OP ECCENTRICITY AND GRADUATION. 



25 



corrections always are. Much exercise of good judgment is, however, 

 essential : if the curve were drawn through all the points, or, what is the 

 same thing, if the computed local corrections were adopted without any 

 adjustment, the error resulting from sporadic defects in the graduation 

 would apparently vanish ; but it is not certain that actual errors would 

 always be diminished, for any single local correction may be considerably 

 in error, and may also refer to a point not impartially representing the 

 general state of the graduation in its vicinity. The number of points of 

 contrary flexure in the curve must be very small as compared with the 

 number of given points, and in every doubtful case it is safer to err on 

 the side of proximity to the axis of S. The local corrections in the 

 eighth column of Table VIII are not large, but they show unmistakable 

 signs of systematic arrangement. The mean local corrections in Table 

 IX were accordingly obtained from them by the process just referred to. 

 There is one point of contrary flexure in the curve not far from *S'= 68°. 



Table IX. 



As this series of supplementary corrections is a somewhat typical one, 

 its significance should be recognized. Disregarding the abberrations of 

 individual lines, the actual and mean arcs are coincident at points near 

 15°, 68°, and 117°. The mean arc overlaps the actual arc at both ends; 

 the mean length of divisions of the latter is. therefore, too small; they 

 are actually too small between 0° and about 55°, too large from 55° to 



