ON SURVEYING WITH THE THEODOLITE.

SECTION VI.

A DESCRIPTION OF THE THEODOLITE-ITS ADJUSTMENT IN THE FIELD-TAKING ANGLES-VERNIER SCALE.

THE student who has carefully considered what is contained in the preceding sections, must have acquired some knowledge of surveying. It has already been observed that the principles of the art are the same, whatever may be the extent of work to be performed, or the kind of instrument used. This he will find to be the case as we proceed.

The Theodolite (plate VII.) is the most perfect instrument used in surveying, as it gives the horizontal angles without reduction.* It is composed of a telescope, TF; with a spirit level, O, attached. A vertical arc, V, for measuring angles of elevation and depression. A plate, termed the horizontal circle, H, having upon it cross spirit levels, S, S. A compass. Parallel plates, with four vertical screws, G, for levelling the horizontal circle. A clamping screw, A, to prevent the horizontal circle from moving round. A tangent or micrometer screw, B, to turn the instrument slightly, after being clamped by the screw A. A screw, P, for fixing the upper or index plate to the horizontal circle, H, which may then be slightly

* An explanation of the difference between angles taken with a theodolite or compass, or those measured with a sextant or other reflecting instrument, will be found in treating of the pocket sextant.

turned for a nice adjustment of the telescope to an object, by means of the micrometer screw, N. The instrument is mounted on three stout legs.

When in perfect adjustment, the horizontal circle is truly level. The vertical arc is in a plane, perpendicular to the horizon. The line of sight, or of collimation (i. e., axis of the telescope), must be true, and the level attached to the telescope must be parallel to the line of collimation.

The theodolite is set up thus:-Place it over the station mark, spread the legs to about three feet apart, and move them until the vertex of the legs is exactly over the mark. A small stone dropped, or a plummet suspended from a hook, immediately under the vertex, will indicate when this is effected. Being satisfied as to the position of the instrument, press the legs firmly into the ground, and proceed to level it. Two spirit levels are generally fixed to the upper plate of the instrument, at right angles to each other. The four parallel plate screws, G, act upon this circle. Bring one of the spirit levels into a position parallel, if I may say so, with two of those screws that stand opposite or diagonally to each other. Now, by raising one screw, and lowering, at the same time, its opposite, the position of the horizontal circle will be changed. Continue working these screws until the bubble of the spirit level acted upon, rests in the middle of the open space: then work the other pair of screws, until a similar effect is produced upon the other spirit level. The adjustment of the latter will, however, throw the other level somewhat out, rendering a return to it necessary. The horizontal circle is not truly level, or parallel to the horizon, until the bubbles of both spirit levels stand in the middle of the open spaces during a revolution of the in

strument.

An angle is measured with the theodolite thus:-S is the

station of the instrument: required

the angle between the windmill n

and the spire w. Plant the theodolite over the station point, as directed above, carefully attending to all the instructions just given. Make zero of the vernier scale to coincide with zero of the

น

horizontal circle, and fix them so by tightening the screw, P. Place the intersection of the hairs in the telescope on the windmill n, and fasten the clamping screw, A; then, if the object n is not found to be exactly covered by the point where the hairs cross each other, turn the micrometer screw, B, which will enable you to fix it with the utmost precision. This effected, loosen the screw, P, which will release the index or vernier plate from the horizontal circle; then turn the upper part of the instrument until the cross hairs cut the object w. The vernier micrometer screw, N, enables this to be done very exactly, on tightening the screw, P. Then the number of degrees and minutes passed over by the vernier, or index, shows the measure of the angle.

The vernier scale, which is applied to instruments both for measuring angles and distances when great accuracy is required, must now be noticed. The horizontal circles of ordinary theodolites are divided to half degrees, and are most convenient when numbered from zero to 180°, as recommended for the prismatic compass. Now, without such a contrivance as the vernier, we can only guess at the number of minutes, when the index does not exactly agree with one of the subdivisions; but, by means of a vernier, we are enabled to read off an angle on the circle of an ordinary theodolite to a single minute; and may, if the

horizontal circle be very large, read off to twenty seconds with the greatest certainty.

ΟΥ

VERNIER SCALE-to one minute of a degree.

15

5

20

-ல

5°

09

14 degrees, or 29 half degrees.

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The construction of this ingenious contrivance is simple. Suppose we want to read off to one minute. Take the length of 29 half degrees on the horizontal circle, and divide that distance into 30 equal parts; this forms the vernier, which is marked for convenience, 5, 10, 15, 20, 25, 30, from one end, or the zero. Place the vernier to the horizontal circle, so that zero of the former may be in contact with zero of the circle; then the last division, marked 30, of the vernier will, of course, agree with 1410, or 29 half degrees of the circle. And the proportion of each division of the vernier will be to a division of the circle as 29 to 30. If the zero of the vernier be moved from the zero of the circle, then the first coincidence that takes place between a division of the vernier with one on the circle, indicates the number of minutes passed over. To read off an angle on the horizontal circle, use a magnifying glass, and notice how many degrees have been passed over by the zero of the vernier : for example, let us suppose that the arrow at zero of the vernier has passed the 21st degree of the circle; then, for the number of minutes in addition, look along the vernier, until one of its divisions is found to agree exactly with a division on the circle below it. You find, we will suppose,

25

130

12°

11°

10°

that the 14th division of the vernier does so: then the angle is 21° 14'.

A careful and minute description of the various parts of the theodolite, with instructions for their adjustment before proceeding to the field, will be found further on; aided by which, an intelligent person may, with a little practice, rectify every derangement to which the instrument is liable.