Harxer— The Use of the Protractor in Field-Geology. 19 
(xv). Given the thickness of a group of beds, to find the 
depth it will occupy of a vertical boring, or vice 
versa. 
The ratio of the depth to the thickness is the secant of the. 
angle of dip, which we suppose to be known. The method to be 
followed is similar to the preceding, except that the angle is to be 
taken on the tangent-scale of the protractor instead of the 
_ cotangent-scale. 
{xv). Given the width of the outcrop of a group of beds on 
level ground, to find the depth they will occupy of a 
vertical boring. 
The ratio of the depth to the width of outcrop is the tangent 
of the angle of dip (supposed known). Place the edge of the 
simple scale along that of the protractor, the zero-points of the 
two coinciding. Take the angle of dip on the tangent-scale, and read 
off the corresponding number on the simple scale; this is the ratio 
required. ‘To find the ratio of the width of outcrop to the depth 
of the boring occupied by the beds, use the cotangent-scale instead 
of the tangent-scale. 
(xvi). A vertical shaft is sunk at a given spot: to find the 
depth at which it will strike a lode, the position and 
hade of which are known. . 
The ratio of this depth to the (known) distance of the shaft 
from the outcrop of the lode is the cotangent of the hade, and is 
found as in the preceding question, using the cotangent-scale of 
the protractor. 
(xvi). A vertical shaft is sunk at a given spot: to find at what 
depth it will strike the intersection of two known 
lodes. 
The shaft is of course supposed to be sunk at some point on the 
line of direction of the intersection, as determined in (1x). The 
distance of the shaft from the point in which the lines of outcrop 
(produced if necessary) intersect is supposed known. The ratio of 
the required depth to this distance is the tangent of the angle of 
inclination of the line of intersection, as determined in (1x). This 
ratio is therefore found as in (xv). 
C2 
