S. L. Pen field — Stereographic Projection. 



19 



a sphere is preserved in the stereographic projection of the 

 circles. The method of measuring is illustrated by figure 12. 

 ABC is a right spherical triangle, and to measure the angle 

 B, draw through B a tangent tt' ; the angle formed by tt' and 

 the diameter GC determines B. To draw accurately the 

 tangent tt' , locate two points a and h, equally distant from B, 

 on the great circle ABA'. A line joining ab would be a 

 chord of the circular arc ABA', and a line through B, paral- 

 lel to ab, is a tangent to the circle. An ordinary protractor 

 PP, preferably a transparent one.* centered at B by means of 



]2 



a needle, can be employed for measuring the angle. The 

 0°-0° line of the protractor is made to coincide with tt', and 

 the angle (78° 15' in the illustration) is determined from the 

 graduation of the protractor. It is not necessary to construct 

 the tangent tt' except when great accuracy is required ; it is 

 simply necessary to turn the protractor until the arc ABO 

 intersects the circular arc of the protractor at equal distances 

 from its two 0° points when its 0°-0° line will be tangent to 

 the arc ABA' at B. In case the spherical triangle is an 

 oblique one, ABB, to measure B draw two tangents, tt' and 

 ft"', then measure the angle between them. Whether it is 

 easier to construct tangents and measure with an ordinary pro- 

 tractor, as illustrated by figure 12, or to construct the arc of a 

 great circle at 90° from B, as illustrated by figure 11, and 

 measure by means of protractor No. II, plate I, is a matter 

 which must be determined by experience. It is far simpler to 



* Protractor No. II, plate I, which is printed on transparent celluloid and is- 

 divided at the periphery into degrees, can be employed. 



