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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=1 mile.

20 chains=1 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 chair, 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.

For example, in measuring the horizontal distance between A 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 Then remove them!

'B staves and place them at b and d: 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 of the plate DE, and screws firmly into the curved part of the second horizontal plate FG.

A hollow conic spindle passes through the middle of the ball, and the hollow frustrum with which it is connected. To this spindle, a third horizontal and circular plate HI, called the limb of the instrument, is permanently attached. Within this spindle, and concentric with it, there is a second spindle, called the inner, or solid spindle. To this latter, is united a thin circular plate, called the vernier plate, which rests on the limb of the instrument, and supports the upper frame-work. The two spindles terminate at the base of the spherical ball, where a small screw enters the inner one, and presses a washer against the other, and the base of the ball. On the upper surface of the plate FG, rests a clamp which goes round the outer spindle, and which being compressed by the clampscrew K, is made fast to it. This clamp is thus connected with the plate FG. A small cylinder a, is fastened to the plate FG: through this cylinder a thumb-screw L passes, and works into a small cylinder b, connected with the clamp. The cylinders b and a, admit of a motion round their axes, to relieve the screw L of the pressure which would otherwise be occasioned by working it.

Directly above the clamp, is the lower telescope MN. This telescope is connected with a hollow cylinder, which is worked freely round the outer spindle, by the thumb-screw P having a pinion working into a concealed cog-wheel, that is permanently fastened to the limb of the instrument. Ву means of a clap-screw Q, the telescope is made fast to the limb, when it will have a common motion with the limb and outer spindle.

The circular edge of the limb is chamfered, and is generally made of silver, and on this circle the graduation for horizontal angles is made. In the instrument described, the circle is cut into degrees and half degrees; the degrees are numbered from 0 to 360.

On the circular edge of the vernier plate, is a small space of silver, called a vernier; this space is divided into 30 equal parts, and numbered from the line marked o to the left.

There are two levels attached to the vernier plate, at right angles to each other, by small adjusting screws; one of them

with the inner spindle. It is made fast to the limb of the instrument by the clamp-screw S; after which the smaller motions are made by the tangent-screw T.

There is a compass on the vernier plate, that is concentric with it, the use of which will be explained under the head compass.

The frame-work which supports the horizontal axis of the vertical semicircle UV and the upper telescope, with its attached level, rests on the vernier plate, to which it is made fast by three adjusting screws, placed at the angular points of an equilateral triangle. The vertical semicircle UV, is called the vertical limb; its motions are governed by the thumb-screw 2, which has a pinion, that works with the teeth of the vertical limb. On the face of the vertical limb, opposite the thumb-screw Z, the limb is divided into degrees and half degrees : the degrees are numbered both ways from the line marked o. There is a small plate resting against the graduated face of the vertical limb, called the vernier; it is divided into 30 equal parts, and the middle line is designated by 0.

On the other face of the vertical limb, are two ranges of divisions, commencing at the point, and extending each way 45°. The one shows the vertical distance of any object to which the upper telescope is directed, above or below the place of the instrument, in 100th parts of the horizontal distance : the other, the difference between the hypothenusal and base lines: the hypothenuse being supposed to be divided into one hundred equal parts: therefore, by mere inspection, we can ascertain the number of links, which must be subtracted from every chain of an oblique line, to reduce it to a true horizontal distance.

The supports of the upper telescope are called the wyes, and designated Y's. Two loops, turning on hinges, pass over the telescope, and are made fast by the pins c and d; these loops confine the telescope in the Y's. By withdrawing the pins, and turning the loops on their hinges, the telescope may be removed for the purpose of being reversed in position; and in both situations, the telescope can be revolved in the Y's about its axis.

In the telescopes attached to the theodolite, are two printhe eye is placed, is called the eyeglass, the other the object glass.

In order that the axis of the telescope may be directed to an object with precision, two spider's lines, or small hairs, are fixed at right angles to each other, and placed within the barrel of the telescope, and at the focus of the eyeglass. The vertical hair is moved by two small horizontal screws, one of which, f, is seen in the figure ; and the horizontal hair, by two vertical screws, and h.

Before using the theodolite, it must be properly adjusted. The adjustment consists in bringing the different parts to their proper places.

The line of collimation, is the axis of the telescope. With this axis, the line drawn through the centre of the eyeglass, and the intersection of the spider's lines, ought to coincide.

FIRST ADJUSTMENT. The first adjustment regards the line of collimation: it is, to fix the intersection of the spider's lines in the axis of the telescope.

Having screwed the tripod to the instrument, extend the legs, and place them firmly. Then loosen the clamp-screw S of the vernier plate, and direct the telescope to a small, welldefined, and distant object. By means of a small pin i, on the under side of the telescope, slide the eyeglass till the spider's lines are seen distinctly; then with the thumb-screw X, which forces out and draws in, the object glass, adjust this glass to its proper focus, when the object, as well as the spider's lines, will be distinctly seen: after which, by the tangent-screw T and the thumb-screw Z, bring the intersection of the spider's lines exactly upon a well-defined point of the object.

Having done this, revolve the telescope in the Y's, half round, when the attached level mn, will come to the upper side. See, in this position, if the horizontal hair appears above or below the point, and in either case, loosen one, and tighten the other, of the two screws that work the horizontal hair, till the horizontal hair has been carried over half the space between its last position and the observed point. Carry the telescope back to its place; direct again the intersection of the spider's lines, to the point, and repeat the operation till the

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