Diagram (Fig. 261) showing the adjustment of the instrument for taking sections on curves and the variation of the tangential angles for each section.
Fig. 261. If the centre pegs be taken as slope pegs, the diagram applies to illustrate the setting out of half widths.
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Having set up the instrument at A, Fig. 261, over the centre peg of the series in the manner before described, ascertain the tangential angle for the first chain of the curve by dividing the constant, 1719, by the radius of the curve in chains, which gives the angle in minutes or 1719 ÷ 50 = 34′ 24″, and set the angle repeater to give a movement of double this angle or 1° 8′ 48″, ready for application at each change of section.
Set the horizontal arc to the tangential angle for the seventh peg from the instrument at which the first section has to be taken, or 34′ 24″ × 7 = 4° 0′ 48″, and direct the telescope to the peg. Zero is now on the chord line AD, which is parallel to the tangent at the seventh peg, and at an angle of 8° 1′ 36″, from the tangent line AB, which divided by 7 gives the variation of the tangential angle at each section, or 1° 8′ 48″, to which the angle repeater has been set. Release the horizontal arc and bring it round to an angle of 90° from zero, and the vertical arc will be at a right angle to the line A D and parallel with the section line at the seventh peg. Release the telescope from the arc and turn it at right angles thereto in the direction of the zero line AD. Now, by working the back adjusting screw of the tribrach, tilt the instrument until the cross web comes somewhat above the seventh centre peg, then tilt the vertical arc until the cross web is parallel with the lateral inclination of the ground surface. Clamp the arc and note the angle thereon to determine the inclination of the base to plot the sections from, and the instrument is then in adjustment for taking the first section at the seventh peg in the manner already described, being careful that the lateral bubble on the instrument is in a perfectly level condition. To take the second section at the sixth peg, one movement of the angle repeater must be made and the lateral bubble adjusted, which operation must be repeated for every succeeding section.
The movement of the angle repeater brings the vertical arc parallel to the section line at each peg, and the adjustment of the bubble maintains the angle of the inclined base uniform throughout.
When the sections are all taken on this side of the instrument, the telescope is turned to the other side and the operation continued until the whole fifteen are completed.
From the above detailed description it may be thought that the adjustment of the instrument for the operation is somewhat complicated, but in practice it is not so. After the first experience and the method is understood, it is only a matter of two or three minutes, and once in position the sections may be taken as rapidly as on level ground, and the saving of labour is practically the same as in taking sections when the line is straight.
597.—To set out Half Widths or Slope Pegs when the Line is straight.—In commencing this operation it is necessary in the first instance to set out two or more half widths, according to the length of the cutting or embankment. These may be a quarter of a mile apart, or so far as a ranging rod may be clearly seen from one point to the other. The pegs put in at these points act as normals from which to "bone" or range in all intermediate pegs by sight simply, without further recourse to levelling measurement or calculation. If the ground surface be comparatively flat, these normals may be put in in the usual way by using the instrument as a level, but if the surface is much inclined and the slope deep, a simpler method may be adopted, which will be hereafter explained.