490 CHESTER K. WENTWORTH 



diameter line, the value of which in terms of the vertical scale at 

 the side is the required angle of dip. 



As an example, let it be required to find the angle of dip in a 

 direction 40 from the strike, of a plane of which the maximum 

 dip is 5 . Following the 5 curve to its intersection with the 40 

 radial line and interpolating this point between the 3 and 4 

 parallel lines we find the value of approximately 3°i5 / which is the 

 desired angle of dip. 



The particular field of usefulness of this device is in projecting 

 the plane of a given stratum whose dip and strike are known from 

 a plane table set up on the outcrop. We have in this case the dip 

 and strike of the plane and the direction of the line of sight for 

 which we wish the dip. The horizontal diameter line of the pro- 

 tractor is laid parallel to the strike as recorded on the oriented 

 plane-table sheet and the alidade set on the required line of sight 

 with its edge passing through the center on the protractor. At the 

 intersection of the ruler edge with the appropriate dip-curve is read 

 the required angle of elevation or depression to be set on the tele- 

 scope to project the plane. This graphic solution of the problem 

 in the field and directly on the plane table is much more rapid 

 than a combined protractor and dip-table solution and is suffi- 

 ciently accurate for reconnaissance and mapping purposes where 

 projecting the outcrop on topography is the "best guess" the field 

 man has in many instances. 



The protractor as shown is made only for angles up to io° 

 because occasions for projecting dip in cases of higher dips are 

 much more rare and correspondingly less accurate, and greater 

 accuracy for the low angles is attained by putting fewer lines on 

 the celluloid. The radii of the several dip circles are constructed 

 proportional to the tangents of the respective dip angles, as is also 

 the spacing of the parallel horizontal lines which are tangent to 

 them. Thus if A is the nominal dip of any plane, B the required 

 oblique dip, and C the angle of obliquity, we have 



. „ tan B 



sin C= 7 



tan A 



