It was

22nd July, 1864; it has a total length of 25,956 metres. driven from the bearings and distances calculated from the results of a survey made with extreme accuracy by means of the theodolite and spirit-level from a number of points.

of the holings were as follows :—

ERNST-AUGUST ADIT LEVEL.

The results

To drive a tunnel through a hill, the line of the tunnel is set out over the hill, and carefully levelled from the commencement at the foot of the hill. When it is thought that the level of the starting-point has been reached, or, in other words, when the rises are equal to the falls, an assumed mark is placed, and the levels accurately calculated. The assumed mark is then moved up or down the height by which the rises and falls differ, to give the

exact position of the floor of the tunnel on the farther side of the hill.

If the levelling is effected by the theodolite instead of by the spirit-level, the total of the calculated bases of the various drafts gives the length of the tunnel.

Sinking Shafts from Several Levels. Similar problems to those relating to galleries are presented by shafts which have to be sunk from several levels. If the shaft to be sunk is near an existing shaft, the problem is comparatively simple, as it is then merely necessary to drive headings from that shaft at different levels until their ends reach the axis of the shaft to be sunk.

The conditions are not always so favourable; the shaft to be sunk may be at a considerable distance from any existing shaft. In such a case, points are selected at each level of the mineworkings, as near as possible to the shaft to be sunk. From these points headings are driven to the axis of the shaft. The length and direction of these headings may be calculated from surveys made at the various levels of the mine. It is, of course, necessary that the surveys shall be made with extreme accuracy with the theodolite.

This method was employed in the Harz for sinking the Königin Marie shaft, the first perpendicular shaft sunk in that district. In 1851 it was decided by the Government authorities to drive a deep water-level at a depth of 1201 fathoms under the ErnstAugust deep adit, by which the mines of the Upper Harz were then drained. The new deep water-level was intended to serve as a great common water-reservoir for the mines of the district. From this level, which is 324 fathoms below the surface, and 116 feet below sea-level, the water is raised to the Ernst-August adit. For the reception of the engine for raising the water, it was decided to sink a new perpendicular shaft, the Königin Marie shaft, which should also be utilized for raising the ore from several mines.

In order to expedite as far as possible this important work, the shaft had to be sunk from several levels. It was sunk from the surface to the deep George adit, a depth of 146 fathoms, and at the same time commenced at a level 202 fathoms below the surface, and at another 270 fathoms below the surface.

Careful surveys having been made at each level, the shaft was set-out from the points obtained from the calculated co-ordinates. The different holings were successfully effected in 1866.

The accuracy of the work was then tested by suspending a plumb-line in the shaft, and determining the position of the shaft at the three levels. The plumb-line at the surface was exactly in the centre of the hoisting compartment of the shaft, at a

distance of 40 inches from each of the long sides, and 70 inches from each of the short sides.

Designating the shaft as A B C D, the distance of the plumbline from the sides at the different levels was as follows:-

From these results it follows that the deviation of the shaft

from the vertical was as follows:-
:-

Thus, the Königin-Marie shaft presents a brilliant illustration of accurate mine-surveying.

The Cubical Content of a Mine-Reservoir may easily be determined by the aid of a levelling-instrument. The cubical content must be calculated so as to ascertain the quantity of water which the proposed reservoir will hold. In shape, a mine-reservoir resembles most closely a truncated pyramid. It is therefore supposed to be cut, at given vertical distances, parallel to the surface of the water. The cubical content of the reservoir is. then determined from the area of these horizontal sections and their vertical distance apart.

When a suitable site for the reservoir has been selected, and the height of the dam fixed, the highest level (1, Fig. 86) of the water is marked by a stake fixed into the dam. The water-line of the reservoir is then determined by finding with the spirit-level a number of points lying in the level of 1. All these points are then marked by numbered stakes. Some 2 to 3 yards vertically below the first stake, a second stake is fixed into the dam. The contour of the reservoir

Fig. 86.

at this level is then determined by the spirit-level, and marked

by numbered stakes. In a similar way, contours of the reservoir at lower water-levels are determined and marked out. The contours marked out by the numbered stakes are then surveyed by means of the dial, the prismatic compass, or the plane-table, and laid down on a plan to a large scale. From this plan, the areas, the cubical content of the reservoir is calculated by means of the formula V = } h (B + √√Bb + b), where h is the vertical height and B, b the area of the ends.

For example. In the mine-reservoir, shown in Fig. 86, five horizontal sections were determined at vertical distances of 1.000, 1.050, 1000, and 0.875 fathoms apart. The vertical distance from the fifth and last section to the bottom of the reservoir was 0.375 fathom. Each of the five water-levels were distinguished by numbered stakes, so marked that all belonging to one section had the same number. The five horizontal sections were then surveyed with the compass, and plotted on a suitable scale (1: 1,000). The cubical content was then found to be 41814 13 cubic fathoms as shown in the following table:—

The cubical content of a dump-heap is found in a similar

manner.

Determination of the Strike and Dip of the Line of Intersection of Two Veins. It is important to determine the position of this line, as it is frequently found to be a line near or along which a run of rich deposit is likely to be met with. It is also of value

in solving problems relating to the dislocations of veins. Rules for determining by means of spherical trigonometry the strike of the line of intersection are given in the treatises on mine-surveying by Von Oppel (1749). Kaestner (1775), and Lempe (1782). The simplest trigonometrical solution to the problem is that given by A. Rhodius.*

The problem may be solved by construction. Let a b' and b" c (Fig. 87) be the lines of strike, at a given level, of the two lodes dipping at angles of a and a'.

In order to determine the line of intersection, the perpendiculars ik and Im are let fall in the direction of the dip of the lodes, and made the bases of right-angled triangles, the hypothenuses of which are inclined at angles of a and a respectively, the perpendicular being the same (h) in both cases. The lines kn and mo are then drawn parallel to a b′ and b" c, and continued until they intersect in the point e. Then e is a point of intersection of the two lodes at a level which is deeper than the point of intersection b, by a distance h, and consequently be is the line of intersection of the two lodes. The strike of this line can be measured with the protractor.

Fig. 87.

By constructing a right-angled triangle with its base equal to the line of intersection, be, and its perpendicular equal to h, then the angle at e represents the angle of inclination or dip of the line of intersection. This angle may be measured with the protractor.

The preceding construction is generally to be recommended. The problem may, however, be solved by means of plane trigonometry. The following is the solution given by Rhodius:-If be, as in the first solution, represents the line of intersection of the two veins a b' and b" c, then eq and er, lines parallel to i k and 7 m, are lines at right angles to the strike of the veins. The angles which eq and er form with the line of strike be of the line of intersection being indicated by x and y respectively, the following equations are obtained :