The chief points to be attended to in chaining are, 1°, to keep the chain in a horizontal position; 2°, to avoid straying from the line; 3°, to record without error the number of chains.

The first condition will be secured by the surveyor supporting, when necessary, the middle of the chain, and directing the elevation or depression of its extremities.

The second condition will be readily attained by the foreman fixing his attention upon the flag-staff or object of sight, thus drawing the chain constantly in line. His march will be corrected by the hindman, who will cry out "RIGHT!" "LEFT!" as the occasion may require.

Error in record will be guarded against by employing ten iron pins which should be turned at the top into a small ring, and tied with a piece of red flannel, the better to be seen. The foreman takes the ten pins and draws out the chain, the hindman, as it is near being stretched, cries "DOWN!" when the foreman, giving the chain a wave to bring its parts in line, pulls it tight and puts down a pin. Marching on he repeats the same operation, until, coming out empty-handed, he puts his foot upon the extremity of the chain to secure it in place, and cries "TALLY ONE !" and the hindman responds "tally one!" that the number may be fixed in the memory, also recording it in some way, as by a notch in a stick or a pebble put in the pocket, if thought necessary. He then, quitting the hind end of the chain, marches up to the foreman, who counts the pins to assure himself of the reception of the ten; when, stretching on, the second tally is executed like the first. A field may be surveyed by the chain alone, as illustrated by the subjoined

Field Notes.

Contour. AB = 237, BC= 4'67, CD=5'00, DE=4'98, EA=3'67, Diagonals. BD = 483, BE = 5'25 chs.

Required the angles of the pentagon.

The question naturally arises: ought we not to measure the inclined plane rather than its horizontal projection, since the surface of the former exceeds that of the latter? The answer to this question must be given in the negative, and for two reasons; 1o, a uniformity in surveying different lands is desirable, that they may be the more readily compared with each other, and it is obvious that this uniformity can be attained only by reducing them to their horizontal projections; 2°, the real value of a field cannot exceed

that of its horizontal projection, since no more soil will rest on an inclined plane than on its horizontal projection, and the same number of plants will stand upon the one as on the other. For let abcd represent a vertical section of the soil of an inclined plane; it is only equal to its horizontal projection efgh, the vertical depth ad being supposed equal to eh; and trees will grow as thick together on the inclined as on the horizontal plane.

The Surveyor's Cross.

t

Fig. 78.

The Cross has been already described and the method of using it in surveying pointed out. [See Book Second, Section First.] The student may now employ the chain and cross to survey a small field, and then compute its angles.

The Compass.

The Surveyor's or Azimuth Compass consists of a horizontal circle to which are attached sight-vanes, and a magnetic needle delicately balanced on its centre, by which the vanes may be directed to any point of the horizon so as to determine the inclination of Fig. 79. lines to the magnetic meridian, and, consequently, to each other. The degrees, marked on the limb of the instrument, are numbered from the north and south points, N. and S., both ways to the east and west, designated by the opposite letters, W. and E., for a reason that will presently appear.

To use the compass, set it firmly upon its staff (better and usually a tripod), furnished with a ball and socket joint, capable of being loosened or tightened at pleasure, by the aid of which and two spirit levels, placed at right angles to each other on the face of the instrument, the limb is to be brought into a horizontal position. When this is effected will be known by the bubbles remaining in the middle of the levels while the instrument is made to revolve on its axis. The needle is now to be let carefully down upon its pivot by a screw in the under side. See that it plays with its points just skimming along the graduated edge of the limb. Turn the vanes into the required direction by sighting at a staff wound with a red flag, and held vertically in line by an assistant stationed at a suitable distance. Observe if the needle settles with

a free motion, describing nearly equal arcs, slowly decreasing, on each side of a definite point, and if it finally rests at that point. Should there be any doubt as to this, the needle must be agitated, either by the attraction of a knife, or by gently tapping the tripod with the fingers, and be permitted to settle a second time. To insure a correct position of the needle is the principal difficulty in operating with the compass.

In order to prevent mistakes, that sight should be turned toward the flag staff which will bring the north end of the needle into the part of the compass marked N., or with the fleur de luce. The bearing will then be read off by the forward end of the needle, using the letters it stands between, as in the figure, N. 30° E., if the course be northerly, or S. 30° W., if in the opposite direction; both ends, however, are to be observed in estimating the amount of the angle. Back sights should be taken at each station in order to verify the bearings.

The Vernier or Nonius is a slip of metal, fitted to slide upon the graduated limb of an instrument, and to serve the purpose of an extended and impracticable subdivision.

