altitudes or depressions on the vertical limb. Any one who has paid attention to the directions given for adjusting the transit theodolite will easily understand the method of adjusting the instrument now in question.

To adjust the line of collimation.

"First make the intersection of the horizontal wires coincide with some well-defined part of a distant object, then turn the telescope half round in its 'y's,' till the level lies above it, and observe if the same point is again cut by the centre of the wires; if not, move it one-half the quantity of deviation by turning the two screws at d, d, releasing one before tightening the other, and correct the other half by elevating or depressing the telescope; now if the coincidence of the wire and object remain perfect in both positions of the telescope, the line of collimation in altitude or depression is correct, but if not, the operation must be repeated carefully until the adjustment is satisfactory. A similar proceeding will set the line of collimation correct laterally." With regard to the other adjustments we have only to repeat what we have said already about reversing the telescope, as to the manner of taking the instrument out of its "y's."

To make the telescope level parallel to the line of collimation.

The clips b, b, being open, and the vertical arc clamped, bring the bubble to the centre of its run by means of the tangent screw O; this done, carefully lift the telescope out of its "y's," and turn it end for end. If in this reversed position the bubble resumes its centre, all is right; but if otherwise, it will be evident that the axis of the level is not parallel to that of the telescope. By means of one of the capstan-headed screws correct one-half of the deviation, and the other half by turning the tangent screw 0; by repeating this operation the adjustment will be made perfect. But to complete the setting of this level, that it may maintain the centre of its run when inclined a little on either side from its usual position under the telescope, it requires adjusting laterally, which is done by turning, if necessary, the two screws k. Should the former adjustment be disturbed by this operation, then the whole must be carefully repeated.

With good instruments, duly cared for, these adjustments are but very rarely required.

COLONEL EVEREST'S THEODOLITE.

This instrument has important distinctive features, which are

USE OF THEODOLITE,

87

illustrated at Fig. 65. The horizontal limb L consists of one plate only, on which the degrees are graduated; and the verniers V are at the end of bars radiating from the centre, and another bar carries the clamp C and the tangent screw for the verniers. At S are shown the clamp and slow-motion screw of the horizontal limb. The vernier bars are connected with the upper portion of the instrument carrying the telescope, vertical limb M, &c., and turning upon the same centre they show the angle traversed by the telescope.

The tripod support B is provided with parallel plate screws, P, P, P. One advantage connected with this instrument is, that it may be used with a three-legged stand, the same as those already described, or be disengaged from the top of this staff and placed upon the top of a wall, or in other situations where the ordinary tripod could not be used.

It will be seen by the drawing that the telescope and vertical limb are supported in a manner very similar to the transit theodolite already described, the horizontal axis connected with the telescope resting at Y, on two supports only, one of which is seen in the drawing. These are supported by a flat horizontal bar, El, to which is attached a spirit-level, only one end of which is seen in the drawing; this level is for adjusting the axis to the horizontal plane. The vertical arcs, M M, attached to the telescope, move with it in the same vertical plane.

MEASURING ANGLES WITH THE THEODOLITE,

We must now suppose that the instrument is in adjustment,* and fixed to its three-legged support ready for use, The first thing to be then done is to plant the instrument somewhat about level, exactly over the station from which you are going to observe, giving the three legs a wide spread, and fixing them as

It may be as well to observe here to the beginner that but little anxiety need be felt as to the adjustments of an instrument turned out of the work shop of a good maker, though the student may make an examination of the value and condition of the instrument as soon as he feels confident he has mastered the principles and details of its construction; that which he has really to apprehend is, the danger the instrument is liable to when brought into use, and this not from his own hands but from those of others, particularly chainmen, whose hands it is difficult to keep off the instrument when his back is turned for a short time; let him therefore be advised never to leave an instrument on the ground without its being under the care of some person on whom he can thoroughly depend, for the curiosity of an ignorant man, and his desire to handle that of which he has no conception, is often unrestrainable where there is, as he thinks, no fear of detection, and has often led to serious errors. When the day's work is over restore your instrument to its case, and keep the key; the sense of security thus ensured more than repays the few minutes of trouble incurred.

firmly in the ground as circumstances will admit; the length of this tripod is made such that when a sufficient spread is given, the height of the eye-piece of the telescope will be such as to be convenient to the observer; the position of the centre of the instrument being exactly over the centre of the station, is ensured by the plummet and line hanging from the centre of the instrument being close over it, if it be a peg in the ground, or in the hole itself, when a flag pole has been removed to make place for the theodolite; now set it level by means of the parallel plate screws, p, p, until the bubbles of the two spirit-levels on the vernier plate keep the centre of their run, whilst the telescope is turned steadily quite round on its centre; the instrument is now ready for measuring angles.

