468.—Field Book.—This book is generally made 8 inches by 4 inches, covered with red leather, with elastic closing band and sheath for pencil, as an ordinary pocket-book. It contains about 100 pages of good stout writing-paper. Two lines are ruled in red ink, ¾ inch apart, vertically down the centre of each page. The column between the lines is used for distances measured by the direct chain line at which hedges are crossed, stations, offsets, or other measurements are taken. In the right and left columns observations are made of objects desirable to be recorded or triangulated.
469.—For superior triangulation, definite and prominent fixed objects are taken at as great distances as possible, so as to include the details of measured triangles within a superior triangle. A church steeple, for instance, is a favourite sighting object. This cannot, however, generally be made, a station for future triangulation unless a scaffold is built up around it. Generally the most convenient method on fairly level ground, if the survey is large, is to have an ordinary scaffold pole, 20 feet or so in length, carefully straightened by a village carpenter with a stretched chalk line and then painted white. This may be squared at the end and fixed vertically in a socket formed of crossed boards to a depth of about 3 feet in the ground, with long crossing tail pieces rammed firmly with the soil to keep it steady. When this is used for a triangulating station, the pole is taken out of its socket and its exact position is centred for placing the theodolite. Flags are sometimes used to indicate stations: their defect is that the wind may blow them from or to the observer and thus render them invisible. Other methods will be found in practical works on surveying. This subject will also be reconsidered in Chapter XVII.
Fig. 195.—Diagram bisection of circle.
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470.—Elimination of Instrumental Errors during Triangulation—Changing Face.—It is generally advised to change face with the theodolite after angles are taken in the ordinary way, that is, to take first the initial angles reading from the face vernier with the tangent screw on the right hand, and then to take the same angles with the back vernier, the telescope being transitted. This, of course gives a reading on a different part of the circle and corrects the error of position of the vernier, or centring, in the following manner:—In Fig. 195 let a be zero (360°), the reading of the face vernier. Let the opposite reading (180°) be at a′. Suppose at 180° on the left-hand side of the instrument the 180° reads at b, then observe by the telescope an object that cuts this reading, or place a picket to do so. Change face; then the same arc will come to c, and the telescope must traverse cb to come to the first direction. The instrumental error is half bc, which bisected in a′ gives 180° exactly. The same principle of repetition with changed face may be made an any part of the circle, and the mean will be the correct reading.
471.—Repeating Angles.—This is performed by taking all parts of the circle for reading a given angle, so that errors of division and centring of the instrument are eliminated. The process is as follows:—Take the angular positions of two objects in azimuth, commencing with the zero of the horizontal circle, say the two objects subtend from the centre of the instrument 36° 10′; then turning the telescope back from its advanced position at 36° 10′ by releasing the lower or axis clamp, we may bring the first reading to the original zero position. Now clamp the lower clamp and release the vernier plate clamp and take again a forward reading. If this reads 36° 10′ + 36° 10′ = 72° 20′, the circle and centring appear so far correct; but it will probably read 72° 21′, and the corrected reading would be the mean 36° 10′ 30″. If we continue this system round in ten pairs of readings the whole circle will be embraced, then the mean of the sum of the minutes divided by the number of pairs of observations will give the true reading of the minutes. By taking the readings of two opposite verniers separately, the circle would be encompassed by five readings. This plan is followed in all important triangulations where the work is submitted to calculation. Such refinement is scarcely necessary for direct plotting with the protractor.
472.—It may be observed that if the horizontal circle is placed with its zero constantly to magnetic north—not necessarily for taking angles in reference to this—that the same part of the circle will always be used in the same direction; so that the sum of errors of the whole circle must necessarily tend to tie, even if the division is to a certain degree imperfect, provided also that the protractor used in plotting is also kept in one direction. This plan has otherwise no inconvenience, as any arc or angle may be taken by the difference of the circle reading in any position in which it may happen to fall. This does not mean that it is advisable to survey above ground by the needle—it is quite otherwise. It is best to have some distinct, sharply defined object to which all angles are referred, and therefore called a referring object, as the general index. The magnetic bearing need only be the initial position of the horizontal circle of the instrument.