Harker— The Use of the Protractor in Field-Geology. 17 
OQ (fig. 4) represent the respective dips, OM, drawn perpendicular 
to PQ, will represent in direction and amount the inclination of 
the axis. 
(tx). Given the hades of two lodes (in direction and amount), 
to find the direction and inclination of their line of 
intersection. 
This is a similar case, except that, since we are dealing with 
inclinations of planes to the vertical, we must use the cotangent- 
seale. ‘To read off the result as an inclination to the horizontal, 
we must, however, use the tangent-scale as usual. The two lodes 
are supposed not to strike in parallel directions. 
Next we proceed to find the relation between the true dip of a 
bed and its apparent dip in any direction oblique to that of true 
dip. The inclined plane which meets the vertical diagram (fig. 3) 
along the line Cp, meets the horizontal diagram (fig. 2) along the 
line xpy, perpendicular to POp, and Op represents the co-dip of 
the inclined plane, or, in other words, is the distance corresponding 
to the dip of the plane reckoned on the cotangent-scale of the 
protractor. It is therefore easily laid down. Also, if any vertical 
plane through O meet the diagram-plane (fig. 2) in the line XOz, 
a being a point on our inclined plane, then Oz represents in like 
manner the co-dip of the line in which this vertical plane cuts the 
inclined plane. We deduce the following constructions :— 
(x). Given the true dip of a bed, to determine ° 
_ its apparent dip in any vertical section 
having a direction inclined to that of 
true dip. ne 
To do this draw OM (fig. 7) to represent the Fic. 7. 
co-dip of the given bed; that is, take the distance OM corre- 
sponding to the given true dip on the cotangent-scale of the pro- 
tractor. Draw the line MP at right angles to OM, and draw OP 
in the given direction to meet MP at P. Then OP represents 
the apparent co-dip for a vertical section in that direction, and the 
apparent dip may be read off on the cotangent-scale. 
(x1). Given the strike of a bed and its apparent dip ina certain 
direction, e.g. on the vertical wall of a cutting, to find 
the true dip. 
SCIEN. PROC. R.D.S., VOL. VIII., PART I, or 2 C 
