of the Earth's Magnetic Force in Absolute Measure. 215 



f denoting the moment of friction. Now, this being constant 

 for a given instrument, cos w Aw is so likewise : and we have 



cos w A« = s, 



e denoting the value of Aw corresponding to « =0, or the 

 limit of the error due to friction in the natural position of the 

 needle, under the influence of the earth's magnetic force alone. 

 To find the error in the value of R, corresponding to Aw , 

 we have only to differentiate the equation of equilibrium with 

 respect to R and u , and we have 



AR sin u + R cos u Au Q = ; 

 and substituting for cos ?/ Aw , its value above given, 

 AR _ -g 

 R "sin Uq 



We see, then, that the relative error in the value of the 

 force resulting from friction, in either part of the process, is 

 inversely as trie sine of the angle of deflection ; and that it is 

 therefore requisite for accuracy that these angles should be 

 considerable. The angle of deflection may obviously be as 

 large as we please in the first part of the process, where the 

 deflection is caused by a weight ; but in the second, a large 

 deflection can only be produced by a massive magnet, and 

 such a magnet cannot be employed in the first part without 

 impairing the accuracy of the result by the increased friction. 

 The conditions of accuracy required in the two parts of the 

 process are therefore incompatible. 



We evade this difficulty by employing the inclinometer for 

 one only (namely, the second) of the two observations, and 

 completing the process by the determination of the magnetic 

 moment of the bar in the ordinary method. This method 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.), 



sin u 



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 quautity deduced by the ordinary me- 



* 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. 



