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Instead of only taking the single angle of depression to the distant station B, and noting the heights of the vane at the intermediate stations, a, b, c, &c., angles may be taken to marks the same height as the instrument set up at each of these intermediate points, which will equally afford data for laying down the section; but the former method is certainly preferable.

The details may be kept in the form of a field-book*; but for this species of levelling, the measured distances and vertical heights can be written without confusion on a diagram, leaving the corrections for refraction and curvature (when necessary) to be applied when the section is plotted.

Where a number of cross sections are required, the theodolite is particularly useful, as so many can be taken without moving the instrument. It is also well adapted for trial sections, where minute accuracy is not looked for, but where economy both of time and money is an object.

The theodolite is likewise used in running check levels to test the general accuracy of those taken in detail with a spirit level. Reciprocal angles of elevation and depression, taken between bench marks whose distances from each other are known, afford a proof of the general accuracy of the work; and if these points of reference are proved to be correct, it may safely be inferred that the intermediate work is so likewise.

Instead, however, of observing reciprocal angles of elevation and depression between marks at measured distances, levelling for sections, where minute accuracy is required, is performed with a spirit level, or some instrument capable of tracing horizontal lines. The different instruments used for the purpose, and their adjustments, will be first described; and the most approved methods of using them, and keeping the field-book, as well as plotting the detail on paper, will be afterwards explained.

The species of level formerly in general use, termed the Y level,

* Bruff's "Engineer Field Work," page 122.

+ Marks on stumps of trees, mile or boundary stones, &c., or any convenient permanent object on which the staff is placed to obtain the comparative level of these intermediate points of reference. They are useful either for the subsequent laying out of the detail of work, or for comparison in running check or trial sections. Bench marks should be conspicuously marked and clearly described in the field-book, that no doubt may arise as to their identity.

owes its name to the supports upon which the telescope rests. This instrument, as well as Mr. Troughton's improved level, and the dumpy level introduced by Mr. Gravatt, are described at length in Mr. Simms' "Treatise on Mathematical Instruments." It is decidedly inferior to the two last mentioned, its only claim to notice when compared with them being the greater ease with which its adjustments are made; though this advantage is again partially negatived by the equal facility with which they are deranged.

The first adjustment in the Y level is for the line of collimation; and the method is the same as that described in page 23 for the theodolite, half the error being corrected by the screws acting upon the diaphragm containing the cross hairs.

The second adjustment (that of the spirit level attached to the telescope) is also similar to that for the theodolite *. After the air-bubble has been brought into the centre by the plate-screws, the telescope is reversed in the supports, and if it has moved to either end of the level, it is brought back to its central position, one half by the screw at one end of the level, and the other half by the plate-screws, there being no vertical motion as in the theodolite. This correction will probably require two or three repetitions.

The third adjustment is for the purpose of bringing the Y supports exactly on the same level when the previous corrections have been made, so that the optical axis of the telescope may always revolve at right angles to the vertical axis of the instrument. This is effected by first levelling the telescope when placed over two opposite screws, and then turning it round so that the eye-piece and the object-glass may change places.

If in this reversed position the bubble is no longer in the centre, it must be adjusted, one half being done by turning the milled headed screw A, placed directly below one of the Ys, which is thereby raised or lowered in its socket, and the other half

* Before adjusting the focus of the object-glass, that of the eye-piece should be always attended to, both in the spirit level and theodolite; it should be drawn out till the cross wires are clearly defined, and there is no instrumental parallax; so that on fixing their intersection on some distant object there may be no displacement of the contact on moving the eye sideways to the right or left.

by the plate-screws. This operation must be repeated with the other pair of plate-screws, and care must be taken that the screw represented by A in the sketch is never touched except for the purpose of making this adjustment.

In Troughton's instrument, the spirit level, being fixed to the telescope, has no separate means of adjustment, and the line of collimation must therefore be determined by its assistance. The telescope also, being bedded in a sort of frame, cannot be reversed end for end; the level is first adjusted by correcting half the error when turned round, by the screws which act upon the supports, and half by the plate-screws; the line of collimation is then made to agree with the corrected level by noting the height of the intersection of the cross wires on a staff about 200 or 300 yards distant. The instrument and the staff are then made to change places, and if the difference of level remains the same, the optical axis is already correct; if not, half the difference of the results must be applied to the observed height of the vane on the staff, and the cross wires adjusted to this height by means of the screws of the diaphragm at the eye-piece of the telescope.

