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. By means of a clamp-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 is seen in the figure. The vernier plate turns freely around 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 Z, 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 0. 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 o 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 horizontai hair, by two vertical screws, g 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 scope is revolved. A similar process will arrange the vertical hair, and the line of collimation is then adjusted.

SECOND ADJUSTMENT. -To make the axis of the attached level of the upper telescope, parallel to the line of collimation.

Turn the vernier plate, till the telescope comes directly over two of the levelling screws, between the plates DE and FG. Turn these screws contrary ways, keeping them firm against the plate FG, till the bubble of the level mn, stands at the middle of the tube. Then, open the loops, and reverse the telescope. If the bubble still stands in the middle of the tube, the axis of the tube is horizontal; but if not, it is inclined, the bubble being at the elevated end. In that case, by means of the small vertical screws m and n, at the ends of the level, raise the depressed end, or depress the elevated one, half the inclination; and then, with the levelling screws, bring the level into a horizontal position. Reverse the telescope in the Y's, and make the same correction again; and so on, until the bubble stands in the middle of the tube, in both positions of the telescope: the axis of the level is then horizontal. Let the telescope be now revolved in the Y's. If the bubble continue in the middle of the tube, the axis of the level is not only horizontal, but also parallel to the line of collimation. If, however, the bubble recede from its centre, the axis of the level is inclined to the line of collimation, and must be made parallel to it by means of two small screws, (one of which is seen at p.) which work horizontally. By loosening one of them, and tightening the other, the level is soon brought parallel to the line of collimation, and then, if the telescope be revolved in the Y's, the bubble will continue in the middle of the tube.

It is difficult to make the first part of this adjustment, while the axis of the level is considerably inclined to the line of collimation; for, if the level were truly horizontal in one position of the telescope, when the telescope is reversed, the bubble would not stand in the middle of the tube, except in one position of the level. This suggests the necessity of making the first part of the adjustment with tolerable accuracy; then, having made the second with care, let the first be again examined, and proceed thus till the adjustment is THIRD ADJUSTMENT. - To make the limb of the instrument horizontal, or, to make the common axis of the limb and vernier plate truly vertical.

This adjustment is effected, partly by the levelling screws, and partly by the thumb-screw Z. Turn the vernier plate, until the upper telescope comes directly over two of the levelling screws, then turn them contrary ways, till the upper telescope is horizontal; after which, turn the vernier plate 180o, and if the bubble of the level remains in the middle of the tube, one line of the limb is horizontal. But if the bubble recede from the centre of the level, raise the lower, or depress the upper end, one-half by the levelling screws, the other by the thumb-screw Z, till it is brought into a horizontal position. Turn the vernier plate again 180o, and if the level be not then horizontal, make it so, by dividing the error as before, and repeat the operation until the line of the limb is truly horizontal. Then turn the vernier plate 90o, and level as before. The limb ought now to be truly horizontal; but lest the first horizontal line may have been changed, in obtaining the second, it is well to bring the telescope and level two or three times over the levelling screws, until an entire revolution can be made without displacing the bubble from the middle of the tube. As this can only be the case when the level revolves around a vertical line, it follows that the limb will then be horizontal, and the axis of the instrument vertical.

This adjustment being completed, the levels of the vernier plate are readily made parallel with it, by means of the small screws at their extremities. The three levels being then horizontal, and perpendicular in direction to the axis of the theodolite, the bubbles will retain the middle places in the tubes, during an entire revolution of the vernier plate, or of the limb and vernier plate together.

But the levels of the vernier plate may be made parallel with the limb, and the limb made truly horizontal, without the aid of the upper level.

Let the upper telescope be placed directly over two of the levelling screws. One of the levels of the vernier plate will then be parallel to the line of these two screws, and the other level will be at right angles to this line, or parallel to the line of the other two levelling screws. In this situation, let the