The heights in the cross-section are usually taken at every chain's length, to the distance of 10 chains on each side of the line, as will be seen in the following notes; remembering always to take the. levels from the left to the right of the onward direction of the main line, otherwise serious errors might arise by plotting the section in the wrong direction.

The cross-section is usually plotted on the same scale as the main section; some engineers adopt a larger one. The student can have no difficulty in plotting from the following notes. (See Plate XIII., Cross-Section No. 3.)

Cross levels No. 3. on road from Winston to Mold.

(20.) THE APPLICATION OF THE CORRECTION FOR CURVATURE

AND REFRACTION IN LEVELLING.

In the preceding examples on levelling, the application of the correction for curvature and refraction has been avoided, by assuming that the levelling instrument was always placed in observing at or near the middle point between the staves; thus making the errors arising from these causes correct each other. (See note to Art. 11.) But in a case where a very long sight is taken in one direction, as, for instance, the fore sight, the back sight at the same time being a very short one, these corrections must be strictly attended to, as in the following

Example. In taking levels for a projected railway, a swamp of 148 chains in width occurred in the line; the level was placed at the

edge of the swamp, the back-staff was placed one chain behind the instrument, on the level of the swamp, the reading thereon being 5.56 feet; the level being reversed, was found to cut a notch in a post, standing nearly in the line, on the opposite edge of the swamp, and on going round the swamp to the post, and measuring the height of the notch thereon, it was found to be 7.36 feet above the level of the swamp; required the correction for curvature and refraction. By Art. 8, Rule II. (148)2 ÷ 800=27.38 inches=cor. for cur.

Correction for curvature and ref.=23·47=1.95 feet.

for ref.

Therefore 7.36-1.95-541 feet, is the corrected fore sight; the back sight, being at so short a distance, needs no correction: hence the difference of the levels of the edges of the swamp is 5.56 - 5.41 = 0.15 feet.

NOTE. From the above example it will be seen that had the correction not been made, the error in the levels would have been nearly 2 feet.

(21.) When several assistants are employed on the same section, a uniform system should be strictly adopted, and the superintendent of the work should fix upon the bench marks, occasionally checking the work of the others. When a section has been thus taken in several parts at the same time, after putting the parts carefully together, a common datum line must be assumed for them all, and the result checked by adding or subtracting the differences of the reduced levels at the points of junction, accordingly as they rise or fall. Intermediate sights, in ordinary levelling, need only be taken to tenths of feet, as it would be a waste of time to attempt greater accuracy, excepting where the levels are taken to bench marks, in which the same accuracy should be observed as in taking back and fore sights. The height of the optical axis of the level, when on the line, or the level of the line of section, may always be put down as an intermediate sight, if required. It will here be proper to observe that it is not necessary that the levelling instrument should be placed directly on the sectional line, while making observations therewith, but in any convenient position either to the right or left of it.

In taking levels through towns, the operation frequently proceeds in a zigzag direction, such as the streets may present, the length of the required sectional line being determined from a map of the town, and the several heights of the points in the section obtained from the reduced levels, corresponding to the points in the streets where the sectional line crosses them. In a similar manner the elevation of the extreme points of the estates of proprietors and occupiers, who are hostile to engineering operations, are obtained by going round

without the bounds of their premises, or by the nearest roads between the extreme points, the profile of the intermediate space being assumed.

NOTE.-All the methods of levelling, and of laying down sections therefrom, given in the preceding articles of this section, will apply to canals, roads, sewers, drains, &c., with the same facility as if they had been written for these purposes.

LEVELLING BY THE THEODOLITE.

(22.) When the levels are required to be taken over very high and rapidly rising summits, on the acclivities and declivities of which it is found very difficult to fix the levelling instrument, or over steep and almost perpendicular cliffs, where it cannot be fixed at all, the operation would be best performed by the theodolite, which must be set perfectly level, both with respect to the spirit-levels on their vernier plate, and that which is attached to the telescope; and the angles of elevation and depression of the required points, both before and behind the instrument, respectively, taken by means of the vertical arc; the distances on the slope of the observed points from the instrument being, at the same time, measured as correctly as circumstances may permit, from which data the perpendicular elevation and depression of the points, as well as their horizontal distances from the instrument, may be found by the rules of right-angled plane trigonometry. These operations may be repeated for any number of stations, recollecting to make the necessary corrections for curvature and refraction, and to take into account the heights of the instrument and of the objects placed in the observed points. Operations of this kind should be performed when the atmosphere is settled, otherwise the refraction will be found so extremely variable and deceptive as to produce considerable error.

