(11.) The following is an example of levelling performed at only one operation, and will therefore require the correction for curvature and refraction.

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B

It is required to drain a pond by making a cut to a stream at B, at a distance of 60 chains: let a level be set up and adjusted at C, and then directed to a staff, held upright, at the edge of the water at B. The horizontal line CD represents the line of sight, cutting the staff at D, the reading being 15.84; the height of the instrument above the ground was 4.8 feet, and the depth of the pond 10 feet: what is the difference of level between the bottom of the pond and the surface of the stream?

which is little more than 8 inches, and just a sufficient fall to make the water run freely from the bottom of the pond to the surface of the stream at B; it having been found in practice that a less amount of descent than from 8 to 12 inches per mile produces no efficient current for the purpose of drainage.

TO DRAW A SECTIONAL LINE OF SEVERAL POINTS IN THE EARTH'S SURFACE, THE LEVELS OF WHICH HAVE BEEN TAKEN (fig, p. 138).

(12.) Let a, b, c, d, e, f, and g be the several points; then, in order to draw the section to shew the undulations of the ground between a and g, the distances of the several points from a, in

addition to their levels, must be taken; this is usually done during the operation of levelling. These distances, with the back and fore sights, may be arranged in a level book of the following form, which, though not the form practically used, will probably be more clearly understood.

diff. 9.21 the same as the last of the reduced levels.

In this level book it will be seen that the differences 2.15 and 6.75, in the column marked Fall, are added together, making 8.90, thus giving the fall at c, in the column marked Reduced Levels: to this sum the succeeding falls are added, one by one, till we get the fall 25.71 at the bottom of the canal, which is the lowest point. Then the differences in the column marked Rise, are subtracted successively from 25.71 for the falls at ƒ and g; the latter of which is 9-21, the total fall from a to g, which, agreeing with the difference of the sums of the back and fore sights, shews the truth of the castings. The last column shews the distances of the several points b, c, &c., from a, in chains, with other remarks.

DATUM LINE.

(13.) The section might be plotted by laying off the distances in the last column in the preceding level book on a horizontal line, and setting off their corresponding numbers of feet, in the column marked Reduced Levels, perpendicularly below the line; but it is found inconvenient in practice to plot a section in all cases after this method, as in extensive operations the reduced levels would repeatedly fall above and below the line in ques

tion, and thus confuse the operation; therefore a line AG called "the datum line" is assumed at 100, 200 feet, &c., below the first station a; thus making that line always below the sectional line af, of which a clearer view may be obtained.

(14.) In the following practical level book the rise or fall is respectively added to or subtracted from the assumed distance of the datum line, and the next rise or fall, again added to or subtracted from the sum or difference:-thus 2.15, being a fall, is subtracted from 100 (the assumed distance of the datum line) leaving 97.85 feet, the height of the ground at b: the next fall 6.75 is then subtracted from 97.85, leaving 91·10 feet for the height at c; and so on to 3.53, which is the last fall:-the next 6.57, being a rise, is added, as well as 9·93;-thus the last reduced level is 90.79 feet, which taken from the datum 100 leaves 9.21 feet, agreeing with the differences of the sums of the back and fore sights, and of the sums of the rises and falls, and shewing the work of casting to be correct. Thus are obtained a series of vertical heights to be set off perpendicularly to the datum line, through the upper extremities of which the sectional line must be drawn.

PRACTICAL LEVEL BOOK.

(Datum line 100 feet below the bench mark at a.)

In laying down the sectional line from the above columns of reduced levels and distances, the former are always taken from

a much larger scale than the latter, otherwise the undulations on the surface of the ground would, in many cases, be hardly perceptible.

=

Draw the horizontal line A G, setting off the distances A B, A C, &c., as in the column of distances, that is, AB 4.60 chains, AC7.80, &c.; then draw A a = 100 feet, perpendicular to A G and parallel to A a draw Bb, Cc, &c., setting

off their heights 97.85, 91.10, &c., respectively from the column of reduced levels, and through the points a, b, c, &c., draw the required sectional line a g.

NOTE.-The above operations, though extremely simple, require great care, otherwise, in extensive works of this kind, errors creep in imperceptibly, to check which the agreement of the differences in the level-book is essential.

(15.) We shall now give an example of a simple kind to lead the way to more complicated operations. When a section of a line of country has been completed, it is in most cases necessary to check its accuracy by repetition; but in doing this it is seldom requisite to level over precisely the same line of ground, unless there is cause to suspect its general correctness, but to follow the most convenient and nearest route, and at intervals to level to some known points on the exact line of section, which will give their differences of level: the points thus selected are generally what are called bench marks, being notches cut on gate posts, stumps of trees, mile or boundary stones, or any similarly immoveable objects, contiguous to the line of section, and at frequent intervals. These bench marks are made by the person who first takes the section, and are sometimes previously determined upon. When the section is complete, their relative heights with respect to the base or

datum line of the section becomes known; hence they may be considered as so many fixed points on the line, easily recog nisable, from whence any portion of the work may be levelled over and over again.

From what has been said it is clear that in taking running or check levels, the use of the chain and compass attached to the level is not wanted, the distances and bearings having all been previously taken.

An example of this kind of operation is represented in Plate I., where both the ground plan and section are shewn. The strong black line on the plan is that of the section to be checked, and extends from a bench mark at the town A, in a winding direction, to another bench mark in a town B; this originally formed a portion of a more extensive survey. The route taken in proving the work is shewn on the plan by a dotted line, and was confined to the public roads, as being the most convenient route, especially as it crossed the line several times, by which a number of intermediate points could be checked. Previous to giving the particulars of this example, the method of performing the operation of levelling shall be explained more in detail than has yet been done.

The staff-holder must first place his staff perpendicularly on the bench mark from whence the levels are to commence; the surveyor must next set up his spirit level on the most convenient ground that presents itself, and so that he may have an uninterrupted view of the line he intends to level; the station chosen should not be more than four or five chains from the staff-holder, where, having fixed the legs of the level firmly in the ground, the surveyor must adjust his level for observation in the following order:-"first he must draw out the eye-piece of the telescope till he can see the cross wires perfectly well defined; then, directing it to the staff, he must turn the milledheaded screw, on the side of the telescope, till he can likewise distinguish, with the utmost possible clearness, the smallest graduations on the staff: that these two adjustments be very carefully and completely performed, is of more consequence than is generally supposed, for on them depends the existence or non-existence of parallax."

"The adjustment of the eye-piece to obtain distinct vision, when once properly made, is not likely to require alteration for the whole day, unless it be accidentally deranged; but that of obtaining distinct vision of the distant staff (together with the one we shall next describe) must be performed at every station as it varies with the distance of the staff.