18 S. L. Penfield — Stereographic Projection. 



To measure the Angle made by the meeting of Two Great 

 Circles. — To measure the Angle of a Spherical Triangle. — 

 Just as the angle between two meridians at the north pole of a 

 sphere is measured on the equator, so the angle between two 

 great circles crossing at a point A, which may be anywhere 

 within the divided circle, figure 11, is measured on the arc of a 

 great circle at 90° from A. To make the measurement of the 

 angle, draw a diameter of the divided circle through A, and, 

 applying the base line of protractor E"o. I to the diameter, note 

 the distance in projected degrees from N to A ; then locate a 

 point B just as many degrees from the divided circle as A is 

 from N. A and B are thus 90° apart, and, making use of 



scale No. 1, figure 3, the arc of a great circle p p\ passing 

 through B, can be easily drawn. All points on the great circle 

 thus plotted, including the intersections x and y, are 90° from 

 A, and the angle at A is equal to the distance in projected 

 degrees between x and y, as measured with the stereographic 

 protractor on the arc of the great circle p ft ' . 



Provided an angle is located on the divided circle, as at 0,. 

 all that is necessary to do is to draw a diameter of the divided 

 circle at 90° from 6 Y , and measure the angle at O on the pro- 

 jected north and south meridian by means of the graduation 

 on the base line of protractor No. I ; for example, from 

 utov = 59°. 



Another method of measuring the angles of spherical tri- 

 angles depends upon a well known and interesting peculiarity 

 of the stereographic projection, to which the writer's attention 

 was called by Prof. Gr. P. Starkweather of Yale University ; 

 namely, that the angle made by the crossing of two circles on 



