At sea the altitude of an object may be determined by ob serving the angle subtended by it and the verge of the horizon; but upon land a contrivance, called an artificial horizon, becomes necessary, for correctly determining altitudes. The best kind of artificial horizon consists of an oblong trough, t t, filled with mercury, and protected from the wind by a roof, rr, having in either slope a plate of glass with its two surfaces ground into perfectly parallel planes. The angle, s E s', between the object, and its reflected image seen in the mercury, is double the angle of elevation s E H; and, the angle s E s' being observed, its half

will, consequently, be the angle of elevation required. If the angle of elevation be greater than 60°, the angle s E s' will be greater than 120°, and cannot be observed with the sextant we have been describing.

The box sextant is a most convenient instrument for laying off offsets, or perpendicular distances from a station line; for, by setting the index at 90°, and walking along the station line, looking through the hori

zon glass directly at the farther station staff, or any other remarkable object upon the station line, any object off the station line will be seen by reflection, when the observer arrives at the point where the perpendicular from this object upon the station line falls; and the distance from this point to the object being measured, is its perpendicular distance from the station line.

For the mere purpose of measuring offsets an instrument called an optical square is now very generally employed, 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 OPTICAL SQUARE.

The mirrors A and B are fixed in a shallow circular box, so that the vertex E of the isosceles right-angled triangle A B E comes to the circumference of the box, where the aperture for the eye is placed. By this means parallax is eliminated, and a ray of light from the object F, proceeding in the direction F E, and falling upon the mirror A, is reflected in the direction AB, meets the mirror в, is again reflected in the direction B E, and seen by the

eye at E, in the direction E D, at right angles to E F. The mirror B is unsilvered in the lower part, so that the eye, looking along the line ED through the aperture in the rim of the box, sees an object D in this line, by direct vision, in coincidence with the reflected image of the object F, on the line E F, at right angles to E D.

E

F

This instrument cannot be excelled for facility and rapidity of use. To set off a perpendicular from a given point on a line, the observer, standing at this point, and holding the square in his hand, directs the motions of an assistant, who walks out from the line with a rod, so as to keep the reflection of the rod in the mirror в, in coincidence with an object, on the line, seen through the unsilvered portion of the same mirror: the line from the observer's eye to the rod, is, then, the perpendicular required.

Again, if a perpendicular is to be made to fall from a given point upon a given line, the observer walks along the line, until he comes to a point from which he sees an object on the line, coinciding with the image, in the mirror B, of an object at the given point: the observer is then standing at the spot, on which the perpendicular will fall.

THE CROSS STAFF.

Another instrument for setting out lines at right angles to other lines, is the cross staff, which, though old fashioned and cumbrous, is still very commonly used for the purpose.

There are two forms of cross staff. One form consists of four sights fixed at right angles upon a brass cross, which, when in use, is fixed on the top of a staff. The second form consists of a hollow brass cylinder, about three or four inches in diameter, and as many in depth, through which are pierced sights at right angles to cach other: this also, when in use, is affixed to a staff.

To set out with the cross staff a perpendicular to a line, from a given point on it, thrust the staff into the ground at this point, so that through one pair of sights you can see both ends of your main line, by looking first through one of these sights, and then moving round and looking through the opposite one. Having thus ensured a point exactly on the line, and the proper position of the cross, now move round, and, looking across the instrument, through the other pair of sights, have a pole set up in a line with them; and the perpendicular will be set off.

THE LINE RANGER.

We may here notice another application of the law of

reflected light, to the determination of the relative angular position of objects, in Adie's line ranger, a very simple pocket instrument, for setting out straight lines. It is shown in plan

in Fig. 1, and in elevation in Fig. 2. a and b are twe totally reflecting glass prisms, placed one over the other, on a cylindrical base, which serves as a handle. One of the faces of the right angle in the upper prism, is placed flush with one of the faces of the right angle in the lower prism, the other faces containing the right angles being parallel. The observer, holding the instrument in his hand, and looking into the prisms in the direction ef, sees directly before him, in the prism a, the reflected image of a pole at d, on his right hand, and in the prism b, that of another at c, on his left hand; and, when these images are in the same straight line, the instrument is also exactly in the same straight line with the objects c and d.

THE THEODOLITE.

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

This instrument may be considered as consisting of three parts: the parallel plates with adjusting screws fitting on to the staff head, of exactly the same construction as already described for supporting the Y and other levels; the horizontal limb, for measuring the horizontal angles; and the vertical limb, for measuring the vertical angles, or angles of elevation.

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, or chamfered, as it is called, and graduated at every half degree. The upper plate is called the vernier plate, and has portions of its edge chamfered off, so as to form with the chamfered edge of the lower plate continued portions of the same conical surface.* These chamfered portions of the upper plate are graduated to form the verniers,

* In the ordinary mode of construction, represented in section in Fig.

Fig. 1.

1, the perfect coincidence of the junction of the upper and lower plates cannot be effected; but the edge of the vernier plate, slightly overlapping the lower, may produce a small error in the reading, from the

by which the limb is subdivided to single minutes. The sixinch theodolite represented in our figure has two such verniers, 180° apart. The lower plate of the horizontal limb is attached to a conical axis passing through the upper paralle

plate, and terminating in a ball fitting in a socket upon the lower parallel plate, exactly as the vertical axis of the Y level already described. This axis is, however, hollowed to receive

introduction of parallax. This defect has been remedied in some theo

Fig. 2.

dolites by squaring the edges, at the junction between the two platos, as represented in Fig. 2.