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The best constructed levelling staff* consists of three parts, which pack together for carriage in a neat manner, and, when opened out for use, form a staff seventeen feet long, jointed together something after the manner of a fishing-rod. The whole length is divided into hundredths of a foot, alternately coloured black and white, and occupying half the breadth of the staff; but for distinctness the lines denoting tenths of feet are continued the whole breadth, every half foot or five-tenths being distinguished by a conspicuous black dot on each side.

In all work where great accuracy is required, the Y level, above described, is preferable to either of the others; but both Troughton's level and Gravatt's level are calculated, by their lightness, and by their being less liable to derangement when once properly adjusted, to get rapidly over the ground

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In this level the telescope, T, rests close down upon horizontal bar, bb, the spirit level, ll, is permanently fixed to the top of the telescope, and does not, therefore, admit of adjustment, and the compass box, c, is supported over the level by four small pillars attached to the horizontal bar. This construction makes the instrument very firm and compact. The staves, staff-head, and parallel plates by which the instrument is supported, and the vertical axis upon which it turns, are of exactly the same construction as has been already described as used for supporting the Y level.

The diaphragm is furnished with three threads, two of them vertical, between which the levelling staff may be seen, and the third, horizontal, gives the reading of the staff by its coincidence with one of the graduations marked upon it. Sometimes a pearl micrometer-scale is fixed on the diaphragm, instead of the wires. The central division on the scale, then, indicates the collimating point, and by its coincidence with a division of the levelling staff gives the required reading of

* This staff was first introduced into use by William Gravatt, Esq.

this staff; and the scale serves the purpose of measuring dis tances approximately, and of determining stations nearly equidistant from the instrument, since at such equal distances the staff will subtend the same number of divisions upon the micrometer-scale.

In selecting a level of Troughton's construction, and also in testing and adjusting the collimation subsequently, Mr. Gravatt's method, already described, is the best to be used; and, when the line of collimation is thus brought into adjustment, if the bubble be far from the center of its run, the fault can only be remedied by the maker; but, if the bubble settle very nearly in the center of its run, the instrument may be deemed a good one, and, the divisions on the glass tube which coincide with the ends of the bubble being noted, the instrument must be set up for use with the bubble in this position.

The line of collimation is set perpendicular to the vertical axis, in the same manner as in the Y level, by means of the capstan screws, B B, the bubble being made to maintain the requisite position, as above determined, while the instrument is turned completely round on its axis.

MR. GRAVATT'S LEVEL.

This instrument is furnished with an object-glass of large aperture and short focal length; and, sufficient light being

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thus obtained to admit of a higher magnifying power in the eye-piece, the advantages of a much larger instrument are obtained, without the inconvenience of its length. The diaphragm is carried by the internal tube a a, which is nearly equal in length to the external tube. The external tube T T is sprung at its aperture, and gives a steady and even motion to the internal tube a a, which is thrust out, and drawn in, to adjust the focus for objects at different distances by means of the milled-headed screw A. The spirit level is placed above the telescope, and attached to it by capstan-headed screws,

one at either end, by means of which the bubble can be brought to the center of its run, as in the case of the Y level, when the line of collimation is brought to the proper level by Mr. Gravatt's method of adjustment, already explained.

The telescope is attached to a horizontal bar, in a similar manner to Troughton's level, but room is just left between the telescope and the bar for the compass-box.

A cross level, k, is placed upon the telescope at right angles to the principal level 7 l, by which we are enabled to set the instrument up at once with the axis nearly vertical. A mirror, m, mounted upon a hinge-joint, is placed at the end of the level 17, so that the observer, while reading the staff, can at the same time see that the instrument retains its proper position -a precaution by no means unnecessary in windy weather, or on bad springy ground.

The telescope is attached to the horizontal bar by capstanheaded screws, BB, as in Troughton's level, by which the line of collimation is set perpendicular to the vertical axis; and the instrument is set up upon parallel plates, as before described, for the Y level.

