER II. Of the measurement and calculation of Lines and Angles. 81. It has been shown (Art. 62), that at least one side and two of the other parts of a plane triangle must be given or known, before the remaining parts can be found by calculation. When, therefore, distances are to be found, by trigonomet rical calculations, two things are necessary. 1st. To measure certain lines on the ground; and also, as many angles as may be necessary to render at least three parts of every triangle known: and 2d. To calculate, by trigonometry, the other sides and angles that may be required. Our attention, then, is directed, 1st. To the measurement of lines; 2d. To the measurement of angles; and 3d. To the calculations for the unknown and required parts. 82. Any tape, rod, or chain, on which equal parts are marked, may be used as a measure; and one of the equal parts into which the measure is divided, is called the unit of the measure. The unit of a measure may be a foot, a yard, a rod, or any other ascertained distance. 83. The measure in general use, is a chain of four rods or sixty-six feet in length; it is called Gunter's chain, from the name of the inventor. This chain is composed of 100 links. Every tenth link from either end, is marked by a small attached brass plate, which is notched, to designate its number from the end. The division of the chain into 100 equal parts, is a very convenient one, since the divisions or links, are decimals of the whole chain, and in the calculations may be treated as such. TABLE. 1 chain 4 rods =66 feet=792 inches=100 links. Hence, 1 link is equal to 7.92 inches. 80 chains=320 rods=1 mile. 40 chains mile. 84. Besides the chain, there are wanted for measuring, ten marking pins, which should be of iron, about ten inches in length and an eighth of an inch in thickness. These pins should be strung upon an iron ring, and this ring should be attached to a belt, to be passed over the right shoulder, suspending the pins at the left side. Two staves are also required. They should be about six feet in length, and have a spike in the lower end to aid in holding them firmly, and a horizontal strip of iron to prevent the chain from slipping off; these staves are to be passed through the rings at the ends of the chain. TO MEASURE A HORIZONTAL LINE. 85. At the point where the measurement is to be begun, place in a vertical position, a signal staff, having a small flag attached to its upper extremity; and place another at the point where the measurement is to be terminated. These two points are generally called stations. Having passed the staves through the rings of the chain, let the ten marking pins and one end of the chain be taken by the person who is to go forward, and who is called the leader, and let him plant the staff as nearly as possible in the direction of the stations. Then, taking the staff in his right hand, let him stand off at arm's length, so that the person at the other end of the chain can align it exactly with the stations : when the alignment is made, let the chain be stretched and a marking pin placed; then measure a second chain in the same manner, and so on, until all the marking pins shall have been placed. When the marking pins are exhausted, a note should be made, that ten chains have been measured; after which, the marking pins are to be returned to the leader, and the measurement continued as before, until the whole distance Great care must be taken to keep the chain horizontal, and if the acclivity or declivity of the ground be too great to admit of measuring a whole chain at a time, a part of a chain only should be measured the sum of all the horizontal lines so measured, is evidently the horizontal distance between the stations. A For example, in measuring the horizontal distance between and C, we first place a staff at A and another at b, in the direction towards C. Then slide up the chain on the staff at A until it becomes horizontal, and note the distance ab. Then remove the A staves and place them at b and d: B make the chain horizontal, and note the distance cd. Measure in the same manner the line fC; and the sum of the horizontal lines ab, cd and fC, will be equal to AB, the horizontal distance between A and C. 86. We come now to the measurement of angles, and for this purpose several instruments are used. The one, however, which affords the most accurate results, and which indeed can alone be relied on for nice or extensive operations, is called a Theodolite. This instrument only will be described at present; others will be subsequently explained. OF THE THEODOLITE. Pl. 1. The theodolite is an instrument used to measure horizontal and vertical angles. It is usually placed on a tripod ABC, which enters by means of a screw the lower horizontal plate DE, and becomes firmly attached to the body of the instrument. Through the horizontal plate DE, four small hollow cylinders are inserted, which receive four screws with milled heads, that work against a second horizontal plate, FG. The upper side of the plate DE terminates in a curved surface, which encompasses a ball, that is nearly a semi-sphere, with the plane of its base horizontal. This ball, which is hollow, is firmly connected with the smaller base of a hollow conic frustrum, that passes through the curved part |