the vernier-plate together are sometimes termed the horizontal limb, in which case G is called the lower limb. The instrumentmakers' names are (F) plate, and (G) limb.

On the vernier-plate are two uprights or supports, D, D, which support the horizontal axis, C, of the vertical or altitude circle, E. The latter is provided with two indices with verniers at the opposite ends of a horizontal bar, read by the microscopes e, e. The telescope A B is fixed directly upon the horizontal axis.

The horizontal circle is screwed by a flange to a brass vertical axis, K, passing through the collar of a clamp, where it may be fixed or loosened by the clamp screw, k. Below the collar, the vertical axis works freely on a ball and socket joint at its lower end. The ball and socket is placed between the parallel plates, L, M, which are provided with four levelling screws, 7. The vernier-plate is provided with two spirit-levels, ff, and a longer spirit-level, c, is attached to the telescope. The whole instrument is supported on a strong tripod stand.

60

90

60

30

0

The vertical circle is divided into four quadrants, the degrees in each of which are numbered from 0° to 90°, as shown in Fig. 33. In the old-fashioned theodolite the vertical limb is a semicircle. This is surmounted by an oblong flat piece of brass, the stage, to the ends of which are screwed the two forked rests called Y's, by which the bell-metal collars of the telescope are supported. Under the telescope is a long spirit-level. A theodolite of this kind is termed a plane theodolite, whilst one with a complete circle as vertical limb is termed a transit theodolite. The advantages presented by the latter form are the greater vertical sweep of the telescope and the greater accuracy of the readings of the vertical limb.

09

06

09

Fig. 33.

Connected with the horizontal circle and vernier-plate, there are two screws, H, I, one of which, H, is a clamping screw and the other a slow-motion or tangent screw. When H is loose, the two plates, G and F, can be moved independently, but when the screw H is tightened they can only be moved separately by means of the tangent screw I. Beneath the horizontal plates, there are two screws, k and i, one of which, k, is a clamping screw and the other a tangent screw. When the screw k is loose, the whole of the upper part of the theodolite above the screw can be rotated in any direction, in which case the horizontal circle moves upon the double conical axis upon which it rests. On tightening the screw k, the upper part can be moved only by means of the tangent screw i. Two screws refer to the vertical

circle, a clamping screw and a tangent screw d. When the

Fig. 34.

0

clamping screw is loose, the vertical circle can be moved freely; but when it is tightened, the circle can be moved only by means of the tangent screw d.

As an aid to memory, the screws may be divided into three sets, each of which consists of a clamping and a tangent screw. The upper set belongs solely to the vertical circle; the centre set, H, I, belongs to the horizontal circle F; and the lower set, k, i, refers to the entire portion of the instrument above it.

The circular plates with their accompanying sockets are shown in section in Fig. 34. The upper plate carry

ing the compass-box, &c., is screwed fast to the flange of the interior spindle, the lower plate is fastened to the exterior socket, which in its turn is fitted to and turns in the hollow socket of the levelling head.

The telescope consists of two tubes, one sliding within the other, with the object glass at the further end, A, of the outer tube, and with an eye-piece at the nearer end, B, of the inner tube. The object glass is achromatic, that is, made of two lenses, one of crown and one of flint-glass, the curvatures of which are suitably combined. The object glass forms between the eye-piece and its principal focus an inverted image of the object sighted, and the eye-piece, consisting of two condensing lenses, acts as a magnifying glass, and gives a virtual and highly magnified image of the inverted image thus obtained. Sometimes, especially in American instruments, the eye-piece is made up of four plano-convex lenses. An erect image is thus obtained. An erecting eye-piece, however, causes a considerable loss of light, and is therefore not to be recommended. It requires but little practice to get accustomed to the use of an inverting eye-piece, and the brilliancy with which objects appear, owing to the amount of light gained by dispensing with two lenses, is very marked in comparison with the results

The

obtained with an erecting eye-piece of the same power. telescope may be focussed by moving the inner tube by a rack and pinion turned by the milled head, b (Fig. 32).

