Although the theodolite or total station is a very complex instrument the measurement of horizontal and vertical angles is a simple concept. The horizontal and vertical circles of the instrument should be regarded as circular protractors graduated from 0◦ to 360◦ in a clockwise manner. Then a simple horizontal angle
measurement between three survey points A, B and C in the sense of measuring at A clockwise from B to C would be.
(1) The instrument is set up and centred and levelled on survey point B. Parallax is removed.
(2) Commencing on, say, ‘face left’, the target set at survey point A is carefully bisected and the horizontal scale reading noted = 25◦.
(3) The instrument is rotated to survey point C which is bisected. The horizontal scale reading is noted = 145◦.
4) The horizontal angle is then the difference of the two directions, i.e. Forward Station (C) minus Back Station (A), (FS − BS) = (145◦ − 25◦) = 120◦.
(5) Change face and observe survey point C on ‘face right’, and note the reading = 325◦.
(6) Swing to point A, and note the reading = 205◦.
(7) The readings or directions must be subtracted in the same order as in (4), i.e. C − A. Thus (325◦ − 205◦) = 120◦
Measuring a horizontal circle
(8) Note how changing face changes the readings by 180◦, thus affording a check on the observations. The mean of the two values would be accepted if they are in good agreement.
(9) Try to use the same part of the vertical hair when pointing to the target. If the target appears just above the central cross on FL it should appear just below the central cross on FR. This will minimize the effect of any residual rotation of the cross-hairs.
Had the BS to A read 350◦ and the FS to C 110◦, it can be seen that 10◦ has been swept out from 350◦ to 360◦ and then from 360◦ or 0◦ to 110◦, would sweep out a further 110◦. The total angle is therefore
10◦ 110◦ = 120◦ or (FS − BS) = [(110◦ 360◦) − 350◦] = 120◦.
A further examination of the protractor shows that (BS − FS) = [(25◦ 360◦) − 145◦] = 240◦, producing the external angle. It is thus the manner in which the data are reduced that determines whether or not it is the internal or external angle which is obtained.
Amethod of booking the data for an angle measured in this manner . This approach constitutes the standard method of measuring single angles in traversing, for instance.