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CHECK LEVELLING.

291 main line of levels. For a cross section of any length, as for instance, for half-a-mile or mile through the fields across the main line, we proceed in the same manner to avoid inverting in reducing, unless indeed the line of cross levels is to be of great extent. Before, however, levelling to the bench mark, we drive in a stump on the main line and level to it, then to the B.M., and proceed next to set out the line of levels for the cross section, at right angles to the main line, unless it is shown to be required in any other direction on the plan, for it is necessary that, for such cross sections as we are now mentioning, their direction and lengths should be carefully shown on the plan, besides being mentioned on the main section as well as the distance shown at which they are taken; it is also to be observed of such cross sections as these, that they are generally plotted to the same datum as the main line of levels. With regard to the cross sections of roads, it is hardly necessary to mention, that as the levels are taken down the centre of it, they are understood to cross the main line of levels at the same angle as the road itself. Whether or not these cross sections are plotted on the same sheet of paper as the main line, which is generally the case as regards those for roads, they are all carefully numbered according to the reference made to the main section, and sometimes on the plan. Besides the above, other methods are adopted in cross sectioning, but we consider that which we have given as the safest.

Check Levelling, the object of which is to ascertain the correctness of any particular line of levels, requires but very few observations. It has been understood from what has been said above that there is a B.M. at each end of the line, besides inter

a mediate ones ; let it be supposed that such a line has been levelled from end to end through fields, gardens, villages, &c.; the work is check levelled not necessarily by going over the whole of the line again, but by proceeding along the most convenient roads or paths, from one end to the other only; or from end to end, at the same time taking the levels to any intermediate bench marks that happen to be near the roads, canals, rivers, or other important positions that are crossed by the main line. Calling A one end of a line, and B the other, if we level from A to B by one route and then by another, and we find in both cases that the difference of level is the same, then we have a right to assume that both sets of levels are correct. But if instead of levelling by any road whatever, merely from the B.M. at A to the B.M. at B, we proceed so as to take up some of the intermediate bench marks, and find all the differences of levels the same as when the work was first done, then there will be still greater reason to be satisfied.

In check

levelling the chain is not used, differences of levels and not distances being the objects sought; in check levelling, more particularly when pushed for time, much longer sights are taken, but we have generally a better opportunity of making the backsights and foresights approximate to equality. As the observer who takes the check level is not always the same person who had levelled over the line, it is necessary that the first observer should leave some distinguishing sign at the bench marks, or else that he should enter a correct description of them in the level-book, so that the next observer should meet with no uncertainty on the subject. Keeping in mind what has already been said about ascertaining the differences of levels, by merely casting up the backsights and foresights, and subtracting one from the other, it will be perceived that for check levelling it is not necessary to cast out and reduce, as we can obtain the required differences without; but to prevent mistakes in the “tottings up," they should be gone over twice. Although the same description of field-book is used, entries are only made in the two columns of backsights and foresights. Let us suppose we have several pages of check levelling, and that at the bottom of the first page the backsights are greater than the foresights by 92:15, then the difference of level is a rise equal to this amount; to carry it forward to the next page it is entered at the top of the column of backsights, and the casting up again proceeded with as before ; had it been a fall it would have been entered at the top of the column of foresights.

Trial and Explore Levels. The object of trial levels is to try how far it may be preferable to lay down a line in one part of a country instead of another, as by adopting one line instead of another we may avoid not only tunnels and viaducts, but also heavy cuttings and embankments, expensive road crossings, bridges, &c., and all those heavy items which swell up an estimate to such formidable dimensions. For the purpose of taking trial levels, two or three and even more lines may be laid down on a general map of the country, and the salient points in the surface are levelled over, so as to obtain the general features of high and low ground, road, river, and stream crossings; the little undulations or bumps along a rise or fall in the surface it is quite unnecessary to notice, because whatever line is adopted, a survey of the lands will have in the next place to be made, and a regular line of levels taken over it ; neither is it necessary to lay down the centre line with the same care in the field ; indeed it cannot be done if we have only a general map to guide us, as the scale of it will prevent our reading off minute dimensions, and we must be directed by the corners or bends of roads, streams, woods, buildings, &o. Care should be taken to leave bench marks

TRIAL AND EXPLORE LEVELS.

293

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along a line of trial levels for the same purposes as those already mentioned, and more particularly on high and low ground, at roads and river crossings, and near all points where another trial line is shown to join on the general map. Besides, however, taking the levels along the different lines, one after another, the engineer may often do good service by taking levels to points off the line, as to objects to which he can refer on the map by lettering them with letters corresponding to those in his level-book; even to objects at a distance of half a mile or a mile useful observations may thus be made, particularly if a description is added in the column or page of remarks. This may sometimes be done approximatively without sending the staff-holder on to such points, which might involve loss of time. For instance, in taking trial levels along any particular line, we may observe the windings of a road in the distance, and which windings are shown on the map by some feature or other ; or we may take the bearing of it by the compass, or by half a dozen ways explained in our remarks on surveying. Now we may turn the telescope of the level in such direction, and see whether we intersect with the horizontal wire the surface of the road, or a man's or horse's head, the top of a hedge row, some particular clump of branches springing out of a remarkable tree, the top or bottom of a door or window, the roof of a house or chimney stack. Of the first of these we know the heights within a few inches, and the heights of the others may be measured at

