The Practical Miner's Guide

has been constantly kept in view, and the tables can be relied upon, and may be received and applied to the most difficult and important operations in dialling, with the utmost confidence. In conclusion, we have generally used such terms as are common to mining operations, believing that this phraseology will render the work far more acceptable to those for whose use it is designed.

EXPLANATION OF THE DIAGRAMS.

TABLE I. Page 45.

In this scheme the hypothenuse is made radius, consequently the other sides are the sine and cosine of the included angle.

Corollary. Suppose one end of the line A B to remain at A while the other end B is moved round from e to f, then it is evident that the base CB will continue to increase, and the perpendicular B D to decrease, until the whole quadrant has been swept off.

At 45°, or the middle of the quadrant, the base and perpendicular are equal, and from that point to 90° the base will increase in the same ratio as the perpendicular decreased from 1° to 45°; hence the propriety of the arrangement of this table in counting the degrees backward from 45 to 90.

TABLE II. PAGE 51.

Here the perpendicular is made radius, therefore the hypothenuse A C will be the secant, and the base B C the tangent of the angle A. On this principle it is clear, that as the angle increases the base and hypothenuse will continue (throughout the whole quadrant) to increase in proportion.

TABLE III. Page 57.

In this diagram the base is made radius, therefore by mathematical demonstration the perpendicular AC is the co-tangent, and the hypothenuse BC the co-secant, of the angle C; and here it will be plain, that as the angle C is increased, the hypothenuse and perpendicular will, proportionably, be diminished.