160 A. Harher — Graphical Methods in Field Geology. 



In Fig. 6 draw Z B to represent the apparent dip and Z A in the 

 direction of full dip, the perpendicular jB A will cut off a length 

 Z A, which will represent the full dip. 



(iii.) Given the appai-ent dip in two directions, to find the direc- 

 tion and amount of full dip. 



In rig. 7 draw ZB, Z C to represent the two observed dips, and 

 perpendiculars to them at J5 and C, meeting in A ; then Z A I'epre- 

 sents the full dip. 



(iv.) Given the direction and amount of the dip of the strata and 

 of the slope of the ground, to find the direction of outcrop. 



In Fig. 8 draw Z A, ZEio represent the dijj and the slope; then 

 the direction of outcrop is perpendicular to A E. 



To prove this and the two following constructions it is sufficient 

 to notice that a horizontal line (0 B in Fig. 2) drawn perpendicular 

 to the direction of outcrop lies in the plane containing the normals 

 P and Q. Equations (c) also give a proof. 



(v.) Given the directions of strike and outcrop, to find the dip, 

 the slope of the ground being known in direction and amount. 



In Fig. 8 draw ZE to represent the slope, and from Z and E 

 respectively draw lines perpendicular to the given strike and outcrop, 

 meeting in A ; then ZA represents the dip. 



(vi.) Given the direction of outcrop in each of two localities 

 where the slope of the ground is known in direction and amount, 

 to find the direction and amount of the dip, supposed imiform (Fig. 9). 



Draw ZE, ZF to represent the two slopes, and from E, F draw 

 lines perpendicular to the respective directions of outcrop, meeting 

 in A ; then ZA represents the dip. 



(vii.) Given the direction and amount of the dip and of the slope 

 of the ground, to find the angle at which the strata are cut by the 

 ground. 



In Fig. 4 draw ZP and ZQ to represent the dip and the slope, ZE 

 perpendicular to P Q, ZF perpendicular to ZE and equal to the 

 breadth of the protractor ; produce ZE until E 0' is equal to EF, 

 then P 0' Q is equal to the angle required. 



(viii.) In the foregoing problem, given the breadth of the outcrop 

 of any bed, to find its true thickness. 



Measure off 0' G along 0' Q to represent on any convenient scale 

 of magnitude the given breadth, then the length GH of the per- 

 pendicular drawn to 0' P will represent on the same scale the true 

 thickness. 



(ix.) Given in direction and amount the dips on the two sides 

 of an inclined anticlinal axis, to find the direction and inclination 

 of the axis. 



In Fig. 10 draw ZA, ZB to represent the two dips, then the 

 perpendicular ZD on AB represents the direction and inclination 

 of the axis. A trigonometrical solution of this problem is given by 

 Capt. F. W. Button, Geol. Mag. 1874, p. 44. 



(x.) Strata having a dip given in direction and amount receive 

 a secondary tilt given in direction and amount ; to find the direction 

 and amount of the resulting dip. 



