obtained. To use the instrument, two pickets are driven into the ground and adjusted until the plumb-line of the mason's level shows that their heads are truly level.

A

The same operation is more rapidly performed by means of boning-staves, which are simply 3-foot staves having a T-head. Both these methods are very rough and inaccurate, and only suitable for very short distances. The Spirit-level is the instrument commonly used. The spirit-level proper is a glass tube BC, Fig. 55, hermetically sealed at both ends, partially filled with liquid. By giving the tube a slight arched curvature, the bubble may be made to rest firmly in the middle, and by regulating the curvature, the travelling of the bubble may measure small angular deviations from the horizontal line. The tubes are ground on the inside so as to give a similar curvature to the part of the tube under which the bubble travels.

B

Fig. 55.

D

E

F

f

F

(a.) The Dumpy Level.-The term spirit-level is also applied to the levelling instrument, of which the spirit-level proper is the essential part. The instrument most generally used in Great Britain is the dumpy level, invented by W. Gravatt. It is represented in Fig. 56. A is the spirit-level attached by screws at a, a, to the telescope BC. The small circle near the object end B of the telescope represents a small transverse spirit-level used to show whether the cross-wire of the telescope is truly horizontal. DD is a flat bar or oblong plate fixed on the top of the vertical axis E. To this bar the telescope is attached by adjusting screws d, d. The hollow vertical axis turns upon a spindle fixed to the upper parallel plate F, the spindle being continued downwards and being attached to the lower parallel plate G by a ball and socket joint. There are four levelling-screws f, by which the vertical axis is set truly vertical. The lower plate is screwed on the tripod head H. The tripod consists of three wooden legs like those of the theodolite. In some instruments, a compass is carried on the top of the plate d, d for taking the bearings of lines of trial sections.

H

G

Fig. 56.

The telescope of the level is similar to that of the theodolite, except that the diaphragm contains one horizontal wire and two parallel vertical cross-wires, as shown in Fig. 57. This levelling instrument derives its name from its dumpy appearance, due to the large aperture and short focal length of the telescope. The latter is usually 9 to 14 inches in length.

Fig. 57.

(b.) The Y-Level. Of the different varieties of levelling instrument, that termed the Y-level is preferred by American engineers. In this instrument the telescope is mounted on Y's, like those of the Y-theodolite.

A recent form of American Y-level, made by Messrs. Heller & Brightly, of Philadelphia, is shown in Fig. 58. The telescope rests on Y's, and is confined in them by clips fastened by bindingpins. The telescope is 17 to 20 inches long. It has at each end

Fig. 58.

a ring of bell-metal; by these it revolves in the agate bearings of the Y's, and can be clamped in any position. The spirit-level is attached to the under side of the telescope, and is provided at its ends with screws for horizontal and vertical adjustment. The level scale extends over the whole length, and is graduated into tenths of an inch. A clamp and tangent screw are connected with the axis for moving the bar and telescope.

(c.) The Troughton Level.-In the Troughton and Simms' pattern of fixed telescope level, the brass case of the spirit-level is embedded in the top of the outer telescope tube. There are no adjusting screws. These levels are made with telescopes of 10 to 26 inches in length.

The Adjustments of the Level are the same as those of the theodolite. They are as follows:-Temporary Adjustments: 1. For parallax. 2. To place the vertical axis truly vertical by

means of the levelling-screws. Permanent Adjustments: 3. For collimation. 4. To make the spirit-level parallel to the line of collimation. 5. To place the telescope and spirit-level perpendicular to the vertical axis.

The adjustment of the line of collimation in the Y-level is obtained by rotating the telescope on its collars. The parallelism of the level to the line of collimation is obtained by reversing the telescope end for end on its Y's.

The adjustments of the levelling-instruments with fixed telescopes are not so simple, but they are much more permanent. In the dumpy level, the adjustment for collimation is made by the instrument-maker before soldering the telescope tube to the two blocks that support it. In this case, the adjusting-screws of the diaphragm should never afterwards be disturbed. To make the level and line of collimation parallel, a level piece of ground is selected, and after levelling the instrument by means of the levelling-screws, it is directed to a staff held by an assistant at a distance of about 10 chains. The difference between the height read and that of the centre of the telescope above the ground is noted. The instrument and the staff are then made to change places, and the observation repeated. If the results agree, the level and the line of collimation are parallel. If they do not, the inclination of the telescope must be altered by means of the levelling-screws, and the bubble then brought to the middle of its tube by means of the adjusting-screws a, a (Fig. 56).