The operation of determining the difference of level between two stations by observations made at a single station is called simple levelling, and is performed as follows:

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Let A and H be two points whose difference of level is required. Plant the instrument at D, and adjust it to a horizontal position. Read off A c, the height of a staff held at A, then turn the telescope round and read off E H, the height of a similar staff, or of the same staff held at H. Then A c is the height of K, the axis of the telescope above the point a, and EH is the height of K above another point, H; and it is clear that EH-AC=GH, the difference of level between a and H.

In this operation the station A, at which the staff is first read off, is called the back station, and the station H is called the fore station; and, if the reading of the staff at the back station be greater than that at the fore station, the difference of level is called a rise; but, if the reading at the back station be less

than that at the fore, as in the example just given, the difference of level is called a fall.

When, from the nature of the ground, or the great distance between the two points, they cannot both be observed from a single spot, a series of simple levels must be taken, the fore station at each operation being made the back station at the next operation; and from the combination of all the results thus obtained the required difference of level is obtained. In these operations care must be taken, in going over soft ground, lest the staff at the fore station, when turned round to be read as the staff at the back station in the next operation, should sink further into ground; and, to prevent this, the foot of the staff must be placed upon a flat, hard substance, as a piece of slate or tile. There is a simple instrument called a tripod, sold for this purpose by the instrument makers, being simply a plate of iron with a small rounded projection in the center, two small spikes at the side to fix it in its place, and a short chain to lift it by, when the staff-holder wishes to remove from his place.

In determining by this method the difference of level between two distant points, it is immaterial by what route we proceed from one to another, so that such spots may be selected for the intermediate stations as are most convenient for the purpose. The bearings of the stations from the instrument are also matter of indifference; but, the more nearly the instrument is equidistant from the two stations observed at each operation, the more correct will be the result obtained, the errors in the back readings compensating, for the most part, the errors in the fore readings, whether the errors arise from refraction and curvature†, or from the imperfect adjustment of the instrument.

If, then, the object be only to obtain the difference of level of two points, we have only to record in two separate columns the readings of the staff at the back stations and fore stations respectively, and the difference of the sums of these readings

*The error of refraction is that arising from the bending of the rays of light during their passage through the atmosphere, and makes all objects appear higher than they really are.

†The object of levelling is to determine points upon a spherical surface or equally distant from the earth's center, or to determine the differences of the distances of a series of points from the earth's centre. The line of sight, or prolongation of the line of collimation, however, is a tangent to the spherical surface, and therefore the points observed upon this line are really above the level of the point of observation. The correction for curvature is therefore additive, while that for refraction is subtractive.

will be the difference of level required. Thus, if the difference of level between two points A and B, be required, and if the readings at A and B, and three intermediate stations

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Then 22:18 feet is the fall from A to B, or A is 22.18 feet above B. When, however, it is required not only to find the difference of level between two distant points, but to make such observations as shall enable us to draw a section exhibiting the undulations of the ground along some specified route from the one point to the other, then the stations must be so chosen that one of them shall be at the commencement of each change in the inclination of the ground; the distances between the stations must also be carefully measured; and it is further advis able to note the distances and bearings of the stations from the instrument, which it will be more convenient now to place on a point in the specified route between the stations.

In drawing the section, it is the horizontal distances between the several stations that must be laid down. For short distances, or over very irregular ground, such horizontal measurements may be obtained by bidding an assistant hold one end of a measuring tape close to the ground at the highest end of the distance, and holding the other end above the ground, stretching the tape in a horizontal line, a stone let fall from this end then marking upon the ground the point to which the measurement reaches. But, when the ground rises and falls in long regular slopes, the measurements should be taken along the slopes, and then be reduced to horizontal distances by calculation. If the rise or fall is but slight, this reduction may be altogether disregarded, the difference between the horizontal and hypothenusal measurements not exceeding the limits of error in the measure itself.

Care should be taken to record all the observations in a clear and intelligible form, and for this purpose a field book may be prepared of the following form:

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