Surveying and Levelling Instruments, Theoretically and Practically Described. / For construction, qualities, selection, preservation, adjustments, and uses; with other apparatus and appliances used by civil engineers and surveyors in the field.

by William Ford Stanley

594.—Explanation of the Method of Operating with the Inclinometer Theodolite.—For setting out a centre line of railway, etc., and putting in level pegs the instrument may be used as an ordinary theodolite, or even as a level, and the work performed in the usual manner. It may also be used as a level when setting out the normal slope pegs on slightly inclined ground surfaces, but when the inclination is considerable it may be used in a special manner with advantage as hereinafter explained.

595.—To take Cross Sections when the Line is Straight.—It is unnecessary to explain the use of the instrument when the ground surface is comparatively level, so as to require no change in position and resetting of the instrument, it being obvious that in this case it may be used simply as a level with advantage; but when the surface is inclined in the direction of the centre, and also at a right angle thereto in the direction of the section lines, the method of procedure is as follows:—

Assuming that it is desired to take a series of 15 sections (and this is within the limit of the number that can be taken from one setting of the instrument), set up the inclinometer, preferably over the centre peg of the series, in such a position that the two front legs of the tripod stand across the centre line, and the back leg (which has a distinguishing mark) rests upon the centre line. Set the lower limb of the tribrach stand upon which the instrument is supported to a level condition in its lateral direction by manipulating the back leg, and at the same time observing the bubble on the stand. This will enable the instrument to be subsequently tilted to a certain extent in a perfectly vertical position. Clamp the horizontal arc to zero and direct the telescope to the centre line. Clamp the lower limb and bring the arc round to an angle of 90°. The vertical arc is now at right angles to the centre line and parallel with the section lines. Now release the telescope from the vertical arc and turn it again on the centre line, and by working the back adjusting of the instrument (or in case of necessity manipulating the back leg) tilt the instrument until the cross web of the telescope is elevated to a short distance above the seventh or most distant peg of the sections, or site of the first section to be taken. Now tilt the vertical arc until the cross web assumes a position parallel to the general inclination of the ground surface laterally. Clamp the arc to this inclination and note the angle thereon, for this will be the angle of the inclined base from which the whole of the sections will be taken and subsequently plotted.

Commencing at the seventh peg at this side of the instrument, the sections may now be taken consecutively to the seventh peg on the other side by taking readings on a level staff held in an inclined position at a right angle to the cross web or base, as shown in Fig. 259, and oscillated that the lowest reading may be taken. A reading must be taken on the centre peg at each section to establish the height of the base above the peg. The base may be raised or lowered at any section, or part of a section, to meet any excessive elevation or depression of the ground surface which might prevent the staff being read, but a separate reading on the centre peg at each variation of the base must be taken, thus:—Fig. 260.

Fig. 260.

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The bases being parallel the angle of inclination remains the same. The tilting of the instrument produces a variation in the angle of the vertical arc, but this is only to such an infinitesimal extent that unless the tilt be excessive it may be disregarded. The correction, however, may be simply made after the instrument has been adjusted for any operation by ascertaining or simply noting approximately the angle of the tilt, and setting off this angle on the horizontal arc towards the tangent line, thus varying the chord or base line to this extent, or it may be found by referring to a table of natural sines, etc., and multiplying the cosine of the angle of the tilt by the tangent of the vertical arc angle, the result being the tangent of the corrected angle, thus:—if the angle of the tilt be 10°, and the vertical arc angle 25°—Referring to tables, cosine 10° = ·98481, tangent 25° = ·46631. ·46631 × ·98481 = ·45924 = tangent 24° 40′, the corrected angle making a variation of 20′.

596.—To take Cross Sections when the Line is on a Curve.—This operation is similar to that explained above for taking cross sections when the line is straight, except that being on a curve a variation of the tangential angle must be made at each peg or section. As this is performed mechanically by a single movement of the angle repeater and no reading of the angle is required, the work is just as readily performed. To more clearly elucidate the method, we will take a case in point and assume that the number of sections to be taken is 15 and that the radius of the curve is 50 chains, which the accompanying diagram illustrates.