actual angle between any two objects to a single minute. It requires no support but the hand, is easily adjusted, and, when once adjusted, seldom requires re-adjusting.

When the Sextant is to be used, the lid E of the box, is taken off and screwed to the bottom, where it makes a convenient handle for holding the instrument; the telescope T, being then drawn out, the instrument appears as shewn in the figure A is an index arm, having at its extremity a vernier, of which 30 divisions coincide with 29 divisions on the graduated limb ll, and the divided spaces on the limb denote each 30 minutes, or half a degree, the angles observed being read off by means of the vernier to a single minute. The index is moved by turning the milled head B, which acts upon a rack and pinion within the box. To the index arm is attached a mirror, called the index glass, which moves with the index arm, and is firmly fixed upon it by the maker, so as to have its plane accurately perpendicular to the plane in which the motion of the index arm takes place, and which is called the plane of the instrument; this plane is evidently the same as the plane of the face of the instrument, or of the graduated limb 17. In the line of

sight of the telescope is placed a second glass, called the horizon glass, having half its surface silvered, and which must be adjusted that its plane may be perpendicular to the plane of the instrument, and parallel to the plane of the index glass, when the index is at zero. The instrument is provided with two dark glasses, which can be raised or lowered by the little levers seen at d, so as to be interposed, when necessary, between the mirrors and any object too bright to be otherwise conveniently observed, as objects in the direction of the sun. The eye end of the telescope is also furnished with a dark glass, to be used when necessary.

To see if the instrument be in perfect adjustment.—Place the dark glass before the eye-end of the telescope, and looking at the sun, and moving the index backwards and forwards a little distance on either side of zero, the sun's reflected image will be seen to pass over the disc, as seen directly through the horizon glass, and if in its passage the reflected image completely covers the direct image, so that one perfect orb is seen, the horizon glass is perpendicular to the plane of the instrument: but, if not, the screw at a must be turned by the key k till such is the case. The key k fits the square heads of both the screws seen at a and b, and fits into a spare part of the face of the instrument, so as to be at hand when wanted. This adjustment being perfected, bring the reflected image of the sun's

lower limb in exact contact with the direct image of his upper limb, and note the reading of the vernier; then move the index back beyond the zero division of the limb, till the reflected image of the sun's upper limb is in exact contact with the direct image of his lower limb, and, if the zero of the vernier be now exactly as far behind the zero of the limb, as it was at the former reading in front of it, the instrument is in perfect adjustment; but, if not, half the difference is the amount of error, which must be corrected by applying the key k to the screw at b, and turning it gently till both readings are alike, each being made equal to half the sum of the two readings first obtained. When this adjustment is perfected, if the zeros of the vernier and limb are also made exactly to coincide, the reflected and direct image of the sun will exactly coincide, so as to form but one perfect orb, and the reflected and direct image of any line, sufficiently distant not to be affected by parallax, as the distant horizon, or the top or end of a wall, more than a half a mile distant, will coincide so as to form one unbroken line.

To obtain the angle subtended by two objects in, or nearly in, the same horizontal plane.—Hold the sextant in the left hand, and bring the reflected image of the right hand object into coincidence with the direct image of the left hand object, and the reading of the instrument will give the angle between the two objects.

To obtain the angle subtended by two objects in, or nearly in, the same vertical plane.-Hold the instrument in the right hand, and bring down the reflected image of the upper object by turning the milled head B, till it exactly coincides with the direct image of the lower object, and the reading of the instrument will give the angle between the two objects.

It will be seldom that the surveyor need pay any attention to the small error arising from parallax, but, should great accuracy be desirable, and one of the objects be distant while the other is near, the parallax will be eliminated by observing the distant object by reflection, and the near one by direct vision, holding the instrument for this purpose with its face downwards, if the distant object be on the left hand. If both objects be near, the reflected image of a distant object, in a direct line with one of the objects, must be brought into coincidence with the direct image of the other object, and the parallax will thus be eliminated.

For the purposes of surveying, the horizontal angles between objects are chiefly required, and the reduction of these angles from the actual oblique angles subtended by the objects, would be a troublesome process. If the angle subtended by two obiects be large, and one be not much higher than the other,

the actual angle observed will, however, be a sufficiently near approximation to the horizontal angle required; and if the angle between the two objects be small, the horizontal angle may be obtained, with sufficient accuracy, by taking the dif ference of the angles observed between each of the objects, and a third object at a considerable angular distance from them. With a little practice the eye will be able to select an object in the same direction as one of the objects, and nearly on a level with the other object, and the angle between this object and the object selected will be the horizontal angle required.

