O WRIGHT! A GEOLOGICAL PROTRACTOR 



because the radius of the protractor circle is taken to be unity 

 whereas the tangent values may range from zero to infinity, three 

 different cases are to be distinguished: 



(a) Angles A and C are less than 45°; tan A, tan C < 1; 



(b) Angles A and C are greater than 45°; tan A, tan C > 1 ; 



(c) Angle A greater than 45° (tan A > 1) ; 

 angle C less than 45° (tan C < 1) ; 



cos B is always less than unity. 

 To adapt the ordinary protractor to the solution of these prob- 

 lems a thin celluloid arm is so attached that it can be rotated 



Fig. 1. A geological protractor. 



about the center of the circle as an axis (fig. 1). On this arm a 

 tangent scale is printed from 0° to 45°. A series of lines parallel 

 to the base line of the protractor is printed on the face of the 

 protractor as indicated in the figure. The extension of the ro- 

 tating arm below the axis enables the geologist to use the pro- 

 tractor as a hand goniometer for the measurement of the angles 

 between crystal faces. A scale of inches, divided into tenths, 

 and a scale of millimeters are added below the base line of the 

 protractor. 



The methods of solution for the three cases noted above are 

 indicated in figure la, b, c. In figure la OA ( = tan A) is the true 



