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cipal levels, by levelling from one bench-mark to another, if you find that the difference of level prove the same, you may conclude the work so far to be correct: but if you find them to differ by a number greater than the probable error, you must level that part over again from the last bench that you have proved: proceed in this manner through the whole length of the section.
Copy of Field-Book, for Check Levels.
B. Sights. F. Sights.
Difference of level between point
Note. The bench mark on the post at A, is 10 feet above the datum line of the section, and the bench post at the point B where this part of the section closed is 4.33 feet above the bench mark at A, as appears from the fieldbook, whereas, the sum of the back sights exceeds the sum of the fore sights by 4.33 feet; and the bench mark B is above the datum line 14.31 feet; therefore the difference of level between the two places is 14.31-10-4.31 feet. Differing from the original section only 02 of a foot, which proves that the part of the section between A and B is sufficiently correct.
To take Levels for the formation of a Section. The most simple case on levelling is, to take the levels of a line, where the plan is made, and the true position determined, and pricked out. This is no more than the running levels, but that the whole distance at every station from the first point, must be measured.
The section is plotted, thus: First, draw the datum line, which all the horizontal distances are laid off. Then at the end of all the respective distances, perpendiculars are erected to the datum line, and upon these perpendiculars the respective reduced levels are laid off. Then the line joining the extremities of these vertical distances will represent the surface of the natural ground.
In taking levels for a working section, number of ob servations are frequently made at each setting up of the instrument. The field-notes are kept as in the last fieldbook.
Having given directions for levelling roads, canals, &c., with all the preliminary operations necessary, now we will say a few words on making and repairing common roads. It is necessary to remark, that in laying out a common road, the engineer is not so restricted, either in slopes or curvature, as in rail-roads.
He should, as far as economy of expenditure will allow, observe these two rules: namely, to make choice of the straightest line that connects two points, and the one that
presents the best level. These two characters, with a hard, dry, surface, constitute the best line of road.
In laying out a road towards a river, or any place requiring a bridge or tunnel, it is evident the best possible way to approach it is at right angles. If not, skew arches are to be constructed, which in all possible cases should be avoided. When it becomes necessary to lay out a road over a steep hill, some skill is required to keep the slope uniform, and at the same time within moderate limits; this can only be done by a winding course.
When a hill lies between two points which are to be connected, the road should get such slope as that, in descending, the accelerating force of gravity shall not effect the carriages travelling with the usual speed. The slope that would render it safe for carriages must not be greater than the angle of friction.
And as the angle of friction varies according to the materials forming the road covering, the slopes may vary; in this inquiry we shall restrict ourselves to a well formed M'Adamised road, upon which the inclination should not exceed 1 in 35; down such a plane a carriage may be driven with safety at the rate of 12 miles an hour. The angle of friction can only be ascertained by actual experiments: by allowing a carriage to descend on a road of variable inclination, until the friction shall overcome the force that caused the motion.
The following are the results of experiments, the load moved being one ton:
1.—On well made pavement the draught is 33 lbs.
2.-On broken stone surface laid on a flint road, 65 lbs. 3.—On a gravel road, 147 lbs.
4. On a broken stone road, upon a rough pavement foundation, 46 lbs.
5.—On a broken stone surface, upon a bottoming of con crite formed of cement and gravel, 46 lbs.
Now it may be seen, that in the first case, the angle of friction is represented by or nearly; which shows that the slope in this case should not exceed one perpendicular to 68 in length: for the same reason, in number 2 and 3, the slope should not exceed 1 to 35, and 1 to 15, and in numbers 4 and 5, 1 to 49.
Now it is plain, that you can find the angle of ascent or descent by knowing the rate of inclination. Then having the several angles of inclination known, you may set the telescope of the theodolite to that position, and when the direction of the road is not limited, as is the case when you only want the best level between two points, make the assistant remove the pole right or left on the cross section until you cut the vane which is to the height of the cross wires when the telescope was horizontal, then will that point on the surface be on the required level. Proceed in this manner from station to station throughout the whole: So will you have the road staked or poled out without making a section at all.
The maximum slope is limited by the equality of the amount of friction and force of gravity along the road.
When it becomes necessary to connect two points, one higher than the other, or to pass a hill at a higher point than either ends, the direct line should be followed as long as the slope is found to be within the above limits. But when, on account of some obstacle, it becomes necessary to change the direction, a circuitous one with a slope within the prescribed limits, must be chosen; every change of direction should be a part of a circle. The natural obstacles which oppose the making of the best line of road, are hills, valleys, water courses, marshes, and want of good materials. In crossing a valley, the road should be carried round the bosom of the hill, by which means the up and down directions may be avoided: When a line of road is encumbered with numerous and useless ascents, it is plain
the number of feet ascended is increased many times more than is necessary, if each height, when once gained, where not lost again.
When the road runs through a flat plain it must be raised, otherwise it never can be kept dry or in good repair. It is of the greatest advantage to command a fall to carry of the water: an inclination of one in one hundred would do.
Although the circuitous route may be greater than the length of a direct line, yet if the inclinations in the former case are much less than those in the latter, it is evident that more may be gained in speed, with the same expenditure of power, than is lost by the increase of distance. Thus, if two roads rise, one at the rate of 1 in 20, and the other at the rate of 1 in 35, the same expenditure of power will move a weight through, 20 feet of one, and 35 feet of the other, at the same rate.
Drainage. A thorough system of drainage is necessary to have a road made sufficiently solid to bear any great traffic; consequently due regard must be taken to make such drains along the line as will carry off the waters from the formation and surface. In order that the rain water on the road may fall off, the centre should be raised six inches higher than the sides. The best curve to give the cross-section of the surface is that of an ellipse. To preserve the cross-section uniform, the overseer should procure a wooden guage resembling a semi-ellipse, by which he can try the surface curve as he proceeds. This apparatus should be surmounted by a plume and line, by which the instrument is properly adjusted to the road, and an equal inclinat.on from the centre secured.
The engraving fig. A, represents the level employed by road surveyors in laying out new roads. On the horizontal bar AB, are placed four guages, a, b, c, and d, which move in dove-tailed groves cut in the bar, and when ad