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CONTOUR BENCH MARKS.

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ling; and pegs should be put in level with the surface of the ground, as A, Fig. 265, and beside it should be drawn another peg

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B

Fig. 264.

B

to mark its position, which may be two or three inches out of the ground. This peg should be cut as explained in Chapter II., and the particulars of its height marked upon it. We now proceed to establish the other bench-marks, as are shown in Fig. 266. In this case we assume that the vertical intervals shall be 10 feet, so that F is 50 feet above A. I have elected to give in Fig. 267 a rough illustration of the method by which these lines of bench-marks are determined. Suppose the levelstaff be held on the peg at A, and the back sight to be 13-50, then, because we want to establish a peg at в 10 feet above A, we must deduct 10 feet from 13.50 3.50, which the staff should read when a peg has been driven level with the surface of the ground at B. The fore sight at a will be 0.17.

=

Fig. 265.

The instrument is moved beyond c (the staff remaining at a); and when adjusted the back sight is 12.85. Now the difference between the last back sight and the point в is 350 0.17 3.33, which is on account of the fresh altitude at c; therefore 10.00 - 3.33 = 667 feet, which is the difference; and if we deduct this from 12.85 (the new back sight), the staff held on a peg at c should

read 6.18; and as it is necessary to make a change, we determine the fore sight as 3.00, which gives a rise of 3.18 in favour of the next vertical altitude at D. At b the back sight is 13.12; and as we have 3.18 towards D, the rise from b will be 10.00 - 3.18

50

40

30

20

10

-ZERO

Fig. 266.

= 6.82, which, deducted from 13.12.

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6.82=

6.30, the intermediate at D. Now the fore sight is 0.40, which is 5.90 towards the vertical interval at E; the back sight at E is 9.10; and if from

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this be deducted the difference between 10.00 and 5.90, we shall get 5.00 as the intermediate at E, whilst the fore sight is 0.19 at d and 5.00 0.19 4.81 towards the last vertical interval. Here

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CONTOUR FIELD BOOK.

the back-sight is 7.30, from which must be deducted

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5.19, or

the difference between 10.00 and 4.81, which will give a reading I have thought it desirable to give this as a simple

at F of 2.11.

illustration, as being more readily understood. The following is

the level-book :—

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CHAPTER XI.

SETTING OUT CURVES.

PRACTICAL Surveyors are nowadays required to perform so many more duties than heretofore, that any work upon the subject of their duties would be incomplete if it did not treat upon the setting out of curves. It does not necessarily follow that these curves are only for railway work, as in the development of property it is often requisite to lay out new roads and boundaries, which, for economical and other reasons, frequently are required to take the form of regular curves.

The most accurate and satisfactory method of laying out curves is by means of a theodolite, but for approximate results the operation may be performed by tangents and offsets, or chords and ordinates.

Now in all cases a curve is used to connect two straight lines, whose relative positions are such that one forming an angle with

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the other they intersect each other at some given point. In Fig. 268 it will be seen that the lines A a and c c intersect at the point B. It matters not how acute or obtuse the angle of intersection may

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be, there is some curve, great or small, which will connect these two lines, and whose connection will be tangential therewith.

In considering a railway, as an illustration, it simply consists of a series of straight lines, whose directions form angles with each other, whereby it is necessary to connect each with the other by means of curves, as is illustrated in Fig. 269, by the five lines A B,

E

Fig. 269.

B C, C D, DE, E F, and four curves a a, b b', c c', and d d'. Here we have the angles A B C, B C D, C D E, and D E F, without knowing the value of which it is impossible to set out the curves upon the ground.

It may be well here to mention that for railway work it is better to lay out these straight lines and make them the base-lines of the survey. This may be done either by traversing or, preferably, by taking the included angles with the theodolite. It need hardly be explained that for the purpose of taking up the features on the right and left hand of these lines a complete system of triangulation must be adopted.

Having obtained an accurate record of the relative positions of these straight lines, which should be plotted to as large a scale as possible, together with the details of the survey, it will then be possible to determine the various radii of the connecting curves.

Limit of Radii.—In speaking of the radii of curves, I may say that curves of less than 12 chains' radii are not desirable for railway work. I have known less, but for many reasons sharp curves are to be avoided. It is a very mistaken theory that curves of small radii enable the engineer to economise in the design of his work, or in other words to avoid undue severance of property; and it is a very questionable policy, for against a small saving in the purchase of the necessary land (which is settled once for all) must be placed the constant wear and tear of the permanent way and rolling stock, which, if capitalised at a period of years, will prove a very formidable amount. Again, in these days of high speed it is absolutely out of the question to adopt sharp curves. There is no fixed rule to govern the limit of radius of curves, as

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