proper regard for accuracy will induce him to limit the distance, between successive positions of the level, to about six hundred feet. Under such circumstances, each turning-point is made a bench.

51. The methods of establishing benches are various. In a rocky section, some conspicuous point is marked either by drilling or grooving the rock. In villages or cities, stone steps, or projecting courses of masonry to dwellings, curb-stones, and fence-posts afford good benches, and admit of easy identi fication.

In sections where trees abound, a notch is cut in the side of a trunk near the root, in such a manner as to leave a projecting point upon which the rod may be held vertically. A nail driven full length into the projection, gives it the necessary firmness for a bench.

In marshes or prairies, where there are neither rocks nor trees, the engineer is compelled to resort to long stakes, firmly driven into the ground to such a depth as to be undisturbed by the frost; no portion of the stakes being allowed to project above the surface. The top of each is trimmed to a kind of blunt point, into which a nail is driven its full length.

A re-survey of a route, to detect possible errors in levelling, is accomplished by taking the heights of the "benches" only, and is called a cheek level."

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DRAWING THE PROFILE.

52. When the "section level" of a line of work has been completed, the "profile" is next to be drawn. The method of doing this is very simple.

A horizontal line to represent the datum line, is first drawn, and the distances from the first column of notes are laid off

along it, to a convenient scale: this for ordinary working drawings is about two hundred feet to an inch.

The "surface heights" corresponding to these distances are next laid off at right angles to the datum line, and above it, but to a scale usually ten times as great as that employed for the horizontal distances; that is, an inch upon the vertical lines represents one-tenth as many feet as upon the datum line. A line joining the upper extremity of the verticals, is the profile.

By thus employing two different scales, the irregularities of the surface are made more apparent to the eye, and the subsequent adjustment of the "grade-line" is rendered much easier, and more accurate.

53. Every earthwork of importance requires, in addition to the working profiles, a general map, in which the plan drawn from the transit survey is represented upon the same sheet as the profile.

The horizontal distances of both portions of the map being drawn to the same scale, and one being placed directly above the other, corresponding points in plan and profile are readily compared.

In published maps of this kind, representing extended works, and drawn for convenience to a very small scale, the vertical scale of the profile is frequently several hundred times as great as the horizontal.

ESTABLISHMENT OF THE GRADE.

54. The determination of the height which the finished road or canal, shall have above the datum line at different points, is called "Establishing the grade."

The position and inclination of grade-lines are influenced

1st. The character of the work. A street admits of an inclination of five, or even eight feet in a hundred, and requires about one foot for its drainage, while a rise of two feet in a hundred upon a railroad is exceedingly rare. A canal is, of course, level, the change of height being effected by abrupt transitions at the locks.

2d. The economy of construction. It is desirable to make the earth excavated, form the required embankments, or, in the language of the engineer, "to make the cuttings balance the fillings."

It is, however, sometimes more economical to throw away, or "make a spoil bank" of the earth of an excavation, than to transport it the required distance for the embankment. Embankments, for similar reasons, are often constructed of earth obtained outside of the road limits ("borrowing pits"); or, when such means are not available, are often made of timber framing, (trestle-work).

3d. The natural obstacles, which render the construction difficult; such as rocky ledges, marshes, lakes, streams, and quicksands.

In either case, the engineer determines, by inspection of the maps, at what points the grade-line shall intersect the natural surface. Thus the inclination of the grade, and, consequently, its height above the datum line, for each "distance," are easily found.

Another column of notes is now made, recording these "Grade Heights;" each being placed against the corresponding surface height.

"The following example, with its accompanying diagram, illustrates the method of establishing a grade and recording the notes. It will be observed that the profile, with its "distances" and "surface heights," are the same as in the preceding problem.

We will suppose it is required to establish, in the following profile, a grade-line whose inclination shall not exceed 3 in 100; the grade to begin at station 0, at the surface.

It is an easy matter to represent any required inclination of grade on the profile map; nothing more being necessary than to lay off the proper distances on two different verticals, and draw a line through the points of measurement. For in

would intersect the vertical at 6, eighteen feet lower, and the vertical at 7, twenty-one feet lower.

Moreover, by consulting the notes, we find that a gradeline from 0, whose height is 29.5 feet, ending at the surface at 7, whose height is 11.5 feet, descends 18 feet in 700, or 2.57 in 100.

Either of these lines would fulfil the required conditions. The first would, however, require in its construction a large excess of excavation over the embankment (as may be seen by drawing a faint line in the diagram). The second would give an excess of embankment.

It is best, generally, that the cutting should be slightly in excess, as nearly all kinds of earth shrink a little in the process of removal.

The cuttings and fillings of the profile may be balanced with tolerable accuracy, by stretching a thread across the profile so as to intersect at the 0 point, and then varying the inclination, until the areas cut off by the profile line on opposite sides of the thread appear equal.*

The column of Grade Heights must now be filled. It is easily and rapidly done. The height of Grade, at 0, is, by the conditions, 29.5. At station 1, it must be 2.7 lower, or 26.8; at 1.60, 4.3 lower, or 25.2; and at 2, 5.4 lower, or 24.1, &c.

The remaining columns of "cut" and "fill" contain simply the differences between corresponding "surface" and "grade heights." Where the surface is higher than the grade-line, the construction requires a "cutting;" when the established grade

*The advantage of a thread over a ruler lies in the fact, that while using the thread, the areas on both sides of it are seen at once.

In the present example, a line from 0, descending 2.7 to 100, seems to accomplish the desired purpose. The line being drawn, the "cut" and "fill" areas are measured, to determine if they are properly balanced.

The complete computation of the earthwork, by which the exact position of the grade line is determined, is explained in the next section.