A. Harker — Graphical Methods in Field Geology. 161 



In Fi^. 11 draw ZA to represent the original dip, and a line J.B 

 in the direction of the secondary tilt : draw ZD perpendicular to 

 AB and produce until Z) C is equal to the breadth of the protractor; 

 join A C and make an angle A CB equal to the amount of the 

 secondary tilt; the lines A£ and CB meet in B; then ZB represents 

 the resultant dip. 



(xi.) If in the foregoing problem the direction of the secondary 

 tilt be at right angles to that of the original dip, the construction is 

 much simplified. 



Draw ZB (Fig. 6) to represent the original dip, and BA from B 

 to represent the secondary tilt ; then ZA represents the final dip. 



When the angle the direction of the secondary tilt makes with 

 that of the original dip does not differ widely from a right angle, 

 and the amount of the tilt is small, the same construction gives an 

 approximation to the true result ; for instance, if the original dip 

 be 30°, the amount of the tilt 20°, and the angle between their 

 directions 60°, the error in the direction of the resulting dip is 3°, 

 and in its amount 2°. For a strict solution the method in (x.) 

 must be employed, 



(xii.) Given the direction and amount of dip of strata which have 

 suffered a tilt of known direction and amount, to find what the 

 direction and amount of their dip was before tilting. 



This is the same problem as (x.) worked backward, and a similar 

 construction will suffice. 



(xiii.) To find the direction and amount of the tilt required to 

 change the dip of strata from a given initial direction and amount to 

 a given final direction and amount. 



In Fig. 11 draw ZA, ZB to represent the initial and final dips, 

 draw ZI) perpendicular to AB and produce until DC is equal to 

 the breadth of the protractor; then AB is the direction of the 

 required tilt and A CB its amount. 



Further Remarlis. 



"When an angle is near 90 degrees, its tangent is very great, and 

 therefore the line representing it very long. Some of the above 

 constructions are then slightly modified. For instance, if strata 

 have a vertical position the line representing their dip in the 

 manner described above would be of infinite length, but it is 

 only necessary to draw this line for a short distance, and if another 

 line has to be drawn to the infinitely distant extremity of the 

 former, make it parallel to it, according to the geometrical principle 

 that " parallel straight lines meet at infinity." 



In some cases it is convenient to use a construction which employs 

 not the angle of dip or slope, but its complement, that is, its defect 

 from 90 degrees. The line indicating the dip is drawn in the 

 direction of the dip, but of a length corresponding on the edge of the 

 protractor to the complement of that angle. This line will be pro- 

 portional to the cotangent of the angle of dip and will be longer or 

 shorter according as the dip is small or gi'eat. As an example we 

 will take the problem of finding the true dip from two observed 



DECADE III. — VOL. I. NO. IV. 11 



