312 



Transactions . 



Tabulating these values and resolving each into two, one in the direction of 

 the meridian and the other at right angles to it, we obtain the following : — 



12e sin E = - 6-3 - log = 0-79934 

 12ecosE = -51 -9 -log = 1-71517 

 E = 186° 55' + log tan E 9-08417 



e = + 4"-3 4- logl2e = 1-71864 



s = A (-291)= -24" 

 A single reading of the vernier A requires a correction for eccentricity of 



+ 4"-3 sin (a -186° 55') 



The distance between the verniers is 180° - 24" = 179° 59' 36". 



Having found the error in the readings due to eccentricity and the con- 

 stant angle between the two verniers, we may correct the observed readings 

 for these errors, and the residuals will be the errors due to the graduation 

 of the circle and accidental errors of reading. 



A circle may be graduated by copying a certain number of the main 

 divisions directly from the dividing-machine, and then the smaller divisions 

 between these points are performed automatically by setting the machine 

 in motion. 



If the circle is not truly centred with the dividing-engine there will be 

 an error in the main divisions due to the eccentricity and an error in the 

 divisions of the smaller arcs, with a shorter period, depending on the 

 number of main division directly copied from the dividing-engine. 



These may be investigated in the same manner as for the centres of the 

 circle and the alidade not coinciding, or they may be determined by the 

 method of harmonic analysis as follows by putting 



y = A + Aj cos a + A 2 cos 2a + &c. 

 + B x sin a + Bj sin 2a + &c. 



(8) 



