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CHAIN ANGLES_GENERAL RULES.

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lines A B, BC, CD, and D Е, so as to get a survey of the banks of the stream ; A B is produced to a, and CB to c; the small triangles about B are then measured, to plot the position of C B with regard to A B, and the small triangle about C to fix the position of DC with regard to the line BC, and the same with regard to the small triangles about D, to fix the line D E with regard to CD. It will entirely depend on the accuracy of sighting, measuring, and laying down of Ba and Bb and ab, as also Bc, B d, and Cå, that the correctness of the angle A B C depends; and therefore the position of B C as to AB; as regards that of C D with regard to BC, matters are still more critical, depending entirely on the little triangle gCf, whereas there is a check, such as it is, by the measurement of cd as against ab, and of ac as regards them both ; but whenever the lines to be fixed are much longer than the sides containing the chain angles, there is no dependence to be placed on such work. In the surveys of long narrow slips of land, such as those made for railways, canals, roads, &c., this method by chain angles is often adopted; but then, when properly done, it amounts to a well-laid system of triangulation on a small scale, because the sides of the chain angles bear some considerable proportion of length, and because besides it is so contrived that other important lines shall fully check the chain angles. The subject is merely mentioned here, as relating to chain-surveying, to guard the student against adopting without due caution a system that may lead to very erroneous results ; on short lines, which do not exceed three or four times the lengths of the sides about the chain angles, it may do well enough, but nothing more. We may

conclude this portion of our subject by reminding the reader of the following rules in laying out the chain lines of a survey, which is one of the most important parts of the business, for once that he can chain and book correctly, this is always the same, whilst the setting out constantly varies. Carefully explore your boundaries as the first step of all, and

do this look behind you as well as before; it is not necessary to abide exactly by the boundary side, but rather to take advantage of every adjacent acclivity that commands the ground forward as well as in the rear, as also towards the interior of the proposed survey; do not be anxious to commence operations until you have made yourself master of the leading features of the ground so as to have a rough map of it in the mind's eye.

If possible select your bases so that they shall lay across your survey in the longest directions and command at the same time a good view here and there of your district, more particularly at the extremities of these main lines, so that you may be able

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not only to see from them, but to them; it is not of the slightest importance that they be exactly on the boundaries of your survey, or exactly in the centre.

Do not let the angles of your triangles be too acute or obtuse if you can help it; be very careful in sighting your lines and fixing your principal poles, and mark most carefully the intersections of the base lines.

In chaining these lines leave sufficient marks so that you may be always able to find their directions when required, and look out carefully for intermediate stations for your secondary triangles, which are only second in importance to your main ones; select them so that you may chain as many lines to or from them as possible, never losing a chance of producing lines when it may be convenient instead of throwing up the sides of fresh triangles.

Never omit tie-lines; if it does so happen that there are no offsets they are soon run.

CHAPTER III.

Instruments for Laying Down and Plotting Chain Surveys.—

Contraction of paper.Precautions to be taken in consequence.-Beam Compasses.

BESIDES a pencil and a pair of full-sized compasses, there are required for laying down and plotting a chain survey a straightedge, a scale, a beam compass for long lines, and a needle-point. With the use of the compasses we suppose every one acquainted, and we can only add here that in describing with these the sides of triangles by means of arcs, it is always desirable to lay down the longest side of the triangle first, and from the ends of this side describe your arcs ; and that the legs of the compasses must be kept as upright as possible: with long chain lines we must resort to the use of a beam compass, which will be presently described.

In a former place we have already said something of scales; Fig. 8 shows a short chain scale divided to two chains to one inch ; it will be observed that it is numbered from 0 to 12 both ways for convenience of reading ; each main division, as 1, 2, 3, is, in fact, a miniature scale of a chain, and each subdivision counts for ten links. In first laying down your scale by the side of your chain line after you have drawn it in, be careful to place zero at the commencement of your chain line, and not at the end of it. Having done this, and ascertained that your chain line has been correctly laid off in length, with your field-book before you, you prick off with your needle-point* all the distances at which you have taken offsets, all your stations,

, and intersection of fences; round the station marks draw a little half circle in pencil as you prick them off, and mark with a little cross line all your fence intersections; this is of assistance when you come to lay off the offsets. Having thus pricked off all

your distances on the chain line, lay a short scale across it at right angles, and one after another plot your offsets as you find them in the book, and at about every ten or twenty chains,

* Ivory needle-points are sold by instrument makers, but a very good one may be made by taking a very fine needle in a pair of pincers and driving the head of it into a pencil top, leaving out about the eighth of an inch, and then pointing your pencil.

