246 



PROCEEDINGS OF SECTIOIiT C. 



dii'ection of dip of geological structures (beds, dykes, fault planes, &c.). 

 The apparent angle of dip in the direction of the section is always less 

 than the true dip measured in the field. It is this apparent dip which 

 has to be determined and plotted. The geometrical constniction by 

 means of which it is determined is as follows : — 



Let the angle be- 

 tween the directions of 

 true and apparent dip 

 be called the direction 

 angle. Draw a straight 

 line AB of any con- 

 venient length. Make an 

 angle BAG equal to the n 

 angle of true dip. Draw 

 BC at right angles to 

 AB. Make an angle 

 BAD equal to the direc- 

 tion angle. Produce CB 

 to meet AD in D. Draw 

 DE at right angles to 

 AD. Make DE equal to 

 BC. Join AE, then the angle DAE is the apparent angle of dip 

 required. 



If P is the angle of true dip, Q the angle of apparent dip, and R 

 the direction angle, it is easily shown that — • 



tan.Q — cos.R. tan. P. 



The slide rule enables this value to be read ofi at once. 



RULE. — Place the zero of the cosine scale opposite the graduation 

 on the tangent scale corresponding to the angle of true dip. Read the 

 value on the tangent scale opposite the graduation on the cosine scale 

 corresponding to the direction angle. The reading is the amount of 

 apparent dip required. 



Table 1 gives the values to the nearest half-degree of apparent 

 dip for eveiy 5 degrees difference of true dip and direction angle. 

 Intermediate values may easily be inteiTiolated. As a rule, the prob- 

 able error in observation of angle of dip is rather large, and there is 

 little certainty of absolute uniformity of dip over considerable areas. 

 Therefore a high degree of accuracy in determination of apparent dip 

 is unnecessary. 



The diagram (plate 2) affords another means of reading off 

 the apparent dip. True clips ai'e plotted along the horizontal axis, 

 and direction angles along the vertical axis. The con-esponding lines 

 for apparent dip angles form a series of hyperboloid curves. These 

 have been drawn for every 5 degi-ees of apparent dip. In order to 

 use the diagram, follow the horizontal line corresponding with the 

 given direction angle to its intersection with the vertical line corre^ 

 spending with the given true dip. The appai'ent dip required will lie 