(d.) Cushing's Reversible Level. On account of the inconvenience attending the adjustment for collimation in levelling-instruments where the telescope is fixed, it occurred to Mr. Cushing, Inspector of Scientific Instruments to the India Office, to make the eye-end and object-end of the telescope interchangeable. For this purpose he fixes to the internal tube of the telescope a gun-metal socket, which is turned and ground with a short conical fitting and wide flange to receive the eye-end, with its eye-piece and diaphragm. On the opposite end of the outer tube, a precisely similar fitting receives the cell containing the object-glass. Both ends are identical as regards the fitting, though the object-end is necessarily rather longer than the eyeend on account of its having to carry on the outside the cover or dew-cap. The line of collimation is adjusted by reversing the collimation stop, which in this level is a glass disc with lines engraved upon it by a fine diamond, instead of the ordinary cross-wires.

The Levelling-staff serves to measure the vertical distance from the horizontal line formed by the axis of the telescope down * Min. Proc. Inst. C.E., vol. lix., 1880, p. 278.

to the station on the ground. Formerly the levelling-staff consisted of a wooden rod, furnished with a sliding vane or target, which was raised or lowered by the staff-holder in response to signals from the observer. Such staves are now rarely used. The principal objection to which they are liable is that the observer must depend on the staff-holder to read the height observed, or if the latter is not sufficiently intelligent to perform so important a duty, must himself go and read off the height of the vane. In this way great loss of time is caused, and there is uncertainty in the results, as the vane may possibly have shifted in the meantime.

A very perfect staff of this kind, known as the New York target rod, is largely used in the United States. It is graduated to hundredths of a foot. To indicate where the horizontal line cuts the staff, a target is used, the face of which is divided into quadrants painted with two alternate colours. In the face, there is an opening a tenth of a foot long, through which the figures can be seen on the face of the rod. The right edge of the opening is provided with a vernier, by means of which the staff can be read to thousandths of a foot.

In order to avoid entrusting the reading of the staff to an attendant, Mr. W. Gravatt invented a staff, the face of which was graduated distinctly enough for the observer himself to read off the figures through the telescope of his instrument. The sliding vane is thus dispensed with, and the staff-holder has nothing to do but to hold the staff vertical.

The levelling-staff usually consists of three parts, sliding one within the other, and, when opened out for use, forms a staff 14 to 16 feet in length. It is made of mahogany soaked in boiled oil, and painted with several coats of oil paint. The whole length is divided into hundredths of a foot, coloured alternately black and white, and occupying half the breadth of the staff. The patterns of levelling-staves are very various. The form shown in Fig. 59, invented by T. Sopwith, F.R.S., is that most frequently used. In this the feet are represented by large red figures, the tenths are shown by odd black figures, and the hundredths are coloured alternately black and white. Between the odd figures representing tenths, a black diamond is painted to indicate the alternate five-hundredths. The top of every figure represents its value. Of the black and white divisions, the bottom of each black space represents odd hundredths, the top even hundredths. The staff is usually 14 feet in length, and divided into 3 parts, which, when drawn out, are held in position by a spring clip

Fig. 59.

at the back. When closed, they form a staff about 5 feet 3 inches in length, 3 inches wide, and 11⁄2 inch deep.

An important modification has been introduced in the graduation by Mr. A. G. Thornton, of Manchester. It consists in the repetition at each 3 inches of the number of feet in small red figures on the left of the staff. This improvement will be found very advantageous, especially with short lines of sight, as an exact reading can be taken on any part of the staff where the cross-wire falls, without the necessity of raising or lowering the staff. It is important that the staff be held truly vertical while it is being read. To help the staff-holder in this, a small plummet is suspended in a groove cut in the side of the staff, by means of which its verticality can be determined in one direction. The observer himself can detect by means of the two vertical wires of the telescope whether it inclines in the other direction. The plummet may be replaced by a round spirit-level, the tangential plane of which is perpendicular to the back of the

staff.

The error caused by the staff being inclined is considerable. Let h be the reading on the staff when it is held vertical, and h’ the reading when the staff is inclined at an angle of d from the

If necessity should compel the staff to be used without a plummet or round spirit-level, it should be moved backwards and forwards by the staff-holder; the lowest reading will be the most correct one.

A triangular piece of sheet iron, about one-tenth of an inch in thickness, having the corners turned down, is used to rest the staff on. The corners are pressed into the ground. By means of this iron plate, the staff is kept on the same spot, and at the same height from the ground, while the observer is reading the back- and fore-sight. A chain and ring are attached to the plate for the convenience of the staff-holder in lifting it from the ground, and in carrying it from station to station.

Mine Levelling-Staves. For levelling underground, staves may be employed similar in construction to those used at the surface. They must, of course, be shorter. The best sizes are feet 6 inches, or a

a 9-foot Sopwith staff to close down to 3 6-foot Sopwith staff to close down to 2 feet 6 inches. The staff is illuminated by means of a miner's candle or a safety-lamp.