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of cross-section paper and a small protractor we can probably do the work equally well and equally fast.

The stadia method is often found very convenient for obtaining topography where the above methods would fail to give good results.

But besides taking the contours, the topographer must also take note of the courses of streams, etc., on each side of the line within a distance (usually) of a few hundred feet. The bearings of these he can take with a small prismatic-compass. He should also be constantly on the lookout for anything which may be of service in making up the preliminary estimates, such as indications of the probable classification, the flood-marks of water-courses, etc. If the topographer does his work thoroughly, he usually has difficulty in keeping up with the transit and level; but this is rarely a disadvantage, as the chances are that there will be occasional "backing-up" to be done by the party ahead.

62. The GENERAL PLAN of the "preliminary" survey showing the alignment, topography, etc., is usually plotted to a scale of 400 feet to an inch, as in Figs. 15 and 16, thus agreeing with the horizontal scale of the profile.

FIG. 15.

In Fig. 15 let abcdef represent a portion of the preliminary line as shown on the general plan, plotted to a scale of 400 feet to the inch; and let the line have been run to a +1.25 p. c. grade, and the contours be given for every 5 feet vertical. Then if each station at which the instrument was set up was at "grade," the grade-contour will pass through each of these points, but gradually rising from one contour to another, crossing them successively at distances of about 400 feet apart; so that if, as in Fig. 15, station a happens to fall on a contour-line,

the grade-contour will cut the next line above, 400 feet farther on, at c; and since the next station d is only 200 feet from c, it will be situated about half-way between two of the contours. Now this grade-contour is the line which, if adopted for the final location, would give no cuts or fills at all, so that it is the line which would render the cost of construction a minimum. The judgment of the engineer here comes in to decide how much it is advisable to deviate from this limit. So far the work has been more or less mechanical, for there are usually enough governing-points along the route to decide within two or three hundred feet the course of the preliminary line; but fitting the final location on to the plan is quite another matter. Suppose that the engineer considers that the straight line AB (Fig. 15) is about where the final line should be located. Then the shaded portions in the figure show cuts and fills alternatelyshaded vertically being "cut," and horizontally "fill;" and the points where the line AB intersects the grade-contour will of course be the " grade-points." The amount of centre-cut and centre-fill can be read off at any point-not by scaling, but by counting the number of contour spaces there are between the line AB and the grade-contour. Thus, e.g., at a point in AB opposite c, there are 2 contour spaces, equivalent to 12 feet vertical, so that at this point we should have a 121ft. centre-cut. By taking in this way a few points here and there, the engineer can, by means of Table XIV, form a fair idea of the number of cubic yards in each proposed cut or fill, making allowance of course where the surface-slope is steep, as shown in Sec. 69.

In this way, then, there is no great difficulty in obtaining a line which will make the cuts balance the fills, this being simply a matter of a few trials. Where curvature, however, is involved, it is not so much the question of balance as of the total amount of cut and fill, which needs consideration.

By having the various curves drawn on a horn protractor, or on a piece of tracing cloth, the result of adopting any certain curve can be seen at once by sliding it up and down over the plan.

Then, again, a change of grade for a short distance may appear advisable, which necessitates altering the grade-contour. The question of overhaul, too, has to be considered, and the avoidance as much as possible of long shallow cuts. The

probable classification, too, will of course affect the balance of cuts and fills. The advisability of raising the grade to avoid an expensive rock-cut also needs consideration. A little experience, however, goes a long way, and the engineer usually finds that there is little doubt to a few feet as to where the line ought to go.

63. The main features of the final location having been determined as above, and drawn on the plan, the approximate position of the points of curvature, etc., can be taken off by scale, and the line thus located on the ground; any little alterations being made, the advantages of which have become apparent when the line is seen actually staked out.

A fresh set of levels must of course be taken over the new alignment, and a profile constructed showing the rates of grade, etc., finally adopted.

As regards compensating for curvature where transition curves are not used, the rate of grade should be changed at the P.C. and P.T. Many engineers, however, prefer making the change at the nearest "full" station; it makes little difference, however, which way is adopted.

Bench-marks should be given at distances of a third of a mile apart or so, and guard-stakes set solidly beside the hubs. If the location is being "rushed," there is no need to fill in the transition curves, for that can be done equally well by the section-engineer when he takes over the work for construction. When these curves are omitted, however, it should be so shown on the plan, as in Fig. 16.

64. It often happens that after the line is located a considerable distance ahead an alteration in the alignment is deemed advisable, necessitating a shortening or lengthening of a certain portion of the line. This causes a break in the "throughchainage." Such a break as this should, wherever possible, be referred to a point where there is a change of grade, or at least to a point on a tangent, so as to simplify the running of the grades and curves as much as possible. It should be indicated conspicuously in the notes and on the plans and profiles in the form of an equation; the station on the line which comes first being read first. Thus if the left-hand side of the equation is the greater, it means that the line has been lengthened; but if the right-hand side be the greater, it has

been shortened by an amount equal to the difference of the two sides.

65. The method of locating described above is of course suitable only to rolling or mountainous country; but where there is any doubt as to whether or not it is better to take contours, the engineer may generally come to the conclusion that it is better to do so. There is among some engineers an idea that the time spent in taking the topography might have been

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better used in running a series of trial lines. Of course in many cases this is true; but it must be remembered that a preliminary line with topography well taken to a distance on either side of, say, 500 feet (as is perfectly feasible in ordinary rolling country) covers a width of 1000 feet so completely, as to render the running of a trial-line within that area entirely needless; and that in order to settle the question absolutely as to the location through, say, a valley half a mile wide, two or at the most three lines run as above are all that can ever be required; while by the method of trial lines how many are needed before the engineer can feel satisfied that he has finally obtained as good a line as can be got? And then it is only the best of the trial-lines that is usually selected, which in all prob

ability will be inferior to the line selected from the contour plan.

Besides this, if topography is taken, the engineer can at any future time show evidence as to the advisability of having adopted the route which he finally selected. It is a duty he owes to himself as well as to the Railway Company to be able to prove that the location has been good, and how is he to do this if he has simply trusted to the correctness of his eye?

66. In country where the running is easy, one or two triallines usually show pretty closely where the final line ought to go, for the long courses may then be converted into tangents, and curves be substituted for the shorter ones as in Fig. 17.

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If the long courses predominate, it is usually better to get their location fixed first, and then join them by curves; but when the shorter ones are in excess, it is the curves that have to be first located, and the tangents made subservient to them. If the notes of the courses are kept by "Latitudes and Departures," the exact curve necessary to replace such courses as ABC can be at once found according to Sec. 77.

67. An engineer with a good "eye" can often tell by merely looking over the ground what degree of curve is wanted to fit the surface, i.e., where the difference between a 3° 30' and a 3° 45′ makes very little difference. Table II, of Tangents and Externals, is a good guide to this in many cases. For instance, by getting into position near the apex of the required curve, the engineer, with the aid of a hand-level and a prismatic compass, can often tell about how far from where he is standing the curve should pass. Thus, suppose he finds the angle of intersection to be about 40°, and that the curve should pass about 120 feet from the apex: he then finds from the Table that for an intersection-angle of 40° a 1o curve gives an external distance of 368 feet, therefore the

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