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THE PRACTICE OF LEVELLING.

(9.) To find the differences of the levels of several points on the
earth's surface, and to trace a sectional line of them.

Let A, B, C, D, E, be the points on the earth's surface, a sectional line of which is required to be traced. Set up the levelling staves

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perpendicularly at A and B; between which fix the level L on the ground; make the spirit-level horizontal, and turn the object-glass of the telescope to the back-staff A; then the staff A is cut at a by the horizontal line of sight aa' of the telescope, through which the observer can read off the height Aa. Now turn the object-glass of the telescope to the staff B, the horizontal line of sight aa' cutting it at a', and read of the height Ba': then the difference between the heights Ba', Aa, is the number of feet that B is lower than A, because the line aa' is horizontal. Now let the staff A be removed to c, the staff B remaining in the same position, excepting that its graduated side must now be turned towards c, and having removed the level L, place it between B and C, and the spirit-level being again made horizontal, the line of sight, in this case, being bb', read off the heights Bb, cb' the difference of which is the number of feet that c is lower than B, as before.

In this manner, by alternately moving the levelling staves, placing the level between them, and reading off the heights below the line of sight or collimation, the operation is conducted to F.

Now, as there is a continued fall from A to D, the sum of the differences of the readings at B and A, at C and B, and at D and C, will give the actual fall vertically from A to D; in the same way the rise from D to F is estimated: if, therefore, the fall from A to D be greater than the rise from D to F, the difference of these two will be the actual fall from AF, or the distance in feet, estimated vertically, that the station A is higher than the station F.

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The difference of the sums of the back and front readings of the staves, or "back and fore sights," as they are termed, will also give the difference between A and F: thus

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But in order to draw the section to show the undulations of the ground between A and F, the horizontal distances of the several points B, C, D, E, and F, must be measured from the first station A; this is usually done with the chain during the operation of levelling. These distances with the back and fore sights may be arranged in a Field-Book of the following form, which, though not the practical form, may probably be better understood by the student.

50 ft.

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7.26 diff. the same as the last of the reduced

levels

In the above Field-Book it will be seen that the differences 4:07 and 2.35 in the column marked Fall are added together, making 6.42 for the fall at C, in the column of reduced levels: to this sum the next difference 2·96 is added for the fall at D. The other differences, in the column marked Rise, are successively subtracted from the last sum 9.38 for the falls at E and F: the latter of which, agreeing with the other difference, shows the accuracy of the castings. The last column shows the horizontal distances of the several points B, C, &c., from A.

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In plotting from the above columns of reduced levels and distances, the former are always taken from a larger scale than the latter,

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otherwise the variations in the ground would, in a great many cases be scarcely perceptible; the horizontal scale used in plotting the following section is 10 chains to an inch, and the vertical one for the reduced levels 25 feet to an inch, which latter scale has been thus chosen, that the section may be the same as that in the figure to Article 9, the vertical scale practically used being commonly 50 or 100 feet to an inch.

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Having drawn the horizontal line Af, set off the distances Ab 6 chains, Ac 12 chains, &c., from the column of distances, on a scale of 10 chains to an inch; then set off the vertical lines bв, cc, &c., respectively, 4.07 feet, 6·42 feet, &c., from the column of reduced levels, on a scale of 25 feet to an inch, and through the points A, B, c, &c., draw the line ABCDEF, which is the section required.

THE DATUM-LINE.

(10.) It is found inconvenient in practice to plot a section generally by the method already given, as the reduced levels, in extensive operations, would alternately rise and fall above and below Af (see last figure), and thus produce much confusion: therefore, a line HI, called a datum line, is assumed at 50, 100, or 200 feet, &c., below the first station A, so that it may be always below the sectional line ABCDEF. To or from this assumed distance of the datum line the rise or fall is respectively added or subtracted, and the next rise or fall added to or subtracted from the sum or difference, as in the following Level-Book; thus giving a series of vertical heights to be set off, always upwards from the datum line, through the upper extremities of which the section line is to be drawn.

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Having set off the distances on the datum line HI, draw the vertical lines HA, MB, nc, oD, pE, and IF, setting off their heights as in the column of reduced levels, and through the points A, B, &c., draw the required section ABCDEF.

(11.) It will be seen that the operation of levelling is extremely simple, as are also the castings of the Level-Book, and the plotting of the section. Great care is, however, necessary in reading off the staves, which ought, at the same time, to be held in a perfectly upright position; the castings in the Level-Book ought also to be carefully checked by taking the respective differences of the sums of the back and fore sights, and of the sums of the rises and falls, also of the datum number and the last reduced level; which three differences must agree, as shown in the preceding Level-Book, otherwise errors will be found in extensive operations to creep in imperceptibly.

NOTE.-Calculations to find the corrections for curvature and refraction are sometimes necessary in levelling, but as these would be extremely tedious, especially in extensive operations, they may be obviated by fixing the level always halfway between the staves, as nearly as the eye can judge, and thus the errors in both become equal and opposite, and consequently correct each other.

The general practice of levelling being now laid down in a brief manner, more details shall next be given.

TRIAL-LEVELS.

(12.) The general direction or route of a proposed line of railway between two places being determined upon, the line is marked out on such a map or plan of the district or country as is most convenient. (For this purpose the ordnance maps are the best, if the line be in England or Ireland.)

The levels are then taken, as near as possible to the direction thus marked out on the map; if any deviations are made from the projected line, they are confined to the intervals between where it crosses turnpikes and other public roads, the relative heights of the points where it crosses these roads being always determined; also marks, usually called bench marks (abbreviated B. M.), are made in or near them, these marks being described in the Level-Book for future reference. Cross-levels are also frequently taken, especially on the roads, to show the inclination of the ground to the right and left of the line, so that the engineer may know how to improve the line, and prepare it for further operations.

If the line, thus obtained, be thought not satisfactory, other directions, embracing either the whole, or only part of the distance between the two places, are tried in the same manner, and that direction which includes the fewest engineering difficulties is adopted.

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