For laying off long offsets, or perpendicular distances from a station line. The pocket sextant is a most convenient instrument for this purpose: for by setting the index to 90°, and walking along the station line, looking through the horizon glass directly at the further station staff, or any other remarkable object on the station line, any object off the station line will be seen by reflection, when the observer arrives at the point where the perpendicular falls from this object upon the station line, and the distance from this point to the object, being measured, is its perpendicular distance from the station line.

THE OPTICAL SQUARE.

For the purpose of measuring long offsets and perpendiculars, this instrument is now very generally used, which consists of the two glasses of the sextant fixed permanently at an angle of 45°, so that any two objects seen in it, the one by direct vision and the other by reflection, subtend at the place of the observer an angle of 90°.

THE THEODOLITE.

The theodolite is the most important instrument used by surveyors, and measures at the same time both the horizontal angles between two objects observed with it, and the angles of elevation of these points from the point of observation.

The instrument may be considered to consist of three parts; the vertical limb for measuring vertical angles, the horizontal limb for measuring horizontal angles, and the parallel plates, in the lower of which is a female screw, adapted to the staff-head, which is connected by brass joints with three mahogany legs, so constructed as to shut together and form one round staff, a very convenient form for portability, and, when opened out, to make a firm stand, be the ground ever so uneven.

The horizontal limb is composed of two circular plates L and V, which fit accurately one upon the other. The lower plate projects beyond the other, and its projecting edge is sloped off, and graduated at every half-degree. The upper plate is called the vernier plate, and has portions of its edge sloped off, so as

to form with the sloped edge of the lower plate continued portions of the same conical surface. These sloped portions of the upper plate are graduated to form the verniers, by which the limb is subdivided to minutes. The five-inch theodolite, represented in the figure, has two such verniers 180° apart. The lower plate of the horizontal limb is attached to a conical axis passing through the upper parallel plate, and terminating in a ball fitting in a socket, upon the lower parallel plate. This axis is hollowed to receive a similar conical axis, ground accurately to fit it, so that the axis of the two cones may be exactly coincident. To the internal axis, the upper, or vernier

plate of the horizontal limb is attached, and thus, while the whole limb can be moved through any horizontal angle required, the upper plate only can also be moved through any desired angle, when the lower plate is fixed by means of the clamping screw C, which tightens the collar D. T is a slowmotion screw, which moves the whole limb through a small space, to adjust it more perfectly, after tightening the collar D by the clamping screw C. There is also a clamping screw c for fixing the upper plate to the lower, and a tangent screw t, for giving the upper plate a slow motion upon the lower, when so clamped. Two spirit levels B, B are placed upon the horizontal limb, at right angles to each other, and a compass G is also placed upon it, in the centre between the supports FF of the vertical limb.

The vertical limb N, N is graduated on one side at every 30 minutes, each way from 0 to 90°, and subdivided by the vernier, which is fixed to the compass box, to single minutes. Upon the other side are engraved the number of links to be deducted from each chain, for various angles of inclination, in order to reduce distances measured on ground rising or falling at these angles, to the corresponding horizontal distances. The axis A of this limb must rest in a position truly parallel to the horizontal limb, upon the supports F F, so as to be horizontal when the horizontal limb is set truly level, and the plane of the limb N N must now be perpendicular to its axis. On the top

of the vertical limb N N is attached a bar that carries two Ys (so called from their shape), for supporting the telescope, which is secured by two clips c, d; and underneath the telescope is a spirit level ss, attached to it at one end by a joint, and at the other by a capstan-headed screw. The horizontal axis A can be fixed by a clamping screw C; and the vertical limb can then be moved through a small space by the slow-motion screw i.

Before commencing observations with this instrument, the following adjustments must be attended to:

1. Adjustments of the telescope for parallax and collimation. 2. Adjustments of the horizontal limb for setting the levels on the horizontal limb to indicate the verticality of its axis.

3. Adjustment of the vertical limb for setting the level beneath the telescope to indicate the horizontality of the line of collimation.

1. Parallax and collimation. Move the object-glass o by the screw M, and the eye-glass E with the hand, till distant objects and the cross wires within the telescope, appear clearly defined; and the adjustment for parallax will be completed. Next, direct the telescope to some well-defined object at a