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marked so distinctly that they can be read by the observer without the use of a vane, or the necessity of trusting to an assistant; the figures are inverted to suit the inverting telescopes now generally used, and instead of moving about a heavy iron tripod on which to rest the staff, a species of shoe with a hinge is attached to it, which allows the face to be turned round in any required direction without the staff being moved off the ground. Though much more convenient, and less liable to mistakes in reading than the old species of staff, the same degree of accuracy cannot be obtained with it.
To proceed to the method of using the spirit-level or other instrument for tracing horizontal lines, and also of keeping the field-book in levelling for sections. In the system formerly pursued, the instrument was set up at one end of the line A, of which a section was required; and having ascertained the accuracy its adjustments, and levelled it by the plate-screws, an assistant was sent forward with the levelling-staff to the first station, and the difference between the height of the vane when intersected by the cross wires of the telescope, and the height of the optical axis of the instrument from the ground, gave of course the difference of level between these two points. The distance was then measured and entered in the field-book, and the level moved on to the first station, the staff being sent on to the second, where the same process was repeated.
It is self-evident that this manner of levelling is vitiated by the
errors of curvature and refraction, which, if not allowed for in a long section, would in the end produce a considerable error. But the necessity for these corrections is avoided by simply placing the instrument half-way between the two stations, and either in the line of section, or on one side of it.
Thus the level * being set up, as in the figure at a, the difference between the reading on the staff set at the back station A, and at
the forward station (1), gives at once the difference of level between the ground at these points, without any correction for refraction or curvature, and also without taking into account the height of the instrument; a slight error in the line of collimation of the telescope also does not impair the results, as the elevation or depression of the optical axis would have the same effect on both staves; whereas in levelling entirely by the forward station, the least error in the adjustment of the instrument is fatal to the accuracy of the section, being always carried on, whether additive or subtractive. This assertion, however, supposes the instrument to be exactly equidistant from the two stations, which in ground having a great inclination is often impossible; nevertheless, by good management, any reference to the table of curvature and refraction may generally be avoided, and if this correction is necessary, it should be made merely for the difference between the distances.
In keeping the detail in the field, the horizontal and vertical distances are sometimes written on a sort of rough diagram, as recommended in levelling by angles of elevation and depression with the theodolite; but the most general and best plan is to enter all the dimensions in the field-book, particularly if the distance to be levelled is considerable, and references are made to benchmarks. There are slight differences in the modes in which this field-book is kept; but the following example, with the description
* By having two assistants, with levelling-staves, one for the back and the other for the forward station, much time may be saved.
below, will show the usual method of entering the details, so as to render them at once available for transferring to paper* :
This table almost explains itself: the first column headed "Distances," contains the distances measured between each place where the staff is put up†. The second and third columns are for the readings of the staff at each back and forward station, the differences between each of which are entered under the fourth and fifth columns, headed and under the two last, headed + "Rise" and "Fall," are carried out the total rise or fall of each place where the staff was placed, above or below the starting point.-The bench-mark at the end of the fourth station being in the line of the section, the distance is entered as usual; but that at the seventh, being out of this line, and its level merely ascertained for a future reference, there is no dimension entered in the column of "Distances," so that it is not plotted in the section.
* For more detailed instructions on the method of levelling for and plotting sections see Mr. Simms' work. Where very great accuracy is required, the level is always read over a second time, the instrument being thrown out of adjustment and readjusted-a certain amount of difference only is allowed-about 003 ft. A levelling staff, with an improved vane, is also used, instead of the now common staff without a vane.
+ Where only lineal distances or sectional areas are required, a chain of feet is the most convenient for use, instead of the Gunter's chain used for determining superficial areas in
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 spiritlevel.
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, 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.