M A G N E TIC B S E 11 V A T I O N S . 



207 



From the data already given, the value of X was next computed hy means of the 

 formulae 



sh, ( ) = — ^ — - |jH _j_ §3 s in '(' -f g cos J ' + © sin 2f ' + g cos 2 s "] 





sin <$ 



// 21 + s ^ sin £ -f £ cos £ + £} sin 2£ + @ cos 2 S ' 

 The individual results obtained from the observed values of are as follows: 











Value of x 



Station. 









Admiralty Standard 



After Azimuth 





Compass. 



Compass. 



Salute Islands 



0.91S 





Ceara . 









0.896 





Bahia . 









0.922 





Rio Janeiro. 









°-939 



0.942 



Rio Janeiro. 









0.904 



0.884 



Monte Video 









0.913 



0.814 



Sandy Point 









0.914 



0.S21 



Valparaiso . 









0-954 



0.848 



Valparaiso . 









0-934 



0.886 



Callao 









0.905 



0.820 



Panama 









0.952 



0.861 



Acapulco 









0.947 



0.816 



San Francisco 









0.914 



0.947 



Taking the means, for the Admiralty Standard Compass, we have finally 



a, = 0.924 -b 0.0036 

 and the probable error of a single observed value of ?„ is ^ 0.013. For the After 

 Azimuth compass we have finally 



X = 0.864 -j- 0.0107 

 and the probable error of a single observed value of /I is ^ 0.034. 



Z' 



In order to determine these coefficients which depend upon the value of — , we 



Z 



have equation (6 a), which is 



, Z' , cos l , sin l 7 1 







But as E is liable to a slow change, a term depending upon the time is introduced, 

 and then we get 



Z' cos £* . sin £ ... ,, 1 . . ^ t 







1 — 



COS t, 



Sill (, 



i + * X S- 7iX ianl + * + * X lf+ Ai2X if 



(6 b) 



where Ai2 is the daily change in the value of 7?, and t is the time in days, counted 

 from November 1, 1865. Each observed value of — furnishes an equation of con- 



Zj 



dition of the same form as (6 b), and from all the equations of condition thus 

 obtained the most probable values of </, h, k, E, and AE, can be found by the 

 method of least squares. 



