OF ECCENTRICITY AND GRADUATION. 15 



The one requiring corrections of more than 2' is of course exceptional, 

 but no complaint is known to have been made of it before the examina- 

 tion, though it had seen service at sea, possibly in the hands of some scru- 

 pulous young officer who carried out his reductions to fractions of a second. 

 It is not the most incorrectly centered instrument in the table, however. 

 The probable error, though derived from too small a number of observa- 

 tions to be regarded as j^irecise, is a useful criterion. When much in 

 excess of 5" it implies that either the graduation is inaccurate, the tele- 

 scopic power is too low, the mechanical or optical action of the sextant is 

 imperfect (perhaps, through maladjustment of its parts), the observer is 

 unskillful, or two or more of these unfavorable conditions coexist. Values 

 of less than 3" are frequently obtained, but this is commonly due in part 

 to an accidental avoidance of the larger errors of observation. 



Before proceeding to combine the results of several series of compari- 

 sons it is desirable to know the probable error of the corrections deduced 

 from a single series. The eccentric correction for any reading y . as ex- 

 pressed in (10), may be written : 



r-r' = - \d |- 1.5671 sin \ / + 1.8384 (1 - cos \ /) + 

 ^7.6467 sin \ / - 11.0275 (1 - cos * y')\ sin J ^ -f 

 l- 11.0275 sin ^ / -f 17.9311 (1 - cos * /)] (1 - cos \ *S)|~|. 



