"Obviously the reliability to In- placed in any ".dent 



on the measuremen of angles is determined by tn*- with 



which the angles are measured. Under ordinary conditions, with 

 a transit or sextant reading directly to minutes, it may be assumed 

 that angles will be measured v\ith a probable error of about 3u 

 seconds, and the accompanying curves have been drawn on that 

 basis. For other degrees of accuracy a direct proportion obtains 

 and results may be derived from the curves. Cur\es ha\e been 

 drawn only for the functions of sines and tangents, but their adapt- 

 ability to cosines and cotangents will readily be seen. 



"An example or two will illustrate the use of the curves. Sup- 

 pose it has been decided that in a given traverse or system of 

 triangulation the ratio of error must not exceed >j.-,i .., which corres- 

 ponds to an accuracy of 0.04 per cent. The horizontal line which 

 corresponds to this ratio intersects the ratio curve for tangents 



Size of Angle 

 Fig. 103 



(Fig. 103) at two points whose abscissas are 23 and 67 deg. respect- 

 ively. Hence in this survey, if computations involving tan 

 are to be made, the angles must lie between these limitations. The 

 percentage curve may be used in a similar manner. When sines of 

 angles are involved, the lower limit is the determining factor, 

 the value of the sine changes rapidly only t.r small angU-,, and 

 Fig. 104 may be used in a similar manner. In the case given above, 

 the lower limit would be 20 deg. 



"If it were impracticable, however, to limit the size of angles to 

 23 and 67 deg., then an instrument reading to 20 seconds, or the 

 method of reading angles by repetition, would be 

 Suppose, then, by one of these means the probable M i-ling 



angles were reduced to 15 seconds, or half the former value, 

 curve may then be adapted to this case by changing the num 

 values of the ordinates to half their value, or by dropping the line 





