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. deduct = 3.91 for ref.

Correction for curvature and ref.

Therefore 7.36

23.47 1.95 feet.

1.95 5.41 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 to 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 operation, are obtained by going round without the bounds of their premises, or by going round 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 the venier 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 trigo. nometry. 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 free from vapour, otherwise the refraction will be found so extremely variable and deceptive as to produce considerable error.

NOTE. The method of finding the difference of levels, on ground of the abovenamed description, by the barometer, though recommended by some, is quite out of the question, in respect to accuracy, on account of the continually varying pressure of the atmosphere, on which the indications of this instrument depend. One tenth of an inch of the mercurial column corresponding to 90 feet of elevation, which difference has been observed at the same place in a very short space of time, even in apparently settled weather. A similar difference, under similar circumstances, has also been observed at places on the same level at a short distance from each other. This method can, therefore, only be recommended, where a rough approximation is required.

SECTION II.

PARLIAMENTARY PLAN AND SECTION, ETC.

(23.) 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 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 railway, 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 portion 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 a railway is either a level portion of the line, or an ascending or descending portion thereof; the ascent or descent being always, for the sake of rapid locomotive traction, less than one foot estimated vertically, to 100 feet estimated horizontally. 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.

The usual, and, perhaps, only 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 marked, and a line ruled in the place occupied by it for the first gradient. The second, third, &c. gradients, are laid out in a similar manner to the end of the section. See Art. 26. and the two following notes.

NOTE 1. The excavations and embankments of a railway are made 2 feet lower than the gradients, thus giving a line parallel to the gradients, called the balance line; the 2 feet between the gradients and the balance line being filled up with gravel, to form the road and the beds for the sleepers of the rails. If, therefore, the excavations are not expected to afford any gravel for this purpose, it must be brought from some other place; and the gradients must be, consequently, placed 1 foot higher than would otherwise be required. In this case the end of the thread, by which the balance line is struck, must be placed 2 feet lower than the intended height of the rails at the terminus; a system of balance lines being laid out, in the same manner as was shown respecting the gradients in the last article; and the gradients in this case, drawn parallel to the balance lines, at the distance of 2 feet above them.

NOTE 2. — If the position of the first gradient, though favourable in itself, cause the following gradient, or gradients, to be less favourable, with respect to the quantity of cuttings and embankments, it is advisable to alter the position of the first gradient to one less favourable, provided that the compounded result of cuttings and embankments on the several successive gradients, as now altered, is more favourable than in the preceding case. In this manner, it is highly requisite to change the positions of the several gradients repeatedly, till the minimum, or least possible quantity of cuttings and embankments, shall be required in the construction of the railway, keeping in view the required limit in the ascent and descent of the several gradients; the difficulty of making the excavations, throughout the whole length of the line, being supposed, at the same time, to be nearly equal. But where the geological character of the country, through which the railway passes, differs considerably, presenting for excavation, strata varying throughout the length of the line, from loose sand to hard rock, and vice versâ, through which the facility or difficulty of making the excavations must be carefully considered in laying out the gradients; larger excavations being advisable, where they can be easily made; and smaller, where with difficulty, than would have been made, had no such variety in the strata existed. The least possible expense will be incurred in the construction of a railway, by taking into account all these circumstances. In the late railway mania these important subjects were by far too little considered, partly

through want of time to do so previous to depositing the plans, and partly through the ignorance or wilful negligence of some of the engineers, by which a useless expenditure of several millions of the money of the shareholders in these projects will, doubtless, be incurred before they can be carried into effect.

TUNNELS.

(25.) If any where in the section the excavations reach 60 feet in depth, and afterwards increase rapidly in depth, it is a more economical method of proceeding to make a subterraneous passage, called a tunnel, through the deep part, than to cut the whole open to the surface of the ground, which in many cases would be next to impossible. Tunnels are cut to the width and depth of 30 feet, for railways on the narrow gauge; if on the broad gauge, to the width and depth of 36 and 32 feet respectively, the width and depth being less, in both cases, if the material to be cut be hard rock. The diminished quantity of cuttings, where tunnels occur, must be taken into account in laying out the gradients.

(26.) To determine the rate of inclination of a gradient.

A B, in plate XIII., is the first gradient on the railway section, the cuttings or excavations above it being considered to be equal to the requirements of the embankments below it: at its commencement A, its height AO is 100 feet, and at its termination B, its height BC is 130 feet above the datum line; thus giving a rise of 130-100= 30 feet; the horizontal length OC of the gradient, is 65.60 chains = 4329.6 feet. There is, therefore, a vertical rise of 30 feet in a horizontal distance of 4329.6: hence 30: 4329.6 :: 1: 144.32; or, in round numbers, a rise of 1 in 144, which is called the inclination of the gradient AB, and is thus noted on the section, INCLINATION 1 IN 144.

The rule for finding the rate of inclination of a gradient may be thus briefly enunciated.

Multiply the horizontal length of the gradient in chains by 66, and divide the product by the difference of the heights of the gradient at its extremities above the datum line, and the quotient is the horizontal distance to a rise of 1 foot, or the rate of inclination required.

(27.) The excavations at B being above 60 feet deep, and continuing to increase rapidly, a tunnel BD, to the length of 462 yards, is introduced on the next following gradient; the tunnel, having passed beyond the summit, till its depth at D again becomes 60 feet, its height, as shown on the section, is 21 feet, being the height to which the cuttings are reduced by the ballasting below and the arch above. The gradient, of which the tunnel forms a part, is assumed to extend beyond the limits of the plate; its position, therefore, is not de