any

future time, and we have thus the means of getting an approximation to the relative level of such road at those points as compared with the level of the spot on which we are standing. If there is no road there may be some farm buildings, with labourers or cattle about, or the corner of a wood, and many other objects near marked features on the plan, which a little ingenuity on the part of the observer will enable him to take advantage of. These observations may at times be of the greatest value, more particularly in a country of which the relative levels are not known, or only very imperfectly so. It is to be considered that in trial levels the minutiæ of the surface are quite matters of secondary consideration, and that the objects sought are the levels of the salient points in the formation of the ground. Trial levels are almost always plotted to a small horizontal scale, as three or four inches to a mile, and several lines of trial levels

may be plotted from one datum line, as of course they must all be referred to one datum level. The lengths of these lines will all probably differ more or less, and consequently some will be longer on the section than others. If they all begin or terminate at one point, such points of termination or beginning should be the same on the section. The surface lines of trial levels so plotted must be tinted in different colours to distinguish

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them one from the other. For our own part, we do not like the system of plotting trial levels in this manner, for when the inclinations or gradients come to beshown on them to try comparative merits, the whole often looks very confused. ,

confused. We therefore

prefer to plot the whole of them on one sheet of paper,

but on different horizontal lines, so as to keep the sections distinct, and we tint each surface line of the same colour as that corresponding to the colour of the line on the general map.

Working or Contract Section.—These documents only differ inasmuch as the second is prepared from the first to be delivered to the contractor under his contract. A perfectly correct idea may be formed of a working section from Fig. 136. The different manner in which it is prepared we will endeavour to explain. The horizontal scale to which it is plotted, instead of being 5 or 6 chains, is generally 3 or 4 chains to the inch, and the vertical instead of being 80 or 100 feet, is generally 30 or 40 feet to 1 inch. At every crossing of road, river, canal, stream, brook, &c., is inserted some remark as to the work to be constructed and a reference to the No. of the working drawing prepared ; this may be a special drawing as for a bridge, or a general drawing as for a level crossing and gates, or for a culvert according to the dimensions of the volume of water discharged by the brook. The different borings taken are also shown on the working section.

We have already made some slight allusion to the levels taken for the preparation of a working section, but we will detail them here rather more at large. It is to be understood that the centre line is first stumped out from end to end, that is, a short stump about two feet long and two inches square is driven into the ground at every chain's length, except at junctions of curves where three are driven across the line, one in the centre and one on each side, and the two latter instead of being driven upright are driven in slanting. Some engineers drive these stumps level to the surface, and by the side of each a guide peg is left to point out the direction of the line, in which case where the levelling is carried on the staff is set up on every stump. Others drive the stump to within three or four inches of the top, and the peg is driven behind it down to the surface for the levelling-staff to be held upon it. The advocates of either system are often very zealous for the one plan, but we do not believe that the matter is of the slightest importance. The centre line being thus prepared, the levels are not only taken over the surface at every stump or level peg as the case may be, but also over every little undulation or break in the surface of the ground, and to the bed and surface water of every stream, and to the flood height where attainable. Every indication is also noted in the remarks that

SETTING OUT LEVELS.

295

may determine the diameter of the culvert. Where roads are crossed levels are taken to the centre of the road, to the sides and to the footpath where there is any; to the surface water in canals, to the bottom of the canal and the towing path. With levels thus taken a very faithful document may be prepared in the shape of a working section as giving a true representation of the surface of the ground. Levels are taken to a sufficient number of bench marks, and where none suitable are found ready, large square-headed stakes are driven for the purpose. In preparing the working section vertical lines are drawn in blue at every chain's length up to the surface of the ground, and on each vertical is written the reduced height above datum, not as read off by scale, but from the column of reduced levels in the level-book. The next operation is to lay down the gradients, the one representing the surface of rail and the one below gives the average depth of formation below the level of rail, and is called “formation.”. This being done, the height of formation above datum is calculated from the inclination for every chain's length, and the difference between the reduced level to the natural surface and the level of formation last found is entered as depth of cutting or height of embankment at every chain also on the working, but not necessarily on the contract section. The inclination of the gradient per mile and per chain is also shown, the width of formation and the slopes as 1 or 2 to 1, or whatever it may happen to be. The nature of the borings are also shown. Fig. 136 will sufficiently explain the above observations.*

Setting out Levels.After what has now been said there will be but little difficulty in understanding this portion of our subject.

An inclined plane is one inclined to the horizon, and by the term “gradient,” numerically expressed, we imply the proportion which the height of rise or fall of the inclined plane bears to the length of the horizontal base of the incline, as 1 in 100, 1 in 200, 1 in 300, are expressions which mean, that in 100 feet the rise or fall is 1 foot, that in 200 feet the rise or fall is 1 foot, &c. &c.; and by keeping 1 as a constant number, the various proporti îns which inclined

planes bear to each other is better expressed and understood than by varying both expressions, or employing fractional quantities. Having to ascend or descend to a given point above or below the starting point, and along a given route, we shall know by levels and measurements the height of ascent or descent, and the distance by which the difference of levels will be regulated into one or more inclined planes; for a short distance, and slightly undulating ground, this may often be done by one incline; for any considerable length, more particularly in

* For further information on this subject the reader is referred to Railway Construction, by the author of this volume.

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