M A G X E TI G O B S E 1! V A T 1 N S. 



165 



From the normal equations on page 126, we also have, 



Pa = 32 ^=16 



Pn=W> ^» B = 16 



Pa = 16 



It is therefore evident that the probable errors of B x , C„ D„ and E x , will all be 

 equal to each other. 



The probable error of a single observed value of h has been computed in this 

 way, for each compass, at three stations; namely, Bahia, Sandy Point, and Panama, 

 and the results are given in the following table. The column headed "mean value 

 of r" was obtained by adding together, for each compass, the sum of the squares 

 of the residuals at Bahia, Sandy Point, and Panama; dividing the result by three; 

 and then computing the value of r from the mean value of [iro] thus found. The 

 « r " « r " 



column headed ,.-. gives the probable error of A, ; and the column headed 



V 32 * ' V 16 



gives the probable error of B x , (\, D x , and E x , for each compass, when these coeffi- 

 cients have been computed from a set of deviations observed on thirty-two points. 







Value of r. 





Mean 

 value of r. 



r 



r 



Compass. 



Bahia. 



Sandy Point. 



Panama. 



s/76 



Admiralty Standard . 



± g'. 8 



± 1 2'. 2 



± ii'. 3 



± Il'.I 



± 2'.0 



± 2'. 8 



After Binnacle . 







± 25-8 



± 20. 1 



± 26.2 



± 24.2 



± 4-3 



± 6.1 



After Ritchie . . 







± 30.6 



± 56.6 



± 3§-S 



± 43-4 



± 7.7 



± 10.8 



After Azimuth . 







± 39-3 



± 51. 1 



± 32.6 



± 41.7 



± .7-4 



± 10.4 



Forward Alidade . 







± 19.0 



± 24.5 



± 23.6 



± 22.5 



± 4.0 



± 5-6 



Forward Binnacle . 







± 40.2 



± 31.2 



± 25-3 



± 32.8 



± 5-8 



± S.2 



Forward Ritchie . 







±59-7 



± 30.2 



± 37-8 



± 44-4 



± 7,8 



± II. I 



As an incidental result, this table shows that for ordinary steering compasses 

 (such as the Forward Alidade, Forward Binnacle, and After Binnacle) when read 

 to the nearest eighth of a point, the probable accidental error of a single reading 

 is about half a degree; for Ritchie Monitor Compasses (such as the Forward 

 and After Ritchie) when read to the nearest eighth of a point, the probable 

 accidental error of a single reading is about three-quarters of a degree; and for 

 Admiralty Standard Compasses, read to the nearest ten minutes, the probable 

 accidental error of a single reading is about eleven minutes. 



From the mathematical theory of the deviations of the compass, given in a pre- 

 ceding part of this section, we have 



fd = B t -A& 



and also 



Hence 



®=^""°+T x i 



= -/J,+A(7, + Jtaiifl+ yX-]f 



24 November, 1872. 



