18 THE CORRECTION OF SEXTANTS FOR ERRORS 



The probable error of this correction is therefore : 



t X 



f 1.5671 sin ^ S' — 1.8384 (1 - cos * S') - 0.4802 +1+1 

 I C-7.6467sinJ5'+11.0275(l-cos^/S0 + 1.5671^siu|/S'+ 



! Cll.0275sinJ/S'— 17.9311 (l-cosi;80-l-8384Vl-cosi*S') 



+ 



f 1.5671 sin i S' — 1.8384 (1 - cos i S') - 0.4802 + 



I /'_7.64G7siui>S'+11.0275(l-cosJ/S")+1.5671^sin J/S+ I 



^11.0275 sin J >S'-17.9311 (1-cos J y)-1.8384y 1-cos JaS) 



which will be found in the second column of Table VI for all values of 

 S'. When D' belongs not to one of the fourteen comparisons from which 

 A, B, and X were derived, but to an additional comparison at any point 

 whatever, the quantity inclosed by the first parenthesis in the preceding 

 expression retains only the terra + 1, and the resulting values are given 

 in the third column of Table VI. In all the foregoing expressions of 



probable errors -^— ^must be substituted for t, if iVis the number of series 



V N 



of comparisons constituting the examination. 



Table VI. 



When several series of comparisons are 

 made, they are first reduced separately in 

 the manner already described. It is not 

 absolutely necessary to find the value of X 

 at this stage, or to fill out columns 8 to 13 of 

 the form represented by Table I, but only a 

 little time is saved by these omissions, and 

 useful verifications of the work are lost. In 

 Table VII are given the constants, eccentric 

 corrections, residuals, etc., obtained by the 

 preliminary reduction of three successive 

 examinations of the same sextant. 



The means of the three values of A, and 

 B, and thethree values of Xcomputed there- 

 from by (8) are : 



A= + 5".3 X' = - 24.16 



X" = - 24.94 



B= + 68".0 X'" = - 31.37 



