62 



and completing tlie 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 -^ (and, 



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

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

 formula derived from (5), 



sinw 

 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 mXand -^r, 



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 R cosO =^ X ; and dilFerentia- 

 ting this with respect ^to R and 6, and denoting by £, as before, 

 the limit of the error of position due to friction, 



-=- = £ tan if. 

 M 



But, in the proposed method, the corresponding error is 



AR e 



R sinw ' 



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 sufHciently 

 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. 



