In surveying a kingdom or other extensive tracts of country, an instrument of greater diameter, divided to measure angles to a certain number of seconds, might be used to measure the angles of the great or primary triangles with. But for smaller triangles, and for filling in the survey, the portable five-inch theodolite is by far the most convenient.

Description and Adjustments of the Theodolite.

The theodolite is a circular horizontal ring, divided into 360°. This ring consists of two plates, called limbs. The chamfered edge of the lower limb is marked 10°, 20°, 30°, &c. up to 360°—the intermediate 5°, 15°, 25°, &c. being represented by longer divisions than the single degrees, and the half degrees by shorter lines than the single degrees.

The improved theodolite is furnished with a telescope mounted in Ys, with a spirit-bubble attached. Το the Ys is fixed a semicircular vertical arc, moving in a vertical plane, for measuring vertical angles. In order to enable the observer to bisect objects correctly, a slow motion screw is attached to the upper limb, and also a clamp to prevent the limbs from slipping. To the lower limb are attached a clamp and tangent screw, similar to those attached to the upper. A vernier is fixed to the upper plate, and two bubbles at right angles to each other, by which the instrument is set horizontal. The vertical arc passes through another vernier, which is used for reading vertical angles. In the upper plate is also a small compass; the N. S. line of the compass box ranging with the line of sight.

In reading the above description, the surveyor or young engineer should have an instrument before him, an inspection of which will serve him more than the most elaborate description on paper.

The adjustments of the several parts of the instrument should be particularly attended to, as an error must be the result of every angle taken with a theodolite not properly adjusted.

The first adjustment to be attended to is that of the line of collimation; that is, to make the intersection of the cross-wires in the telescope coincide with the axis of the cylindrical rings in which the telescope turns; to do which, set up the instrument in any position, open the rings which confine the telescope, so as to allow it to turn freely on its axis. Adjust the telescope for distinct vision, by moving the eye-piece and object glass till objects appear through it distinct and well defined. Paying no regard to the spirit bubble, bisect some well defined object with the cross-wires, and clamping the instrument firm, turn the telescope slowly round in its supports, and observe if the bisection continues during a whole revolution: if so, the line of collimation is right; if not, alter the screws which carry the crosswires or diaphragm, by tightening one of them while the opposite one is released, till (turning the telescope round its axis) the intersection of the wires bisect the object during an entire revolution. It is best to rectify one wire first, and then the second.

The line of collimation being corrected, the next thing to be done is to put the level attached to the telescope parallel to the adjusted line of collimation; to do which, open the clips, the vertical are being

clamped; bring the bubble to the middle of the glass tube, by turning the tangent screw of the vertical arc; then reverse the telescope in its Ys, without disturbing the position of the vertical arc, and if the bubble resume its former position in the middle of the glass tube, the thing is done; but should it retire to one end, bring it back one half by the capstan-headed screw, and the other half by the tangent screw of the vertical arc. The level should also be adjusted transversely, by turning the two lateral screws; and if doing this should derange the former adjustment, the process must be repeated.

The next adjustment is to make the azimuthal axis of the horizontal limb truly vertical; to do which, set the instrument (by the eye) as nearly level as you can; bring the spirit bubble over two of the foot-screws, and by their motion bring it to the centre; then turning the instrument half round, if the bubble resume its central station, all is right; if not, correct half the error by raising or lowering the tube itself, and the other half by one of the foot-screws.

When the foregoing adjustments are perfect, the next thing to be attended to is the vernier of the vertical arc, which is correct if it points to zero; if not, rectify it by releasing the screws by which it is held, and tightening them again after having made the correction.

Instrumental Parallax.

Parallax very often produces serious errors in surveying and levelling. When looking through the telescope, you bisect an object, and then moving the eye up

or down, the cross wires do not remain in contact with the point of bisection, but apparently recede from, and approach it, then the instrument requires adjustment, it being impossible to bisect the object correctly from the manifest existence of parallax in this case. To remove this, move the eye glass in or out, according as the case may require, till you obtain a clear and well defined view of the cross wires; then communicate motion to the slide, carrying the eye-piece and cross wires till you obtain a clear view of the object, and if on moving the eye all round, the intersection of the wires remains in contact with the object, the effects of parallax is

removed.

To take Horizontal Angles with the Theodolite.

A

B

All the foregoing adjustments being completed, set the instrument exactly over the station, as at A, by means of a plumb suspended from the centre of the theodolite; bring zero on the vernier attached to the uppor horizontal plate, to 360° on the lower: then clamp both plates together, and level the instrument by means of the parallel plate-screws, unscrewing one while you screw up the opposite, till the spirit-levels on the upper plate stand exactly in the middle of their respective tubes. All this being done, turn the instrument towards the station on your left hand (towards B), and make the intersection of the cross wires bisect a staff placed perpendicular at that station, using for this purpose the

tangent-screw attached to communicate a slow motion to the body of the instrument.

The body of the instrument being firmly clamped, set the upper plate free (the lower remaining firm), and turn to the second station on the right hand (to C), and bisect a staff set perpendicular there, using for this purpose the tangent-screw which gives motion to the upper plate; then read off the angle in degrees, minutes, and seconds, if the instrument be divided to show seconds, and it will give the measure of the angle A. In bisecting the marks set up at B and C, direct the telescope as near the ground as possible, lest they should not be exactly perpendicular to the horizon.

When extreme accuracy is required, and when both verniers do not shew the same number of minutes and seconds, take the mean of the minutes and seconds of both readings, and annex it to the degrees for the measure of the required angle. Thus one vernier shows 22° 15', and the other shews 16'; then 16+15=31, and 31÷2=15' 30"; hence the required angle is 22° 15' 30".

To Survey a Single Triangular Field by the Chain

and Theodolite.

Place the theodolite at A, and take the angle there, and removing the theodolite to B, take the angle ABC; then measure the side AB, from which the other sides of the A

B

triangle may be obtained by Case 4, in Trigonometry.