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before proceeding farther, draw in your fences, &c., as you go along. The reader must now work this out for himself to understand it more completely. The scale shown in the illustration is only six inches long, which is too short for any extent of survey ; it should not be less than a foot in length; for extensive work it is well to have two or three, of well-seasoned boxwood, about three feet in length.

Fig. 9 is an illustration of a chain scale, with offset attached, but not very generally used. The scale AB has a dovetailed longitudinal groove nearly from end to end, in which slides an accurately fitting sliding piece, to which, by means of a screw, is fixed the offset scale C; it is used in such a manner that zero moves along the chain line, whilst the scale A B is parallel to it, and its zero exactly opposite and at right angles to the beginning of the chain line; the offsets are thus pricked off right and left as the offset scale is made to slide along the chain scale according to the chainage in the field-book. The scale AB, when adjusted to its position, is fixed by weights.

A scale of 4 chains to 1 inch is a very good and useful scale for taking out quantities by, and is one very generally employed for general working plans; by some engineers a preference is given to 3 chains to the inch. These two scales are those adopted for Tithe maps of parishes.

For parliamentary, as railway and canal work, a scale of 6 chains to 1 inch has now been in general use for some years past; it is the smallest admitted without enlargements of buildings. See Standing Orders. A few years ago the scale more generally adopted was one of 5 chains to 1 inch. Where for parliamentary work we come through town lands and numerous buildings, a scale of 6 chains is rather small; for this purpose a scale of 4 chains to 1 inch is becoming more generally in use.

For working plans among town lands a scale of 30 or 40 feet to 1 inch is very commonly adopted.

There are a great number of other scales mentioned in works on this subject, and sold by makers of mathematical instruments; but they are very rarely used in professional practice, and they are therefore not described in these pages.

The scales required are 3, 4, 5, 6, 8, and 10 main divisions to 1 inch, the two latter being generally used for the vertical heights in sections. The three first may be had in box-wood, but the three latter must be in ivory on account of the small size of the subdivisions.

For general maps the scales most usual are 1, 4, and 6 inches to 1 mile. The survey of London and environs has been pubJished to a scale of 1 foot to 1 mile

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Before we entirely dismiss the subject of scales, we must say a few words as to the expansion and contraction that paper is liable to as the atmosphere happens to be damp or dry. Where there is a really extensive survey of great breadth as well as length, this often occasions considerable trouble; we have experienced this more particularly by the sea-side ; after laying down a long chain line on a fine dry day, and the scale is laid by the side of it on a damp one, it will be found that it measures too long, and vice versâ ; the longer, and generally therefore the more important the line, the greater the error; the only way to get over this inconvenience is to lay down two scales of inches divided into tens of chains on your paper by the sides of your work; the one horizontally, and the other vertically; these scales expand and contract equally with the rest of the paper according to the hygrometrical state of the atmosphere, and you can apply your beam compasses to them when you want long distances; for the short lengths the matter is of less importance.

The construction of the beam compass is illustrated at Fig. 10, where A is a long beam, sometimes 5 or 6 feet and more, made of box-wood or well-seasoned mahogany, and may be divided into feet, and inches, and tenths of inches. B and Care two sliding pieces of brass encompassing the beam, on which they are tightened by the clamp screws E and D; to each of them is attached a point, as G and H. When any distance is to be set off with this instrument, the screw E is released, and its sliding piece moved along the beam until the required distance is compassed between the

points G and H, when E is clamped, and any slight deviation from the exact measurement required is corrected by the slow motion screw F at one end of the beam where B is always situate. As we have not as yet had an opportunity of mentioning the slow motion screw, we may here

, observe that it is so constructed to give a slight motion to the piece B when the screw D is clamped. * In this state the instrument is fit for use to lay off distances by having one point fixed where required whilst the other is steadily swept round to describe an arc in the same manner that an ordinary pair of compasses is used; it is scarcely necessary to add that there is the necessary arrangement for a pencil point.

We have now explained the use of instruments for plotting a chain survey as far, we believe, as it is possible to do so; practice must accomplish the rest.

* The beam itself is sometimes divided as a scale, but this is rarely trustworthy; it is much safer to take off the distance from a long scale; or from that laid down on the paper, as shown above.

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