406. Given the distance OL 400 ft., and the angle LON=

;

60°

to find the depth of a shaft at the point of intersection with the vein, and to find the length

Draw OL = 400 ft.; also ON, making the angle LON=60°; and LM to the point M, 250 ft. below the point of intersection P. From the scale take off LP and MN the required distances.

In the preceding problems the angle of 60° was employed for convenience of construction, but the principles would be true for any other angle.

407. Figures 194, 195, 196, represent plan, longitudinal and transverse sections of a developed mine.

The development consists of a vertical shaft, an inclined shaft following the dip of the vein, and 6 one-hundred-foot levels.

In opening mines it is considered good practice to follow the vein for a considerable distance in depth, to be fully satisfied of its continuity, before sinking a vertical shaft for deep working. however, the prospecting shaft The depth to which a shaft is depend upon the Engineer in

Should the vein be vertical, may be made the working shaft. sunk on the dip of the vein will

charge and upon the characteristics of the vein. A careful engineer will not incur the expense of sinking a deep working shaft to intersect an inclined vein, until he has followed the vein for such a distance that the possibility of its terminating, or "pinching out," is quite remote. Should the vein be irregular and not possess well-defined fissure characteristics, the greater the necessity for care in this respect and, in cases of great uncertainty, it ould even be advisable to have the working shaft follow the dip

of the vein. If, on the other hand, the vein is found to be strong and regular, possessing well-defined fissure characteristics to a depth of 150 to 250 feet, the working vertical shaft might be sunk with comparative safety. No rule can be laid down, however, and the Engineer must always exercise his own judgment.

In the example here given, we have assumed the inclined shaft to be sunk to the same depth as the vertical, for if originally sunk to the first cross-cut, 440 feet (Fig. 196), it would be carried down to the point of intersection and used for ventilation.

The method of surveying and plotting such a mine is simply an application of the principles already explained.

408. The calculation of ore-reserves does not come strictly within the province of the surveyor, yet after completing the survey and plot, he is frequently required to make the calculation. We will therefore consider methods of making it.

In practice the methods employed are various. No general rule can be given, as each expert has a system of his own, and different engineers will not agree, within wide limits, as to the quantity of ore-reserves in the same mine. One may assume as the measure of the ore in sight a rectangular block limited by the outcrop, the depth of the shaft or shafts, and the extreme points of the levels, diminished by the amount extracted. Others, but one-half or one-third of this quantity. The former would be considered an excessive estimate in all cases. The latter too low when the vein possesses great strength and regularity, though even this estimate may be too high, when the conditions are the reverse. The surveyor must exercise his own judgment, exercising caution, however, as the calculation is an important

one.

Assume the development shown in Figs. 194, 195, 196, and let it be required to calculate the ore-reserves when the bounding lines are assumed at the extreme ends of the level drifts, or the