stand, on which the forward lamp should be placed. The horizontal and vertical angles should be measured at the second, and all succeeding angular points as at the first. It may be observed that the stands only successively change the order of their position, the lamps retaining their relative positions throughout the traverse. The horizontal angles may be measured as for a traverse (overground) to a fixed line of direction, or independently.

When, at any angular point, the vertical angle for the forward line shall be 90°, the horizontal angle vanishes, so that the relative direction of the next succeeding reference line, making a vertical angle less than 90°, cannot be directly determined with the theodolite. The relative direction of such reference lines may be determined in two ways-namely, with the theodolite and compass by magnetic angles, and with the theodolite and a plane reflector. First, with the theodolite, &c., by magnetic angles :

The compass card, or dial, should be accurately placed in the reference line near the theodolite, so that its centre or point of support shall be observed at the intersection of the cross wires of the telescope, when in the vertical plane of the reference line. After the card has ceased to oscillate, the magnetic angle of the reference line may be read with the telescope. The compass card and theodolite should be removed to the shaft extremity of the succeeding reference line with a vertical angle less than 90°. The compass card should be adjusted in the vertical of the shaft extremity of the last measured reference line by a plumb line, or otherwise, and its index made to read the magnetic angle for that line. The theodolite should be set up in the sight-line, of the compass card, or dial, at a distance from the latter,

and adjusted for observation. The telescope should be directed to the card, without unclamping the upper plate of the horizontal limb, and the bisection of its centre made by working the clamp screw to the lower plate. Now if the card reading be exactly the same as made at the former station, the vertical limb of the theodolite will be in the vertical plane of the measured reference line terminating in the shaft. The theodolite so adjusted will give the angles for connecting the lines. In this manner the reference lines of the survey for passages abutting on the shaft at one level may be connected with those of a like survey at another level, or with the reference lines of an overground survey. This assumes, however, that the magnetic variation does not vary. In many cases the assumption is not well founded, and in all it is open to question.

The second mode for connecting the reference lines of surveys for passages abutting on a shaft at different levels is as follows:

Two points, remote from one another, should be accurately determined in the last measured reference line having a vertical angle less than 90°, which points should be distinctly and finely marked. Adjustable frames, stands, or stools, with lamps and plane muffled glass illuminated orbs, will be suitable for the purpose. On the illuminated orbs fine black rectangular straight lines should be drawn, and the adjustment made by placing their intersection in the vertical plane of the reference line. This should be done with the aid of the theodolite. A plane mirror, on an axis (in, or parallel to, its reflecting surface), should be placed and adjusted above the theodolite, and under the vertical shaft, so as to make the observed, direct and reflected bisections of the marked points identical. The axis of the mirror