120 



S. L. Penfield — Stereographic Projection. 



from G. The obtuse angle B is measured on the great circle 

 z by protractor No. II, page 18. Likewise the acute angle B' 

 is measured on the great circle z\ the portion between the 

 arrow points giving the supplement of the angle. The sides c 

 and c\ from A to B and from A to B', are measured by pro- 

 tractor No. II. 



The results are as follows : 



Calculated. Plotted. Error. 



B = 117° 41' 117° 37' 4' 



C = 20 17 20 11 6 



c = 18 43 18 55 12 



Calculated. Plotted. Error. 

 B' = 62° 19' 62° 20' 1 



6 T = 103 48 103 55 7 



c = 116 1 115 55 6 



21 



The solutions of the seven problems just given were made 

 without knowledge of the calculated values ; furthermore, the 

 results are not a selection of best values, obtained from a 

 number of solutions of the several problems. The results have 

 been given exactly as they were obtained, and hence they serve 

 to illustrate the probable degree of accuracy which may be 

 secured. In solving the two right triangles the greatest error 

 was 6', the average error less than o'. In solving the five 

 oblique triangles the greatest error was 15', the average V . 

 It is evident that by increasing the size of the projection, and 

 using more accurately engraved plates, the errors could be 

 materially lessened. 



One possible case has not been included in the foregoing 

 list; namely, having three angles of a triangle given. Such a 

 problem may be solved graphically, but, having no sides given, 

 the problem is complicated. It may be done somewhat as 

 follows : Referring to figure 19, the great circle Ap, determin- 