E

B

The rays proceeding from the object-glass form a cone of light. In order to get a line from the point of the cone straight through the optical centre of the object-glass, and on, without deviation, to the object examined, recourse must be had to the device of collimation. The collimator of a theodolite telescope is a circular brass diaphragm, with a hole about half an inch in diameter in its centre. It has a rim on its edge, and in this are the collimating screws, a, a. The hole is crossed by three spider-webs or equally fine platinum wires (see Fig. 35), one horizontal, A B, and the other two, CD, EG, deviating slightly to opposite sides of a vertical plane. The point F where the wires cross each other should be exactly in the axis or line of collimation of the telescope. It is adjusted to that position by the collimating

screws.

GD

Fig. 35.

Various Forms.-(a.) Hoskold's transit-theodolite is an instrument of great perfection, specially adapted for mining work. It differs from the ordinary transit-theodolite in the arrangement of the upper plate, which is made to project over the lower plate at the points where the upright supports are attached, so as to enable a larger compass to be employed. Thus, a 5-inch circle will carry a 4-inch compass; whilst in an ordinary theodolite of the same size a 24-inch compass would be used. The Hoskold theodolite presents the further advantage that the compass is not obscured by the appendages of the upper plate. In order to enable short sights to be taken, a pair of folding sights, like those of a miner's dial, are fixed to the top of the telescope. The instrument is also provided with a diagonal eye-piece, which enables the telescope to be pointed vertically without any discomfort to the observer.

In this theodolite and some others, a second telescope is sometimes attached below the horizontal circle. This is used like the outer pair of sights of the Henderson dial, to determine whether the circle has been disturbed during the interval between two observations.

(b.) The Everest Theodolite. This instrument differs considerably from the ordinary transit-theodolite, though the principles of its construction are exactly the same. It was designed by Captain Everest, and was first made by Messrs. Troughton & Simms in 1838. Instead of the upper parallel plate, this instrument has three diverging arms (Fig. 36) with

a vertical levelling screw supporting the end of each. Each screw has a flange at its lower end, by means of which it is held down to the plate forming the top of the staff head. The chief advantage of this construction is that the three levelling screws can be adjusted with one hand, whilst the adjustment of four levelling screws requires both hands.

Fig. 36.

The vernier-plate is represented in the Everest theodolite by four radiating arms, three with verniers, the fourth with clamping and tangent screws. The verniers are read with the aid of an independently moving microscope. The mean of three readings is thus obtained for each observation.

The telescope is permanently fixed to the horizontal axis by means of a collar-like expansion at the middle of the bell-metal axis, into which the telescope is fixed. Instead of a vertical circle, the Everest theodolite has two opposite sectors of about 90° each, so as to be capable of measuring elevations and depressions, as far as 45°. The horizontal axis works in a Y-shaped upright. The spirit-level is not attached to the telescope, but to the index bar. The circular compass-box of the ordinary instrument is replaced by a long compass-box placed above the telescope, reading only a few degrees east or west of the magnetic meridian. The spirit-level for the horizontal circle is attached to a stage below the Y's.

(c.) The Hoffman Tripod Head. The theodolites made by

Messrs. J. Davis & Son are provided with the Hoffman tripod head (see p. 64). Ever since the introduction of the theodolite, efforts have been made to give it the same facility of levelling as is possessed by the miner's dial. The ball and socket motion has been frequently tried. The upper part of a theodolite is, however, much heavier than that of the dial, and requires more binding power than can be obtained with an ordinary ball and socket joint.

The great need for a tripod that can be easily manipulated is apparent, as it rarely happens that there is a level surface on which to set the theodolite, and much of the time in surveying is employed in adjusting the levelling screws. It has been pointed out that it is almost impossible to level up a sensitive bubble so that it will remain in position long enough for a satisfactory sight to be taken, and the difficulty of centering a plummet over a station has also been shown. The latter defect has been obviated by the addition of the sliding-head, which permits the entire instrument, with its plummet, to be accurately placed over a fixed point, after the operation has been approximately performed by moving the legs.

The Hoffman tripod head,* as modified by Professor J. H. Harden of the University of Pennsylvania, is shown in Fig 37.

Fig. 37.

On unscrewing the levelling screws, the plate forming part of the socket of the small ball, the centre of which is the axis of the instrument, and the point from which the plummet is suspended, can be moved in any direction within the limits of the inside opening of the screw cap. It will be observed that besides the small ball and socket, there is an extra and larger ball and socket formed by a part of the plate to which the instrument is fastened,

* Trans. Amer. Inst. Min. Eng., vol. vii., p. 308.