adfgnb, describing the form of the hill, is longer than the line, ab; and, therefore, as the distance, ab, is all that can be allowed in a plan, if a surveyor measures the curve surface of the hill, he must of necessity reduce it to the true horizontal distance.

There are various ways of reducing sloping lines to horizontal ones; but I believe that in practice the following simple method is commonly adopted :

We will suppose that the slope, an, is to be measured downwards, and with the chain. One person holds an end of the chain at n, while another stands with an off-set staff at g, 30, 40, or 50 links down the slope, according to its steepness; the portion of the chain used is then to be drawn tight while held horizontally, represented by the line, hn; an arrow is then placed at g. In this way a succession of short horizontal lines, hn, og, ef, and cd, will give us the length of am, which is the horizontal distance corresponding to the hypothenusal line, a n.

A measuring tape is preferable to a chain for thus measuring slopes, as it is easier to draw it tight; and when one end is held up, so as to make the line of tape horizontal, a pebble dropped on the ground from its extremity will indicate the point from which the next length is to be taken.

ON LEVELLING.

SECTION XVIII.

OBSERVATIONS - LEVELLING WITH A MASON'S LEVEL WITH BONING-STAVES-DESCRIPTION OF A SPIRIT-LEVEL -LEVELLING STAVES - METHOD OF LEVELLING WITH A SPIRIT-LEVEL - DRAWING SECTIONS - LEVELLING WITH A THEODOLITE-TRACING CONTOUR LINES.

LEVELLING may be considered as a branch of surveying; a knowledge of it, therefore, is necessary for the military surveyor. He may have to use a sloping base for a survey, which must be reduced to the true horizontal distance by levelling. Or he may have to drain a marsh; to form a road, either level, or with a certain degree of inclination; to take sections of ground for various purposes; to take profiles of fortifications and field works, &c. All such operations are performed by some kind of levelling process, as will be shown in the course of the following pages.

Writers on levelling generally commence the subject with the theoretical, and then proceed to the practical part; but I venture to think it better to set the pupil at once to work with his instruments, show him how to take levels, and thence lead him on to investigate the theoretical part, rather than perplex him at first with the spheroidal form of the globe, and its influence on levelling operations, as occasioning calculations on account of curvature. Surely this, and the theory of refraction, had better be reserved until the student shall have attained sufficient knowledge of levelling to take an interest in the art; particularly as, in practice, corrections for curvature and refraction are very rarely applied, common levelling operations being usually so managed as to render such corrections unnecessary.

There are three kinds of levelling instruments in use, namely, the ordinary Mason's level, Boning-staves, and the Spirit-level. The two first are often employed by military men when a spirit-level cannot be obtained; or for setting off slopes, and other minor purposes.

The method of using a mason's level is thus :-Suppose we want to know the difference of level between a point, A, and another at B. Drive a picket at A down to the surface

a

b

d

of the ground, and another, distant a few inches less than the length of the level at a, until the eye perceives that the head of the latter is nearly on a level with A; then set the level to rest on the two pickets, and the plumb-line will show when their heads are truly level. A third picket is then driven in at b, a fourth at c, &c., to the heads of which the level is successively applied; and the length of the picket, B d, is the difference of level required: the heads of all the pickets will then be on the same level, represented by the dotted line, Ad.

The same operation is more quickly performed by means of boning-staves, which are simply staves of equal length (usually three feet), having a T head. To level with their assistance, a mason's level is used for the first two pickets, as before; then a third picket being driven at any convenient distance, a boning-staff is held upon each, and the third picket is driven down until the observer at A can see

C

B

that the upper surfaces of the T heads are all in an exact horizontal line: the operation may then be continued by driving in a picket beyond B, to which the boning-staff at A must be removed. Instead of driving a picket at B, a measuring-rod is often used, which being held perfectly upright, a boning-staff is pressed against it, and caused to slide up or down, until its head agrees with those of the other two; when the difference of level is of course the distance between the foot, C, of the boning-staff, and B that of the measuring-rod. Observe that the boning-staves are to be held transversely, or at right angles to the position in which they are shown in the diagram.*

It is evident that levelling by means of a mason's level or boning-staves is only suited to very short distances; and they are but rough methods when compared to that by the spirit-level; for such is the accuracy of the process of levelling with a spirit-level, that an operation carried along a distance of several miles will not produce an amount of error equal to what will generally arise in the course of a few hundred yards, when using the former instruments.

Of spirit-levels there are now three in use-namely, the Y level, Troughton's improved level, and Gravatt's level : these are all carefully described, and their several adjustments given, in Mr. Simms' work on instruments. I shall confine myself to the account of the Y level, as represented in plate XVIII.*

This instrument has an achromatic telescope mounted in Ys, like those of the theodolite; and is furnished with a similar system of cross-wires, for determining the axis of the tube, or line of collimation. By turning the milled-headed screw, A, on the side of the telescope, the internal tube, a, will be thrust outwards, which carrying the object-glass, it is by this means adjusted to its focal distance, so as to show a distant object distinctly.

The tube, cc, carrying the spirit-bubble, is fixed to the under part of the telescope, by a joint at one end, and a capstan-headed screw at the other, which sets it parallel to the optical axis of the telescope. One of the Ys is supported in a socket, and can be raised or lowered by a screw, B, to make the telescope perpendicular to the vertical axis. Between the two supports is a compass-box, C (having a