If a denote the value of a division on the vernier, of which n cover n± 1 divisions of the instrument, we have

from which it appears that the distance, x 1, of the first division of the vernier from the first division of the instrument, will be an nth part of the unit of graduation-the distance, 2x-2, of the second division of the vernier from the second division of the limb will be two nths of the unit of graduation, and so on; so that, by sliding the vernier along the limb, we shall be enabled to measure spaces to the nth part of the smallest divisions of the instrument. Thus, if a scale По 1 2 3 4 5 6 7 have a division of 10ths, and 11 of these be covered by a

0 1 2 3 4 5 6 7 8 9

Fig. 80.

9 10

100

vernier of 10 divisions, we have n = 10, and .. - 1 = √ of to, of to,...; so that, by sliding the vernier along the

... 9

agree in succession, In like manner, if

2x-2 = scale to make the points, 1, 1; 2, 2; 3, 3, there results the measures 01; '02; '03, 30 divisions of the vernier attached to the compass, cover 29 halfdegree divisions of the instrument, we shall be enabled to measure angles to the minute. In some compasses the vernier is attached to the extremity of the needle, and, being carried along by it, the degrees and parts of a degree are read by simple inspection; in other instruments it is on the outside of the limb, and fastened by a clamp-screw from below, which must be loosened, when the vernier will be driven by a tangent screw adapted to the purpose.

The Theodolite.

The Theodolite consists essentially of a verti- [Frontispiece.] cal and horizontal circle, for the purpose of measuring angles in altitude and azimuth. It has, like the compass, spirit levels, by the aid of which and screws, the azimuth circle may be brought into a horizontal position. When this is accurately accomplished, the theodolite is ready to measure any horizontal angle having the angular point at its centre, provided all the parts of the instrument have been carefully adjusted. To this end, direct both the upper and lower telescopes (the first attached to the vertical circle, the second to the axis below the horizontal) to the same mark situated at a distance in one of the sides of the angle. Observe the position of the vernier upon the limb of the azimuth circle, reading the degrees and parts of a degree by one or more microscopes, fitted to this end-unclamp the upper telescope and direct it to a mark in the second side of the angle, clamping and finishing the motion by aid of the tangent screw. Observe, by the lower telescope, whether the azimuth circle has suffered any displacement by the motion required in making the second observation; if no such derangement has happened, the difference of the first and second readings will be the measure of the angle in question. In order to secure greater accuracy, the axis of the azimuth circle may be unclamped, the upper telescope brought back to the first mark, carrying the azimuth circle along with it-the azimuth again clamped, and the angle measured a second time. This operation repeated as often as desirable, the whole amount of arc passed over divided by the

number of observations, will give the angle required with a corresponding degree of exactness. We scarcely need say that the eyeglass must be drawn out or pushed in till the cross wires, indicating the line of sight-line of collimation, as it is called-shall be seen distinctly, and that the object glass is to be moved in like manner till the mark becomes well defined. In a similar way, a vertical angle will be measured by the vertical circle, having previously brought the telescope to a horizontal position and observed the reading, which should then be zero. When this horizontality shall be accomplished, will be determined by a level attached to the upper telescope, or, if no such level exist, by those already mentioned.

There are several adjustments, either permanently fixed by the instrument maker, or, for the execution of which, he furnishes means in screws and parts capable of being detached from each other.

There are five lines that should be respectively perpendicular to each other, viz., the vertical axis, or axis of the azimuth circle, the horizontal axis, or axis of the vertical circle, the horizontal line, or line of collimation when the vertical circle indicates zero, the vertical wire, and the horizontal wire-or

≤ (Ar, A.) = (H,A,) = (H, Ar) = (h,A。) = (v,Ar) = (h,H) = (v,H) = 90° ;

Fig. 81.

also the circles should be perpendicular to their axes. The method of testing these adjustments consists principally in reversing the lines (73); for which purpose the telescope and horizontal axis, one or both, may be lifted from their ys or supports, the object and eyeglasses change places, or the vernier plate carrying the vertical circle and the telescope, revolved 180°. Also the wires, h, v, which form by their intersection the line of collimation, being attached to a ring, may be moved to the right or left, elevated or depressed by screws from without. Fig. 812.

If we direct the line H to a distant and well-defined

mark, and, when the telescope is reversed, find the sight upon the same mark, we may be assured that the line of collimation, H, is perpendicular to the horizontal axis A. This adjustment perfected, the horizontal axis, A, will be perpendicular to the vertical, A., when, passing the line of collimation,

H

Fig. 813.