MAGNETIC OBSERVATIONS. 



207 



From the data already given, the value of a, was next computed by means of the 

 formulae 



sm 6 = , ^ TTO! 21 4- 2^ sin ' -f- G cos f ' -f > sin 2f ' + ( cos 



sin i 



21 + 55 sin f + GO-OS -f ) sin 2 -f < cos 2 



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



H 



Value of X 



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



a = 0.924 0.0036 



and the probable error of a single observed value of /I is ^ 0.013. For the After 

 Azimuth compass we have finally 



a = 0.864 0.0107 

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



Z' 



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



cos 



sn 



have equation (6 a), which is 



Z' . 



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

 and then we get 



Z' 



cos 



sn 



/c , , 

 (6b) 



where AR is the daily change in the value of R, and t is the time iri days, counted 



Z' 



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



JU 



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

 obtained the most probable values of g, h, 7t, R, and AR, can be found by the 

 method of least squares. 



