and the part to which the levelling screws are attached. The latter part always remains parallel to the screw cap of the tripod head, on which the points of the levelling screws rest, so that whatever position the instrument may assume in relation to the tripod head, the screw will always act directly perpendicular to both plates.

Under all conditions, the instrument moves upon a centre common to the two balls, this being the point to which the plummet is attached. It is therefore impossible for the plummet not to be perpendicular to the axis of the instrument.

The advantages claimed for the Hoffman tripod head are as follows:-1. A saving of one-half to two-thirds of the time usually occupied with screwing and unscrewing as in the old plan. The instrument can be levelled approximately without the use of the screws. Less than half a turn is then necessary to bring the instrument to a perfect level, the operation at the same time clamping it. 2. The levelling screws are at all times perpendicular to the plate to which they are attached, and to the plate and screw cap on which they rest. 3. The levelling screws are reduced in length, and their duty to a minimum, the instrument being no higher nor heavier than before. 4. The shifting head for plumbing over a fixed point—an improvement common to all first-class instruments-is retained, and no extra screws are required to clamp the instrument. 5. The levelling screws are covered from dust, and at the same time are no obstruction to the working of the instrument in any position in which it can be placed.

Numerous other attempts have been made to apply the ball and socket motion for levelling theodolites rapidly, and several American devices of this kind have proved very successful. Thus, Messrs. W. & L. E. Gurley, of Troy, have patented a quick-levelling tripod, somewhat similar in principle to that of Hoffman. The spherical surfaces are, in this case, concave, and the friction of these surfaces may be increased or diminished at will by means of spiral springs. Messrs. Buff & Berger, of Boston, furnish their theodolites with a quick-levelling attachment, which does not form part of the instrument proper, but consists of a coupling, with a ball and socket joint, which can be screwed between the instrument and the tripod.

(d.) American Theodolites.-In America, the miner's dial is very rarely used for mine-surveys. In all important work, the transit-theodolite is alone used. This instrument is known in America as the transit. The name theodolite is reserved for the Y-instrument in which the telescope cannot be revolved on its horizontal axis. The transit instrument which has no vertical

circle and no spirit-level attached to its telescope is called the plain transit.

The

An excellent transit-theodolite, manufactured by Messrs. Heller & Brightly, of Philadelphia, is described by Dr. R. W. Raymond.* It is a small portable instrument specially adapted for use in mine-surveying. The principal peculiarity is the ribbing and flanging of the parts requiring strength, so as to dispose the minimum amount of material where it will secure the greatest rigidity. The horizontal circle is 4 inches in diameter, and is read by two double opposite verniers, placed outside the compassbox, the vernier openings in the plate being made very wide so as to allow the easy reading of the graduations. There is a 3-inch magnetic-needle, and its ring is divided to half-degrees. telescope is 7 inches long, with an erecting eye-piece. A sensitive level, 4 inches long, is attached to the telescope. The tripod is furnished with a shifting head for precise centering. Clamps and tangent-screw movements are supplied to the plates and vertical circle. The graduation of the compass ring and of the horizontal circle is continuous from 0° to 360°. The weight of the instrument, exclusive of the tripod, is 5 lbs. The weight of the tripod is 3 lbs. The height of the instrument from the tripod legs is 7 inches, the extreme diameter of the plates 5 inches. The instrument and tripod head are packed in a box 7 inches square, arranged with straps to allow its being carried over the shoulder, while the folded tripod legs serve as a walking-stick. Such compactness and lightness are very important for underground work. This also applies to surface-surveys, especially in a country like America, where the surveyor has often to carry his own instrument.

Its

(e.) Traveller's Transit-Theodolite.-A still smaller transittheodolite is manufactured by Mr. L. Casella, of London, for the use of travellers. It has complete 3-inch circles, both vertical and horizontal, with verniers reading to one minute. It can therefore be used as an altazimuth for determining time, latitude, and azimuth, as well as for ordinary surveying purposes. telescope is eccentric. It is provided with a diagonal eye-piece and a reflector for illuminating the cross-wires. It is thus well adapted for shaft-surveying. It is supplied with a dark glass for solar observations, a finely divided level, and a compass. It packs in a mahogany case, 6 inches by 5 inches, and 4 inches deep; the whole weighing only 3 lbs.

A light tripod stand is added. Many important surveys have been made with the instrument with very satisfactory results.

This instrument is also constructed with the telescope in the centre, the supports being raised to allow it to revolve vertically. By this arrangement, whilst the height is increased, the width is reduced in proportion.

Adjustments of the Theodolite.-Every time the instrument is used, the observer must make the following adjustments:

1. Place the theodolite exactly over the station by means of a plummet hung from a hook directly under the vertical axis. It must next be levelled, that is to say, the vertical axis must be placed truly vertical. The easiest way to do this is to make the vernier-plate truly horizontal, by means of the spirit-levels, ƒiƒ (Fig. 32). For this purpose, the vernier-plate is turned into such a position that the two spirit-levels shall be parallel to the two diagonals of the square formed by the four levelling screws. Two opposite screws must then be turned simultaneously and equally, but in opposite directions, until the bubble is brought to the centre of the level. The other screws are then turned in the same way, until the bubble of the second level is brought to the centre of its tube.