A pool of water furnishes another easy mode of adjusting the line of collimation. A mark being set up at any convenient distance of exactly the same height above the surface of the water as the instrument adjusted for observation, the cross wires have only to be made to intersect each other at this point.

The adjustments of Mr. Gravatt's level (the best of the three) are nearly similar; and will be found described by himself, in Mr. Simms' little work, already quoted *.

The French water level is much used on the Continent, in taking sections for military purposes. It possesses the great advantage of never requiring any adjustment, and does not cost one-twentieth part of the price of a spirit level. From having no telescope, it is impossible to take long sights with this instrument; and it is not of course susceptible of very minute accuracy; but, on the other hand, no gross errors can creep into the section, as may be the case with a badly-adjusted spirit level or theodolite, the horizontal line being adjusted by nature without the intervention of any mechanical contrivance. As this species of level

* Also in page 137 of Mr. Bruff's" Engineering Field Work."

is not generally known in England, the following description is given; which, with the assistance of the sketch, will enable any person to construct one for himself without further aid than that of common workmen to be found in every village *.

ab is a hollow tube of

brass about half an inch in
diameter, and about three
feet long, c and d are short
pieces of brass tube of larger
diameter, into which the long
tube is soldered, and are for
purpose of receiving the
two small bottles e and f,
the ends of which, after the

bottoms have been cut off by tying a piece of string round them when heated, are fixed in their positions with putty or white lead -the projecting short axis g works (in the instrument from which the sketch was taken) in a hollow brass cylinder h, which forms the top of a stand used for observing with a repeating circle; but it may be made in a variety of ways so as to revolve on any light portable stand. The tube, when required for use, is filled with water (colored with lake or indigo), till it nearly reaches to the necks of the bottles, which are then corked for the convenience of carriage. On setting the stand tolerably level by the eye, these corks are both withdrawn †, and the surface of the water in the bottles being necessarily on the same level, gives a horizontal line in whatever direction the tube is turned, by which the vane of the levelling-staff is adjusted. A slide could easily be attached to the outside of c and d, by which the intersection of two cross wires could be made to coincide with the surface of the water in each of the bottles; or floats, with cross hairs made to rest on the surface

* The instrument from which the sketch was made was constructed for me by an ironmonger in Chatham; and I have tried it against a very good spirit-level, and found the results perfectly satisfactory. This water-level is, I find, now constantly used on the Ordnance Survey for interpolating horizontal contours at vertical intervals of 25 feet between the more correct contours, traced at greater distances apart by the spirit-level.

†These corks must be drawn carefully, and when the tube is nearly level, or the water will be ejected with violence.


of the fluid in each bottle, the accuracy of their intersection being proved by changing the floats from one bottle to the other : either of these contrivances would render the instrument more accurate as to the determination of the horizontal line of sight; though one of its great merits, quickness of execution, would be impaired by the first, and its simplicity affected by either of them. For detailed sections on rough ground where the staff is set up at short distances apart, it is well qualified to supersede the spiritlevel, and is particularly adapted to tracing contour lines: which operation will be described in its proper place.

A mason's level and boning-rods also answer very well for taking sections where no better instruments are at hand, and are used as described below.

A horizontal line is obtained by driving two pickets (1 and 2) into the ground, and applying a large mason's level to their heads, which should be previously cut square. The pickets 2 and 3, 3 and 4, &c., can be levelled in the same manner, as far as may be necessary, to obtain a correct horizontal line for a short distance; but if any considerable

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of any two of the pickets already levelled, and the vane of a staff raised or depressed at any required point, till it is on a level with the tops of the boning-rods. The reading of the staff will give the respective depths below the level of the heads of the rods, the heights of which must be subtracted. Boning-rods are chiefly used in laying out slopes in military works, and for setting up profiles to direct working parties. A slope of 5 to 1, for instance, is laid out by measuring 5 feet from a towards b, and driving the head of the picket at the end nearest b, one foot lower than that at a; the heads of boning-rods, of equal height, placed on the tops of these pickets, are evidently on a slope of 5 to 1.

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5 Feet.

The last description of instrument used for levelling is the French

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