62 



and completing the process by the determination of the mag- 

 netic moment of the bar in the ordinary method. This me- 



thod is applicable to the determination of mX and -r^: (and, 



therefore, also to that of ni) in the high magnetic latitudes ; 

 and we have only to substitute the value so obtained in the 

 formula derived from (5), 



„ m.U 

 tt — —. — . 

 smu 



In this manner the relative determination of R, obtained by 

 the deflection of the dipping needle, is rendered absolute.* 



To compare the probable error of R, found in this way, 

 with that of the same quantity deduced by the ordinary me- 

 thod, we may neglect the errors in the values of mX and ^=^, 



X 

 common to both processes, as they are small in the high lati- 

 tudes in comparison with those which arise from the friction 

 of the needle on its supports. Now, in the ordinary method, 

 R is deduced from the equation Rcos9 = X; and differentia- 

 ting this with respect ,to R and 9, and denoting by e, as before, 

 the limit of the error of position due to friction, 



-^- = e tan 0. 

 Jti 



But, in the proposed method, the corresponding error is 



AR £ 

 R sinu' 

 which is to the former as tan(90° - 6) : sinw. This method is, 

 therefore, to be preferred to the old in the high magnetic 

 latitudes, provided that the angle of deflection be sufficiently 

 great; and the relative accuracy increases indefinitely as the 

 observer approaches the magnetic pole. 



* The deflection of a dipping needle by a pair of magnets has already been 

 applied by Mr. Fox, in another manner, to the relative determination of the 

 total intensity. 



