MAGNETIC OBSERVATIONS. 209 



And the resulting normal equations are 



Solving, we find 



g = + 0.11398 

 7i = + 0.00981 



k = 0.0509 

 = 0.3918 

 = -(- 0.3634 



Substituting these results in the equations of condition, the probable error of a 



7' 



single observed value of - - comes out 0.030, and the probable error of a com- 



Z' 



puted value of -~- comes out + 0.010. 



For the Admiralty Standard Compass we found 31 = 0.000, > = + 0.017, and 

 ( = 0.001. We have also 



a = a, ( 1 + >) 1 

 e = a, ( 1 )) 1 



b = x ( - 



Hence 



a = _ 0.0605 

 I = 0.0008 



e = 0.0917 

 d = 0.0008 



(S 



For the After Azimuth Compass we found 31 = 0.000, ) = -f 0.112, and 



0.000. Hence, in the same manner, 



a = _ 0.0396 e = - 0.2324 



6= 0.0000 d= 0.0000 



Collecting our results, we have the following final values of the coefficients of the 



ADMIRALTY STANDARD COMPASS. 

 = o.ooo 

 = + 0.0240 tan 9 + 0.460 JL 0.00102 o.ooi 



0.0016 tan 9 + 0.006 -L _ 0.00023 0.002 



- 







'1 

 z 



= + 0.017 o.ooi 



= - O.OOI O.OOI 



+ 0407 



' 



tan 

 27 December, 1872. 



_ 0.0050 



tan 9 



.1006 + 0.1665 4- +0.000694 4 o -7 



