24 



THE CORRECTION OF SEXTANTS FOR ERRORS 



be scrutinized for that purpose before beginning the reductions. It is not 

 possible, however, to decide in this way whether small abnormal varia- 

 tions exist or not. The agreement or disagreement between the different 

 pairs of values of A and B is also au insufficient test, for a reason already 

 given, but if the preliminary reductions are carried out far enough to 

 determine the eccentric corrections for each series separately, the probable 

 error of this correction at any point, as deduced from the differences 

 between the corrections furnishedby each of the series and their mean, 

 maybe compared with tlie same probable error taken from Table V. 

 The two values can scarcely be expected to agree exactly, but the difference 

 between them should not be too great. The following results were obtained 

 from the data iu Tables VII and VIII. 



In reading a sextant it is not merely the coincidence of a single line of 

 the vernier with one of the limb that is noted, but the relative positions 

 of several adjacent lines are taken into account, or ought to be ; the 

 effect of errors peculiar to individual lines is thereby rendered compara- 

 tively innocuous, for such errors cannot be large without being visible. 

 The most pernicious errors of graduation are progressive displacements 

 in alternating directions, extending throughout the arc in waves 

 more or less regular, but of considerable length. The existence of sys- 

 tematic errors having a period long enough to embrace several of the 

 points which have been examined is indicated by a succession of local 

 corrections with the same algebraic sign. It is sometimes advisable to 

 attempt the correction of such errors, especially when they are large, and 

 when many series of comparisons have been obtained. A convenient 

 process is to plot the values of S as abscissas, and the computed local 

 corrections as ordinates, to draw a fair curve approximating the points 

 thus laid down, and lastly to measure and tabulate the ordinates of the 

 curve as mean local corrections. This method is a rather rough one, 

 but it is useful when the corrections to be adjusted are small, as the local 



