instrument measures. If the vernier be moved still farther forward, till its third dividing line, or second from the zero, coincides with the line of the limb, the zero of the vernier will have moved forward again, a distance equal to the difference between a space on the vernier, and a space on the limb, or altogether twice the smallest measure of the instrument. To take a reading, therefore, from a theodolite divided as above mentioned, observe the number of degrees and half degrees pointed out on the limb by the crow-foot or zero of the vernier, and if this line be a little past one of the dividing lines of the limb, count the number of divisions on the vernier from the zero to a dividing line which coincides exactly with one of the limb; this will be the number of single minutes to be added to the degrees and half degrees indicated by the crow foot.

arcs.

The use of two verniers 180° apart, in correcting for excentricity, may be thus explained. An excentric angle, or one having its vertex not in the centre of a circle, is measured by half the sum of the opposite The mean of the two opposite verniers, therefore, gives the true angle moved over by the telescope. If the number of verniers be increased beyond two, error of graduation and of figure in the circle are proximately eliminated, as well as error of excentricity, by taking the mean of all the verniers.

TRIANGULATION OF A COUNTRY.

This is a process which consists in measuring a base, and taking the angles at its extremities with the theodolite, for the purpose of determining the positions of points, the sides of the triangles thus determined becoming bases for new triangles.*

SURVEY OF A LARGE ESTATE.

A good instrument for the purpose is a compass with telescopic sights, graduated from 0 to 360°. And a good method of proceeding is to select three stations on elevated ground at remote parts of the estate. Setting out from one of them, go in the direction of one of the others, having previously taken the bearing of the line joining them with the compass. This line may be kept by its bearing in plunging into the low grounds, out of sight of the principal stations. Distances must be measured along the line to points opposite objects on either side of it, which are to be introduced upon the map, and offsets to these objects measured. Oblique instead of perpendicular offsets will sometimes be found more convenient,

This will be fully treated in our chapter on Geodesy.

in which case their bearing must be observed with the compass as well as their lengths measured. Or if an object be too inaccessible to measure the offset to it, its bearing with the compass may be taken from two points on the principal line, which will serve to fix its position. The method of keeping the field book is exhibited on the next page but one.

The

The record commences at the bottom of the page, and goes upwards, till one page of the field book is filled, and then commences at the bottom of the next, and so on. * The bearings and distances are entered in the middle column of the page, the offsets on the right and left. Distances are usually measured in chains and links, or decimals of a chain. objects to which the offsets are measured may have their names written, or still better, may be roughly drawn. The points at which streams, roads, stone walls, hedges, &c. cross the principal line, are indicated in the field book by drawing representations of these in the proper direction on both sides of the central column, and where they cross obliquely, recording their bearings upon them.

On reaching the second station, a line is drawn across the page, and a line is run in a similar manner from the second to the third station, and finally from the third to the first.

The sum of all the partial measured distances upon any one of these sides of the great triangle will be the length of that side, and the lengths of the three sides being known, the triangle may be plotted. The offsets will be plotted as described at p. 243, or where they are oblique, in an obvious manner. A turn to the right, on reaching a station, may be marked at the side of the page, and a turn to the left 7.

The great triangle with the offsets being completed, other points may be taken within, as the vertices of smaller triangles having the sides of the large triangle for bases, and, if necessary, other points again within these, until all the systems of triangles with the offsets from their sides include every object desirable to be placed upon the map.

On p. 246 is a map of ground with the great triangle and offsets, and on p. 247 is the corresponding field book.

*This is in order that the book and the ground may lie in corresponding positions before the eye of the surveyor.

B

To survey a town or city the same general method would be pursued. The principal lines run with the compass would be the main streets, and the objects on either side would be brought in by either oblique or perpendicular offsets. The points of crossing of the minor streets would be noted, and their bearings taken.

LEVELLING.

The instrument employed for this purpose is called the level, and consists of a telescope mounted horizontally upon a tripod. At the top of the tripod, firmly fastened to it, is a small horizontal circular plate of brass, parallel to which, and a few inches above it, is another of the same size, the two being separated by levelling screws, and called levelling plates. From the centre of the upper levelling plate rises vertically a spindle,

which fits into a socket in the middle of a horizontal bar, about a foot or more in length. At the extremities of this bar are two stout uprights of two or three inches in length, the tops of which are formed as y', in which the telescope rests, in a position parallel to the horizontal bar. One of these y has a vertical motion, by means of a screw underneath it, which passes up through the end of the horizontal bar. A spirit level is suspended below the telescope and parallel to it, having a horizontal movement by means of a screw at one end, and a vertical movement by the same means, at the other.

1. To collimate the instrument, bring the intersection of the wires upon some well-defined distant point, and then turn the telescope on its optical axis in the y, till the spirit level comes at top. If the intersection of the spider lines be not in the axis of motion, it will depart from the object, and will be as much on the opposite side of the axis after this demi-revolution. It must, therefore, be brought back half way to the object, by the screws which move the wires. This experiment must be repeated till the intersection remains on the object, during the revolution of the telescope on its optical axis.

There are three lines of the instrument which ought to be parallel to each other, horizontal, and perpendicular to the vertical axis about which the instrument turns, viz., the line of collimation, the axis of the spirit level, and the horizontal bar.

2. To render the axis of the spirit level parallel to the line of collimation, bring the air bubble to the centre by turning the levelling screws, having previously placed the level in the direction of the line joining two of them; take the telescope out of the y", and reverse it, turning it end for end; if the bubble remains in the centre, both lines, that is to say, the line of collimation and the axis of the level, are horizontal; if not, bring the bubble half way back to the centre, by means of the screws at the end of the spirit level, and the other half by the levelling screws. Repeat this process until, in both positions of the telescope, the bubble remains in the centre. The axis of the spirit level may also be oblique to the line of collimation in a lateral direction. To ascertain whether it is so or not, turn the telescope on its optical axis as it rests in the Y, till the spirit level comes out at one side, not so far, however, as to cause the bubble to disappear; the lateral obliquity will then be converted into an obliquity partially vertical, which the departure of the bubble from the centre will render sensible. This obliquity must be corrected by the screws at the other end of the spirit level, which give a lateral motion to its tube. 3. To render the line of collimation and axis of the spirit level now