But in order to draw the section to show the undulations of the ground between A and F, the distances of the several points B, C, D, E, and F, must be measured from the first station A; this is usually done during the operation of levelling, but omitted to be noticed in explaining that process to prevent confusing the student. 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.

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 distances of the several points B, C, &c., from A.

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

wise 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.

Having drawn the horizontal line Aƒ, set off the distances A b = 6 chains, A c = 12 chains, &c. from the column of distances, and a scale of 10 chains to an inch; then set off the vertical lines b B, c C,

45.93

B

&c., respectively, 4.07 feet, 6.42 feet, &c., from the column of reduced levels, and a scale of 25 feet to an inch, and through the points A, B, C, &c., draw the line A B C D E F, 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 A ƒ (see last figure), and thus produce much confusion: therefore, a line H I, 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 ABCDE F. To or from this assumed distance of the datum line the rise or fall are respectively added or subtracted, and the next rise or fall added or subtracted to or from the sum or difference, as in the following Level-Book; thus giving a series of vertical heights to be set off from the datum line, through the upper extremities of which the sectional line is to be drawn.

A A

9.211

F

Ei

42 74

Having set off the distances on the datum line H I, draw the vertical lines H A, m B, n C, o D, p E, and I F, setting off their heights as in the column of reduced levels, and through the points A, B, &c., draw the required section A B C D E F.

(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 an 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 foresights, 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 half-way 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 principles and practice of levelling being now laid down in a brief manner, more general details shall next be given.

TRIAL LEVELS.

(12.) The 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 best represents the direction of the line. (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, are made in or near them, these marks being described in the Level-Book for future reference. Crosslevels 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.

CHECK-LEVELS AND SURVEY OF THE LINE.

(13.) Check-levels are sometimes taken to ascertain the accuracy of the trial-levels, if any doubt exists in this respect, and, more especially, if the line be a detached one; i. e. not connected at its commencement or termination with existing lines, nor any where intersecting them. Although this can rarely be the case in these times, both in England and some other countries, where so many railways exist, the sections of which are published, from and to which almost all new lines proceed, so that the elevations of the commencement and termination, or terminii (so called in railway language) of almost all new operations are so well known, not only with respect to these points, but also to other intermediate points of intersection with existing lines, as to obviate the use of check-levels, provided the trial-levels have been taken by a judicious leveller.

(14.) The trial-levels being considered satisfactory, the survey of the surface is immediately commenced, to the width of from 5 to 10 or 15 chains on each side of the projected line, accordingly as the property of individuals may appear to be affected, or the engineering difficulties or requirements of the line may demand. This survey must include every enclosure, building, road, &c., within the abovenamed limits; it is usually on a scale of from 5 to 10 chains to an inch, and may be made by the help of the theodolite, or, in a great many cases, by the chain only. (See Case V. Surveying by the theodolite, and the annexed figure.)

FINAL LEVELS.

(15.) The point of commencement of the proposed railway being determined upon by the previous operations, set one of the levelling staves on that point and call it the first back station, and select a point as near this station as possible, the height and position of which must be entered in the Level-Book, as a mark of reference for future operations. This is called a bench mark, it is marked B. M. in the column of remarks in the Level-Book; it may be either between the first back station and the second, or between the second and third, accordingly as convenient objects for the purpose present themselves. The most proper places for bench marks are foundation-stones of buildings, or other fixed stones, hinges of gates, mile-stones, notches near the roots of trees, &c., the positions of which must be described in the Level-Book. Fix the level firmly in the ground about half-way between the first and second stations, and make the axis of the spirit-level horizontal in all positions; read off the staff at the first back station; this reading is placed in the first column of the Level-Book, marked Back Sights. If neither the bench mark, nor any other intermediate point, requiring notice, occur between the two stations, turn the telescope to the second station, and read off the height; this reading is placed in the third column of the Level-Book, marked Fore Sights. Remove the first staff to the bench mark, or intermediate station (if one occur), having at the time removed the instrument; read off the back sight and enter it in the Level-Book, as before; then read off the staff on the bench mark, and enter the reading in the column marked Inter. ; lastly, read off the forestaff, as before: thus continuing and taking as many bench marks, and other intermediate sights, as may be thought necessary; the chaining of the line proceeding at the same time, the results of which are placed in the column of distances. It will readily be seen that four assistants will be required by the leveller, i. e. two for the staves, and two for the chaining. (For method of keeping Level-Book, see next page.)