CHAPTER XI

THE THEODOLITE

WHEN Surveying land covered with buildings or woods, &c., to such an extent that check lines cannot be measured, it is necessary to measure angles. Angles are measured in surveying for two purposes: (1) To fix the direction of survey lines already measured; (2) To calculate by trigonometry the lengths of lines. The taking of the angles should be done after the chaining is finished. Pegs are inserted in the ground where the surveying poles stood which

Fig. 160 shows Messrs. Thornton's Ardley' Transit theodolite on its tripod stand. It is fitted with a dial compass; pierced illuminated axis lantern; striding bubble; improved locking plates and three-screw adjustment, with shifting centre. The vernier reads to one minute. A 5-inch theodolite with 9-inch telescope and tripod stand, of similar pattern, costs about £32. It can be fitted with any of the diaphragms shown in Fig. 95, Chapter VI.

Instruments are called according to the diameter of their horizontal limbs. Thus a 5-inch theodolite is one which has a horizontal circle of 5 inches in diameter.

Description.-AB is a telescope which consists of two tubes one sliding inside the other. At the A end is the object glass, which inverts the image of the object observed, and at the B end is the eye-piece which magnifies the inverted image; C is the bubble tube fixed to the telescope by the capstan-screws through which

it may be set parallel to the line of collimation; D is the horizontal or transit axis; E and F are the supports which are of such a height that the telescope may turn completely round on its axis or as it is called, transit'; G

is the vertical circle or
limb or face, and H
and I are microscopes
for reading the vernier ;
J is the compass; K is
the upper or vernier
plate and L the lower or
horizontal plate; these
plates are concentric and
are called the horizontal
limb of the instrument;
M is a clamping screw
for clamping the upper
plate and N the slow-
motion screw for giving
accurate bisection of the
object; O is the vertical
axis round which is a

collar that
that may be
tightened by a clamping
screw, thus preventing
the instrument from
turning round; Q is the
slow-motion screw for
obtaining accurate bisec-
tion; R is the tribrach
and S, S, S the levelling
screws by means of which
the horizontal limb is set
truly horizontal; T is
the tripod stand.

Figs. 161 and 162 show the instrument in greater detail. In Fig. 161 will be seen a hook from which a plumb-bob is suspended to enable the instrument to be correctly set up over the station pegs. For

FIG. 160.

ordinary surveying this instrument is the most useful type. Other types are the Everest and the Y.

The Everest differs from the Transit in that it is lighter and more easy to carry; the telescope cannot be completely revolved on its horizontal axis; it has not a complete vertical circle; and

REFERENCE

(a) Transit Axis (b) Bubbles (c, c') Standards

(d) Telescope (e) Eyepiece

(f) Vertical Circle

(9) Clamp & Spring Tangents (h) Striding Level

(i) Reflector for Illuminated
Axis

(5) Axis Collar Clamp
(k) Compass Box
(1) Readers

(m) Magnetic Needle

(n) Needle Lifter

(0) Graduated Limb

(p) Body Piece

(2) Cover Plate

(r) Ring to carry Readers

(8) Plate Screws

(t) Tribrach

(u) Locking Plate

(v) Clamp to Shifting Centre

(w) Bottom Plate

(x) Shifting Centre

(y) Lamp

(z) Central Vertical Axis

FIG. 162.

the bubble tube is fixed to the vernier arm instead of to the telescope.

In the Y theodolite the telescope is supported in two Y's at the end of a bar which is fixed at right angles to the horizontal axis, and on top of the vertical limb. It possesses only a semicircle. (See Fig. 163.)

To Measure a Horizontal Angle.-1. Set up the instrument exactly over the station by means of the plummet which should hang exactly over the

centre of the station

peg.

2. Clamp the horizontal plate and unclamp the horizontal vernier plate; turn the latter until the arrow of the vernier coincides exactly with the 360° on the horizontal limb, accurate bisection being obtained by means of the slow-motion screw and magnifying glass.

3. Level the instrument by means of the foot-screws, as explained in the chapter on Levelling, until the bubble remains always in the centre of its

FIG. 163.

5. Unclamp the horizontal vernier plate and direct the telescope on to the next object until it is approximately bisected. Clamp and obtain accurate bisection by means of the slow-motion screw attached to the vernier plate.

6. The angle subtended at the station over which the theodolite is set up by the two objects may now be read from the horizontal limb and verniers, and their mean taken as the correct horizontal angle.

N

To Measure a Vertical Angle.-1. Set up the instrument over the station, and level the horizontal plates as before.

2. Set the vertical verniers to read zero, and then level the arc by bringing the vertical arc level bubble into the centre of its run by means of the antagonising screws.

3. Now direct the telescope to the object whose angle of elevation or depression is required. Obtain accurate bisection, after clamping with the vertical clamp, by means of the vertical slowmotion screw.

4. The vertical angle may now be read from the vertical verniers, and their mean taken as the correct vertical angle.

The most important points to be observed in angular measurements are accurate centreing of the instrument over the station and correct bisection of the objects. To obtain accurate centreing by means of the plummet requires care and, unless one hits it off approximately at the first setting up of the instrument on its tripod, also time. Some instruments have centreing plates which allow for a movement of about 3 inches each way and make accurate centreing an easy matter, but when there are not centreing plates, the plumb-bob must be centred by shifting the legs only, and pressing them into the ground one at a time, until the bob is exactly over the centre of the station peg. The angle should always be read off on each vernier and the mean taken, so as to minimise errors of graduation of the arc.

Changing Face. When great accuracy is required-in fact one might say on all occasions, and especially when taking vertical angles-every angle should be observed with what is known as changed face, and the mean of the two observations taken. When the observer is standing at the eye end of the telescope of a theodolite and the vertical limb is on his left hand the instrument is then said to be at face left, and when in a similar position the limb is on his right hand, the instrument is at face right.

To Change Face.-After observing the angle with the instrument at face left (F.L.), next observe the same angle with the instrument at face right (F.R.). To do this move the left-hand or A vernier through 180° in azimuth so that the object-glass occupies the position which was occupied by the eye-piece. Now revolve the telescope vertically through 180° on its horizontal axis, and the vertical limb will be on the right hand and the instrument at F.R. The vernier which reads from 0 is called the A vernier, and that which reads from 180° is called the B vernier.

By using both faces of the instrument most errors are eliminated, such as the error of horizontal collimation and errors due to the transit axis not being properly level.

Errors due to eccentricity, i.e. through the vertical axis not being exactly concentric with the upper and lower plates, are eliminated by reading both verniers.

Errors due to imperfect graduation are eliminated by measuring the angle several times on different parts of the graduated limb. When observing to a pole always bisect the bottom of the pole.