OF ECCENTRICITY AND GRADUATION. 



23 



an observer who contents himself with the least count of a 10" vernier 

 cannot reduce his probable error below 2".5 ; but under some circum- 

 stances—as, for instance, in measuring circummeridiau altitudes of Polaris 

 witli the sextant mounted upon a stand — the precision attained in this 

 examination should be closely approached. With practice the vernier 

 may be read as closely as it can be set, for so long as the direction of the 

 necessary movement is recognized, the distance can also be estimated. 

 The 42 residuals are distributed as follows : 



When the preliminary reductions have been carried out in full, as in 

 Table I, the eccentric corrections may also be found by taking the means 

 of the corrections in the different series for the same values of S, and the 

 local corrections by similarly taking the means of the residuals — C ; 

 but the final residuals must be obtained as in Table VIII, with values of 

 X', X", etc., calculated by (8) from the mean values of A and B. 

 Unless this is done the computed probable errors will, in general, be 

 somewhat too small. The effect of local errors upon the determination 

 of eccentricity is usually unimportant. If the eccentric corrections in 

 Table VIII are recomputed after applying the local corrections to the 

 observed values of D, there will be no change amounting to half a second. 



Some test of the general trustworthiness of the examination is always 

 desirable. A sextant may be in such condition as to operate correctly 

 under the delicate manipulation it receives upon the table of the appa- 

 ratus, yet when removed therefrom and handled less cautiously, or 

 returned to its case, a slight displacement of the axis may occur ; so that 

 if compared again the two sets of eccentric corrections will differ con- 

 siderably from each other, although a small probable error is found for 

 each. Any great change of this sort may be detected by comparing the 

 differences D in the successive series of comparisons, which should always 