LEVELLING BY THE ANEROID BAROMETER.

It is often very useful, in going over a line of country, to be able to form a general approximate idea of the levels or altitudes of the ground, without going to the trouble of levelling it in the usual way. For this purpose the aneroid barometer (which is now made small enough for the pocket) is admirably adapted, as it will indicate differences of altitude to a few feet with tolerable precision. Full directions for the use of the instrument are usually sold with it.

It must, however, be borne in mind that the pressure of the atmosphere, even in the same place, is constantly varying, and that therefore, unless this source of error is provided against, the indications of the barometer may be exceedingly delusive. If accurate indications are desired, a duplicate instrument, remaining stationary

in one place, should be constantly watched and registered during the survey, and its indications carefully compared with that carried about over the ground.

SECTION II.

PARLIAMENTARY PLAN AND SECTION, ETC.

(23.) When application is made to Parliament for authority to make a railway, it is necessary to prepare a survey of the intended line, showing both its horizontal and vertical position; the documents exhibiting these features being called the "Parliamentary Plan and Section." Copies of these and some other documents have to be deposited, in due form, at certain places, in compliance with certain rules established by Parliament for the purpose.

These rules are called the "Standing Orders of the Houses of Lords and Commons on Private Bills." They contain many directions not only for the preparation of the plans and sections, but also for the laying out of the lines, all which must be carefully adhered to by the engineer and surveyor, or he will risk the rejection of his Bill. The standing orders are altered and amended from time to time, and it is therefore highly necessary that any engineer who contemplates going to Parliament, should provide himself with a copy of the latest edition, which is sold by Parliamentary stationers at a moderate price.

According to the standing orders of 1863, the Plan must be drawn to a scale of not less than four inches to a mile, and where any buildings are included within the limits of deviation, enlarged plans must be given to a scale not less than of an inch to 100 feet.

The Section must be drawn to the same horizontal scale as the plan, and to a vertical scale of not less than 1 inch to every 100 feet. The line of the railway shown is to correspond with the upper surface of the rails.

A model plan and section usually accompany the published book of standing orders.

Method of preparing a plan and section of a railway, as required by the standing orders of the House of Commons, preparatory to obtaining an Act of Parliament for its construction.

Plate XIII. is a portion of a plan and section, with cross-sections &c., of a railway prepared for the above-named purpose. The plan or map of a portion of the country through which it passes occupies the lower portion of the plate, the proposed centre line of the railway being marked thereon by a strong black line, and by dots where

it passes through a tunnel. The fields, &c., in the parish where the railway commences are numbered consecutively to the boundary of the next parish, where the numbers commence afresh, and so on through the successive parishes or townships; the numbers referring to corresponding numbers in a book of reference, in which are descriptions of the several properties, with the names of owners and occupiers. On each side of the centre line, and parallel to it, at the distance of 100 yards, or 454 links from it, are dotted lines called the limits of deviation: within the space included by these dotted lines, the engineer, on being empowered to construct the railway, is allowed to deviate from the line, as projected on the map, should he think it advisable for the sake of improving the line, or of avoiding expensive severance &c.

The main section, with its accompanying cross-sections, occupies the upper portions of the plate (these sections are the same as those referred to in some of the preceding articles), to prepare which, for Parliamentary as well as practical purposes, it will be first necessary to explain the method of laying out gradients.

THE METHOD OF LAYING OUT GRADIENTS.

(24.) The gradient of any portion of a railway means the inclination of the surface of the rails with respect to a horizontal line. A level line of railway would, doubtless, be preferable to any other; but the unevenness of the earth's surface puts this out of the question in by far the greatest number of railways. It is well to make the gradients as flat as possible, consistent with economy in construction of the works; they were formerly limited to about 1 in 264, but owing to the improvements in the tractive power, they now frequently reach 1 in 100, beyond which they should not go except in very difficult cases. Parliamentary committees exercise a rigid investigation into the necessity of steep gradients in lines brought before

them.

The usual practical method of laying out railway gradients is by applying one end of an extended silken thread to the commencement of the railway on the section, the other end being so applied that the extended thread may cut the curved boundary of the section or profile of the earth's surface, so as to leave an equal portion of space both above and below the thread, as nearly as can be judged by the eye, in order that the cuttings from the spaces or parts of the section above the thread, may produce materials sufficient to fill up the spaces or parts below the thread, or form the embankments of the railway. The position of the thread being thought satisfactory for the purposes required, its extremities are