Let A, Fig. 66, be the station; it is required to measure the angle subtended between B and C ; clamp the zero of the vernier plate V, to zero, or 360° on the limb, and make the coincidence perfect by means of the tangent screw T; examine the zero of the other vernier, and see that it coincides with 180°; move the instrument bodily round towards B, until the intersection of the wires in the telescope is in contact with the object at B; clamp the instrument by means of the screw attached to the collar round the axis, and make the "bisection" of the wires with the object at B perfect, by means of the slow motion screw S; this exact bisection can only be ensured when clear and distinct vision has been obtained by means of the mill-head in the side of the telescope for thrusting out the object glass. The line of sight now coincides with zero, or 360° on the limb, and both bear exactly on the centre of the object at B. Now release the vernier plate by loosening its clamp, and turn it round until the intersection of the wires is in contact with the object at C; now tighten the clamp of the vernier plate, and by means of its tangent screw T make perfect the bisection of the centre of the wires with the centre of the object at C; if there is any considerable difference of distance between B and C from A, the mill-head of the telescope will have again to be turned to ensure distinct vision; the angle is now measured, and there only remains to read it off from both verniers; let the one pointing to C read 62° 37', and let the other vernier show 36′ 30′′ beyond a degree; then the mean of the minutes will be 36′ 45′′, and the measure of the angle will be 62° 36′ 45′′.

In ordinary cases, and supposing a 5-inch theodolite used, the above measurement of an angle, read off with both verniers, will be found sufficient; but where a considerable area is triangulated, or where distant observations are taken from a base line,* as well

Let it, however, be understood that we are not alluding to geodetical operations.

REPEATING ANGLES.

89

as in traverses of several miles circuit, the angles should be repeated, and the mean of all observations taken as the real

measure.

The operation of repeating an angle is performed in the following manner :-Having, as above, taken the first measurement, loosen the clamp of the lower plate, whereby you release the whole body of the instrument, and turn it bodily round upon B: clamp the lower plate, and perfect the bisection, by means of the slow motion screw S; and observe that in doing this you have carried the 360° from its bearing on B, round to c, and the vernier bearing on C, round also so as to bear on B. Now release the upper or vernier plate, and turn the telescope towards C; clamp it, and perfect the bisection by means of the tangent screw T; read off both verniers again; the difference between this reading and the first will be twice the angle BA C, and the mean between this and the first reading is to be taken as the actual measurement of the angle; this one repetition will generally be found sufficient, unless it should so happen that the difference is considerable, say, for instance, 45", or a whole minute, in which case we should repeat the angle a second time, by carrying the circuit further round, in the manner above described; this will not occur with a good instrument.

In taking an angle as above, many persons do not think it necessary to begin by bringing the zero on the vernier to coincide with the 360° on the limb; they simply clamp the two plates together, and take off the reading, whatever it may happen to be; the telescope is then brought to bear on B, and the limb is clamped; the vernier plate is then loosened, and the telescope carried round towards C; the vernier plate is clamped, and bisection perfected by the tangent screw; the reading is again taken off (always by both verniers, and we shall, therefore, not repeat this), and the difference between the first reading and the second will give the actual measurement of the angle. For this mode of acting they allege the errors arising from graduation and eccentricity, and the probabilities that the verniers cannot in consequence be brought exactly to 360° and 180°; but this is one of the first things that should be examined in an instrument; and we should be disposed to reject an instrument in which we could not effect this. Again, the difficulty, under any circumstances, to effect the exact coincidence, is asserted; although, in fact, in a well-made instrument, of sufficient size, say five inches, there is no more difficulty in reading this off, and, therefore, making it perfect, than there is in any other reading. Adopting, however, either way, the angle may be correctly measured; usually, where one angle merely has to be measured without repetition, we adopt the second method, above described;

but where several angles have to be taken at one station, and these have to be repeated, we prefer making the coincidence perfect between the zero of the vernier and the 360° and the 180° on the limb.

The theodolite is the only instrument used in engineering fieldwork for setting out long, straight lines, such as the basis of a system of triangulation, or those of a railway or canal survey; and here the advantages of the transit theodolite are made very evident. To do this, we clamp fast the verniers at 180° and 360°, and observe, with minute care, that the coincidence is perfect; then we plant the instrument at the station through which the base line is to be ranged, and bring the instrument bodily round on the starting-point, and clamp it; perfect the bisection with the back object by means of the slow motion screw S, making this bisection as near the ground as possible, and reverse the telescope by making it revolve on its axis, if a transit, or by reversing the telescope in the clips if the ordinary theodolite; now examine that your verniers remain in perfect coincidence with 180° and 360° on the limb, when you may proceed to set out ranging-rods as far as you can see over the ground; but always make the bisection of the wires as low down on the rod as possible. Probably it is unnecessary to observe, that in doing this, the first operation after fixing the instrument by means of the plummet and line is to level it by means of the parallel plate screws; without which, indeed, nothing is to be done. Having ranged, as far as the theodolite commands the ground, move on to the next commanding situation on the base, and repeat what has just been described. Miles of straight line may be thus

set out.

There is another kind of transit theodolite made by Messrs. Elliott, from a pattern, we believe, of the late Mr. Rendel, in which there is no vertical limb, and which, on most of the occasions arising in practice, we should consider an instrument to be preferred to any we have seen.