A more exact adjustment can be made by means of the larger and more delicate level, c, attached to the telescope. For this purpose, set the instrument approximately level, clamp the axis of the limb by k, leaving the plate free, and move the latter until the telescope is over two of the levelling screws. Then bring the bubble to the middle of its tube by the tangent screw, d. Then turn the vernier-plate, carrying with it the telescope, through half a revolution, and if the bubble is not in the centre of the tube, bring it half way back by the tangent screw, and the other half by the levelling screw. Repeat this until the bubble remains central with the telescope in either position. Then turn the vernier-plate through 90°, so as to place the telescope at right angles to its former position, and repeat the process until at last the bubble remains central during the complete rotation of the telescope. If the instrument is correctly constructed, the vernier of the vertical circle should read 0° 0′.

If the bubbles are not at the centres of the vernier-plate levels, when the bubble remains central in the level attached to the telescope, the vernier-plate levels are not truly perpendicular to the vertical axis, and must be adjusted by means of the screws at their ends. This adjustment is rarely required with a wellmade theodolite.

2. When the image of the object viewed, formed by the object glass, either falls short of or beyond the place of the cross-wires, an error arises, which is called parallax. Its existence may be detected by moving the head from side to side when looking

through the telescope, observing whether the image appears to move. To correct this error, the eye-piece must first be adjusted by means of the movable eye-piece tube, until the cross-wires are seen clearly defined. Then direct the telescope to some distant object, and by means of the milled-head screw, b (Fig. 32), at the side of the telescope, move the inner tube in or out until the proper focus is obtained. When disregarded, parallax gives rise to serious error.

3. In addition to the temporary adjustments described above, there are certain permanent adjustments which should be tested from time to time, but which in a well-made theodolite seldom require correction.

To

The adjustment of the line of collimation consists in placing that line accurately at right angles to the horizontal axis. effect this, direct the telescope to a distant object, making the cross-wires bisect the object precisely. Then carefully lift the telescope out of its bearings, and replace with the ends reversed. Revolve vertically, and again direct the telescope to the distant object. If the cross-wires still coincide with the object, the line of collimation is perpendicular to the horizontal axis. If not, move the cross-wires one-half of the deviation by turning the screws holding the diaphragm, and correct the other half by moving the tangent screw of the horizontal circle. Reverse the telescope again, and repeat the operation until the adjustment is perfect.

In the Y-theodolite, the line of collimation is adjusted by bringing the intersection of the cross-wires upon some welldefined distant object. The telescope is turned round on its collars in the Y's until the level is uppermost. Then, if the cross-wires do not continue to coincide with the object, half the difference must be corrected by moving the cross-wires, and the other half by moving the tangent screw of the horizontal circle.

4. The level attached to the telescope must be parallel to the adjusted line of collimation. To effect this adjustment in the transit-theodolite, the elevation or depression of a distant object is taken. The instrument is then reversed, the telescope revolved vertically, and again directed to the same object. The mean of the two readings will be the true elevation or depression of the object. Set the verniers to this mean angle, and again observe the object, making the intersection by means of the screws retaining the index in its horizontal position. Then, correct the level by its own adjusting screws.

To effect the adjustment in the Y-theodolite, the clips for securing the supports that hold the telescope should be thrown open, and the bubble of the spirit-level brought to the centre of

arc.

the tube by means of the tangent screw attached to the vertical The telescope should then be lifted out of its supports, and reversed. If the bubble does not remain central, correct half the error by the adjusting screws connecting the level with the telescope, and the other half by the tangent screw of the vertical

arc.

5. When the telescope level has been adjusted, and the vernierplate is truly horizontal, it is necessary to note whether the zero of the vertical circle coincides with the zero of its vernier. If it does, there is no index-error. If it does not, the amount of error should be noted and applied as a constant correction to all subsequent readings.

6. The adjustment of the horizontal axis exactly perpendicular to the vertical axis is, as a rule, left to the instrument-maker. In some theodolites, however, there are adjusting screws for the supports of the vertical axis. This is usually the case in instru

ments of American make. In order to determine whether the horizontal axis is perpendicular to the vertical axis, direct the intersection of the cross-wires to an object, the altitude of which is considerable. Then turn the vertical limb, until the cross-wires cut some other well-defined point near the ground. Revolve the telescope on its axis, and turn the vernier-plate 180°. Then if, in raising and lowering the telescope, the line of collimation passes through the two objects, the adjustment is correct. If not, half the deviation is to be corrected by the tangent screw of the horizontal circle, and the other half by the adjusting screws of the supports. The operation must be repeated until the adjustment is correct.

The permanent adjustments described above should be made with great care. Many valuable instruments have been injured by students who were anxious to adjust them, but were unacquainted with the method. It is necessary to be quite certain that an adjustment is required before a screw is touched.

The

Measuring Horizontal Angles.-The theodolite, having been set up so that the centre of the horizontal circle is perpendicularly above or below the station-point, is carefully levelled. horizontal vernier-plate is then clamped at zero. The position of the second vernier is noted, in case it does not read 180° exactly. The horizontal circle and vernier-plate clamped together are turned, until the telescope is directed to the left-hand station. The horizontal circle is then clamped, and the crosswires are made to accurately bisect the point by means of the tangent screw. The vernier-plate is then released, and the telescope carefully moved, the lower supports only being touched, until the right-hand object is bisected. The vernier-plate is then clamped,