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Under the head of "Remarks" are noted the bearings of the different lines of the sections if required to be laid down on a plan; the references to bench-marks; cross-sections; and other information that may subsequently prove useful. If the instrument is placed in the direct line of the section, it will give an intermediate point on the ground between the staves, by measuring its height; this requires again another column, and leads to confusion, without being of much benefit. The difference of the sum of all the back and forward sights should of course correspond with the difference between the quantities under the head of + and and also with the last reduced level, either rise or fall.
In taking trial sections with the spirit-level, to ascertain the best line for a railway or other work, the same form applies as for sections for more particular purposes, either civil or military; but the distances may be longer, as was observed when speaking of the theodolite. The same bench-marks should be always levelled up to in every trial section.
In running check sections, to ascertain the accuracy of former sections, there is generally no occasion for measuring distances: and only a column for "back," and another for "fore" sights, with a third for remarks, are required.
At each bench-mark these columns may be added up, and their difference entered under the column of "Remarks." As already stated, check sections are more quickly taken with a theodolite by reciprocal angles of elevation and depression than by the spirit
In laying down a section on paper, particularly if the ground
A separate column is often kept for "Bearings;" and instead of the bearings and distance between each staff, the angles with the meridian, and the distances are sometimes taken between the instrument and each back and forward station; which arrangement requires two columns for distances, and two for bearings; or, instead of bearings, angles may be taken to some known object.
is of gentle slope and the section of considerable length, it is usual to exaggerate the vertical heights for the purpose of rendering the undulations of the surface perceptible, which necessarily produces a distorted representation of the ground. The horizontal scale is usually made an aliquot part of the vertical, that the proportions between them may be at once obvious. Scales of 25, 50, 100 or 150 feet to one inch*, are appropriate for the latter, according to the degree of detail required in the section; and the horizontal scale may be from to of either of them; or even a less proportion if the section is of great length, and the ground generally flat, as in the figure below, plotted from the specimen of a levelling field-book in page 87.
The horizontal line from 'which the vertical distances are set off, may be either on a level with one end, or some one point of the section; or a datum line may be drawn any number of feet above or below this line, exceeding the sum of all the vertical heights: this latter arrangement makes all the dimensions reduced for plotting either plus or minus. Laying off intermediate horizontal and vertical distances, should be avoided in plotting sections; the former ought always to be measured from the commencement of the section, with as few interruptions as the length of the line will allow; and the latter from the datum line. Both horizontal and vertical distances should, particularly in a working section, be written legibly on the drawing.
Trial sections that have been run for the purpose of ascertaining the best of several routes for a railroad, canal, or other work, should invariably be all plotted on the same scale and paper, and from the same datum line; and commencing at, and having refe
* The plotting scales, already alluded to, are very convenient for laying down sections; and Mr. Holtzapffell's cardboard Engine-Divided Scales will be found useful where a variety of scales are often required; from their method of construction, they can be sold at the low price of nine shillings a dozen, of all descriptions in general use.
rence to, the same points as bench-marks. arrangement their comparison by the eye is facilitated. Cross or transverse sections are sometimes plotted above, and sometimes below the longitudinal section: and if only extending a few feet to the right and left, they are occasionally plotted on the line of section: but, if numerous, this last method causes a confused appearance in the drawing.
A method of combining plan and section has lately been introduced by Mr. Macneil, for the purpose of giving a popular representation of the quantity of excavation and embankment at any part of the section of a line of railway, the direction of which is shown on the outline plan of the coun
try through which it passes by a thick black line, supposed to represent a vertical section of the rail. From the accurate section previously drawn, the heights of the embankments and depths of excavation at the different parts of the line are transferred to this datum line on the plan; and these quantities being tinted
with different colours, or, if engraved, represented the one with vertical, and the other with horizontal lines, show at a glance the general relative proportions of cutting or embankment, as in the annexed figure.
The dark line in both figures represents the surface of the railroad or embankment.
To those unaccustomed to the use of sections, this simple contrivance by which they are rendered intelligible is particularly useful, and has been ordered to be adopted in all plans for railways submitted to the House of Commons. Of course it is only intended to give a general idea of the quantity of work on any line of road, railroad, or canal, and to be explanatory of the report and estimate.
The section which has always to accompany this species of plan must be plotted on a scale, the horizontal distances being not less than 4 inches to 1 mile, and the vertical not less than 100 feet to 1 inch. A line must also be drawn on the section representing the upper surface of the rails. At each change of inclination the height above some datum plane must be shown, and also the rates of the slopes, and the distances for which these gradients are maintained. The height of the railway over or under any turnpike road, navigable river, canal, or other railway, is likewise to be marked at the crossing. A variety of precautions and regulations are enforced by the "Standing Orders" relative to the construction of railways; and there are numerous other details connected with them, for which reference must be made to some of the numerous excellent practical works devoted solely to this branch of civil engineering.
Numerous transverse sections are required for computing the relative proportions of embankment and excavation* on any work, which operation is much facilitated by the use of Mr. Macneil's ingenious tables, calculated upon the "Prismoidal Formula," which shows the cubic content of any prism to be equal to the area of each end + four times the middle area, multiplied by the length and divided by 6; whereas the common methods of taking
* Of the greatest possible consequence, both for the sake of avoiding unnecessary expense, and of laying out the work to the best advantage, valuable information upon this subject will be found in Mr. Macneil's work.
half the sums of the extreme heights for a mean height, or of taking half the sum of the extreme areas for a mean area, are both erroneous; the first giving too large a result, and the second too little.
Mr. Haskoll also gives very useful tables for the calculation of the areas of cross sections in the 2nd vol. of his “Engineer's Railway Guide;" a book containing full information upon all subjects connected with the laying out and construction of railway works.
The last description of levelling by the spirit-level to be noticed, is the method of tracing instrumentally horizontal sections termed "contours," either round a group of isolated features of ground for the formation of plans for drainage, sanitary, railway, or other engineering purposes-models or plans of comparison for military works, &c.; or over a whole tract of country with the view of giving a mathematical representation of the surface of the ground in connection with a national, or other extensive and accurate survey.
As regards the first of these, the tracing instrumental contour lines round any limited feature, or group of features of ground, the manner of proceeding is very simple. The site must be first carefully examined, and those slopes that best define the configuration of the surface, particularly the ridge and watercourse lines, marked out by rods or long pickets at such distances apart as may appear suited to the degree of minutiæ required, and the variety in the undulations of the ground. Where no such marked sensible lines exist, the rods must be placed where they can most readily be observed, being necessary as guides for the levelling staff during the subsequent operations. An accurate survey of the ground on which the positions of these rods are shown is then to be made. This should be laid down upon a scale proportioned to the purposes for which the plan is required, and to the vertical interval by which the contour lines are to be separated.
The scale for towns that has been adopted on the Ordnance Survey is 88 feet to 1 inch, which is sufficiently large for most engineering and municipal works, but can be increased to 40 or 50 feet for illustrating projects for drainage, or for the supply of water by pipes, &c. Estates are generally laid down upon a scale of 3 or 4 chains to 1 inch. For the larger scales the contour