RELATION OF DIP, STRIKE AND OUTCROP 803 



the sloping surface A B C D, has the same compass direction as 

 C H, and hence represents the true strike. The line A C, however, 

 the intersection between the surface A B C D and the plane A C 

 H F, is deflected 45° from that direction, since its direction corre- 

 sponds to that of the line A X, the diagonal of the square A D X Y. 



With a constant surface, as given, and sloping at 45°, the out- 

 crop of a vertical stratum will have no deflection from the line of 

 strike. As the stratum becomes inclined from the vertical the down- 

 slope end will be deflected in the direction of dip, a degree for every 

 degree of departure of the dip from 90°. When 45° of dip are 

 reached the deflection will be 45°. With decreasing dip, i. e., its 

 approach to 0°, the deflection will approach 90°, which is reached 

 when the strata are horizontal. When the slope of the postulated 

 surface is other than 45° the deflection of the strata must be calcu- 

 lated. Designating the dip of the stratum by 6, the angle of inclina- 

 tion of the sloping surface from the horizontal by ^ and the deflec- 

 tion of the outcrop by xl/, we have tan i/' = cot ^ tan ^ or </' = 

 tan— 1 (cot 9 tan </>). 



It sometimes happens that only the outcrop of inclined strata is 

 visible on the surface of a region, the angle of dip not being ascer- 

 tainable. In such a case the angle of deflection (i/') can often 

 be measured directly by taking a reading of the true strike on a 

 horizontal portion of the surface and another of the apparent strike 

 on a sloping surface, where the intersection with the horizontal is 

 at right angles with the strike. The angle of slope of this surface 

 {4>) must also be read by the clinometer. Thus with the values of 

 two terms of the equation ascertained the third or angle of dip 

 {6) may be readily found by the formula tan 6 = tan ^ cot ^ or 

 = tan— 1 (tan <^ cot </'). 



An example may further illustrate this : Given an inclined 

 stratum of which the true strike as shown by the intersection with a 

 horizontal surface is N. 10° E., while the apparent strike on an in- 

 clined surface of the postulated direction of slope is N. 30° W., the 

 angle of deflection of outcrops between horizontal and inclined sur- 

 face, i. e., ip, is therefore 40°. The angle of slope of the inclined 

 surface may be assumed as 30°. Thus the dip is: tan $ =z tan 

 30° cot 40° or 0.6882608; .•. 9 =z about 34° 32'. The direction of 

 dip is to the east, since the deflection was to the west.* 



The above formulas apply only to the case where the inclined 

 surface intersects the horizontal along a line at right angles to the 

 true strike, /. c, when the directions of slope of the inclined strata 

 and surface are at right angles to each other. When the direction 

 of slope of surface varies from this, the amount of deflection will 



