Handbook of Civil Engineering Calculations

2. Find the grade of the drift
   Apply Eq. 48. In Fig. 24Z), OA is a horizontal line in the vein, OB is the horizontal projec-
   tion of the drift, and the arrow indicates the direction of dip. Then angle COD = 430 IO' —
   38°20' = 4°50'; B = angle CDO = 90° - 4°50' = 850 IO'; tan /3 = tan 33°14' cos 850 IO' =
   0.0552; grade of drift = 5.52 percent.


3. Alternatively, solve without the use of Eq. 48
   In Fig. 246, set OD = 100 ft (30.5 m); let D' denote the point on the face of the vein verti-
   cally below D. Then CD = 100 sin 4°50' = 8.426 ft (2.5682 m); drop in elevation from O
   to D' = drop in elevation from C to D' = 8.426 tan 33°14' = 5.52 ft (1.682 m). Therefore,
   grade = 5.52 percent.

DETERMINING STRIKE AND DIP FROM

TWO APPARENT DIPS

Three points on the hanging wall (upper face) of a vein of ore have been located by verti-
cal boreholes. These points, designated P 9 Q 9 and R 9 have these relative positions: P is
142 ft (43.3 m) above Q and 130 ft (39.6 m) above R; horizontal projection of PQ, length
= 180 ft (54.9 m) and bearing = S55°32'W; horizontal projection of PR 9 length = 220 ft
(67.1 m) and bearing = N19°26'W. Determine the strike and dip of the vein by both
graphical construction and trigonometric calculations.

Calculation Procedure:

1. Plot the given data for the graphical procedure
   In Fig. 25a, draw lines PQ and PR in plan in accordance with the given data for their hor-
   izontal projections. The angle of inclination of any line other than a dip line is an apparent
   dip of the vein.


2. Draw the elevations
   In Fig. 256 and c, draw elevations normal to PQ and PR, respectively, locating the points
   in accordance with the given differences in elevation. Find the points S and Trying on PQ
   and PR, respectively, at an arbitrary distance v below P.


3. Draw the representation of the strike of the vein
   Locate points S and T in Fig. 25«, and connect them with a straight line. This line is hori-
   zontal, and its bearing </>, therefore, represents the strike of the vein.


4. Draw an edge view of the vein
   In Fig. 25 J, draw an elevation parallel to ST. Since this is an edge view of one line in the
   face, it is an edge view of the vein itself; it therefore represents the dip a of the vein in its
   true magnitude.


5. Determine the strike and dip
   Scale angles k and a, respectively. In Fig. 25a, the direction of dip is represented by the
   arrow perpendicular to ST.


6. Draw the dip line for the trigonometric solution
   In Fig. 26, draw an isometric view of triangle PST, and draw the dip line PW. Its angle of
   inclination a equals the dip of the vein. Let O denote the point on a vertical line through P
   at the same elevation as S and T. Let /S 1 and /3 2 denote the angle of inclination of PS and