he should glance along the chain held tight in the straight line, by which he will perceive if the chain lie in the trace of the given line. If the chain be not in the trace or vertical plane of the given line, the surveyor should direct the 'leader,' by signal or otherwise, to change his position until the chain be accurately adjusted in the vertical plane of the given line. The surveyor should then pass a few waves through the chain, with a slack hand, to free it from dirt and ringlocks, and holding the handle of the chain accurately to the end, or arrow, as the case may be, direct the leader to keep the chain fully drawn out, and to mark accurately the chain length with an arrow. This should be done on soft ground, or till, by driving the arrow vertically into it: on hard ground, such as rock, roads, &c., the chain length should be marked by scribing two lines with the point of an arrow from the proper point, thus ▲, at which mark an arrow should be left for the follower. If the ground be not horizontal in the direction of the line, the chain length in the horizontal should be determined on the ground as above described. The point should be marked with an arrow. Whenever the follower may be at the lower point the chain length cannot be laid down, for certain, at one operation. In this case the leader should drive the arrow into the ground as near as may be at horizontal chain length, and hold the handle of the chain accurately to or over it, as the follower may require, whilst the latter should determine the chain length in the horizontal, and refer it to the ground as already described. The difference between the point so determined on the surface and that marking the forward end of the last chain length laid down, if any, should be accurately measured and applied (+) to the forward arrow-point, to accurately determine the point for the chain length. To

this point the arrow should be removed before again adjusting the chain in the line. The leader should be careful not to leave any arrow after him except those marking the chain lengths. These the follower should take with him as he completes each chain length in the measurement of the line. The surveyor should not draw the arrow at his end [of the chain length being laid down], before his assistant has finally driven the arrow into the ground, or otherwise marked the point for the forward end of the chain length.

Skilful surveyors, in order to economise time, in measuring on long and uniformly inclined planes, on which there may not be detail, measure a chain length to the horizontal and a corresponding chain length on the inclined plane, and so determines the error due to a chain length on the incline. The surface measure may be that taken for the remainder of the incline. The correction for inclination should be made at the end of the incline by changing the position of the arrow, forward, a distance equal to the ascertained error, on one chain length multiplied into the number of chain lengths measured to the surface. This expedient to economise time should not be adopted, even by skilful surveyors, if a high degree of accuracy is an object, since any error fallen into in the determinations on the one chain length increases with the distance. When each chain length is measured to the horizontal, the errors compensate, to an unascertainable amount, and hence the greater attainable accuracy.

On grounds sloping so that the chain cannot be held to the horizontal at its end, the leader should take up the chain, in downhill work, at a point which he can hold to the horizontal, and refer that point in the horizontal to the inclined surface, as already described. The

point on the chain should be adjusted to the corresponding point on the surface, and in this position handed over to the follower. The remaining part, or parts, of the chain should be held to the horizontal, and their lengths referred to the inclined surface, until the whole length of the chain be so referred: the leader should mark with an arrow the end of the chain length. In uphill work a similar process may be followed, with this difference, that the leader should shift his point on the surface, until the plummet, now used by the follower, marks the point on the surface last determined; then will the leader's point be accurately found. The chain should not be disturbed from the point on the surface to which it is held by the leader, until the follower takes it up for the purpose of laying down the next forward part of the chain length.

The operation of laying down a chain length to the horizontal on the level, and in up hill or down hill work, described above, should be repeated, as may be required, for each successive chain length until the whole distance be measured.

If the measured distance be less than ten chains, the number of arrows taken up by the follower will be the number of chain lengths laid down, to which should be added the links (if any) or fraction of a chain, to find the number for entry in the field-book-the expression in chains and links for the whole measured distance.

If the distance exceeds ten (or any multiple of ten) chains, the arrows must be passed from the follower to the leader at the forward end of each tenth chain laid down, which should be marked with a picket, thus →Y>, so that the acute angle may accurately mark the tenth arrow point. Every change of arrows should be entered on the field-book, so that the whole length of the

measured line may be expressed by adding the number of arrows less than ten, and the links (if any) to the number for ultimate change of arrows, thus 30 + 5 + 0.84 will read and should be entered 35.84. It is customary and advisable to enter the measurement in links (3584).

It has been found, on the Ordnance (detail) Survey of these countries, that fair average surveyors, making large progress in open country, have measured their lines to the horizontal, in the manner described above, with the maximum error not exceeding 1 in 1,000. Like surveyors, in close detail and stiff hilly country, making large progress for the class of work, have brought the maximum errors within 1 in 1,000. Superior surveyors have brought the chain measurement of the sides of triangles, in undulating and hilly districts, to within 1 to 2 links in the mile of the computed distances.*

FINDING HORIZONTAL DISTANCES WITH THE CHAIN AND AN ANGULAR INSTRUMENT.

Let the distance to be obtained be that of a straight line between two distant points in a hilly country.

For the purpose of the survey, two separate parties proceed the one previous to the other-along the surface trace of the line. The surveyor first proceeds to make the measurements with the chain to the surface, in the trace of the vertical plane, passing through the given extreme points. The measurements may be commenced at either end of the line, and should be continued to the other end. In making the detail and reference line measurements, the surveyor should mark

The distances of the sides of the triangles were computed in the trigonometrical survey.

on the ground each change of inclination—such as 1, 2, 3, &c. (fig. 1)—by a picket and pile. The entries of the measurements for these pickets should be distinguished on the field-book by the initial L.P. (level point). After the survey of the line shall be completed, a copy should be furnished to the party for levelling the line.

The theodolite, or 'level party,' when furnished with a copy of the survey of 'detail' and 'level points,' is enabled to follow the trace of the line, and make the angular measurements (4) for inclination of the several planes selected by the surveyor (such as A—1, 1—2, 2—3, &c.). From these data the horizontal distance may be computed for each plane selected, and the sum taken to find the horizontal distance for the whole line (A B).

If the surface be flat, or a plane, the surface trace of the line, viewed on a vertical plane, will be a straight line, horizontal or inclined, according as the surface is horizontal or inclined in the direction of the line. If, however, the surface be concave or convex, as in hollows and on hills, then its trace on the vertical plane will be curves of a corresponding character. These features

Fig. 1.

B

may be illustrated by the sketch (fig. 1), which shows a surface trace on a vertical plane.

In the sketch A B are the distant points; A, 1, 2, 3, &c., B are level points (L.P.) in the surface trace.