to the indicated value of Vi250. This line intersects the ratio curve 

 (Fig. 103) at the points whose abscissae are 11 and 79 deg., and 

 accordingly these angles would constitute the limits for a ratio of 

 error of ^2500 for angles measured with a probable error of 15 sec. 

 Referring to the sine curves it is seen that the lower limit in this 

 case would be 10 deg. 



O 3 5" K) c 15 20 25" 30 35 40' AS* 



Size of Angle 

 Fig. 104 



"In systems of triangulation such as those carried out by the 

 U. S. Geological Survey, the lower limit of the size of angles is often 

 taken as 30 deg. Let us see to what ratio of error this corresponds. 

 From Fig. 103 it is seen that the ordinate for the angles 30 and 60 

 deg. equals a ratio of MJOOO, but this applies to angles measured 

 with a probable error of 30 sec. In such work as has been referred 

 to, the probable error of reading angles is reduced to about half a 

 second, or, in other words, about sixty times the accuracy assumed 

 in the curves shown is obtained. Hence the ratio of error would 

 equal about one-sixtieth of ^ooo, or Viso,ooo. From the sine curve 

 this ratio would be >^4o.ooo. 



180 





