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position of the horizontal magnet, so circumstanced, we can 

 infer those of the inclination itself. 



But the iron bar may have (and generally will have) a 

 certain portion of permanent magnetism, which will concur 

 with the induced magnetism in producing the deflection ; 

 and it becomes necessary to institute the observations in 

 such a manner, as to be able to eliminate the effects of 

 this extraneous cause. For this purpose we have only to 

 invert the bar, so that the acting pole, which was uppermost 

 in one part of the observation, shall be lowermost in the 

 other. The induced polarity will, under these circumstances, 

 be opposite in the two cases ; and the acting force will in one 

 case be the sum of the induced and permanent forces, and 

 in the other their difference. 



Let X and Y denote the horizontal and vertical compo- 

 nents of the earth's magnetic force, m the intensity of the 

 permanent magnetism in the acting pole, and m the magnetic 

 moment of the suspended magnet. The intensity of the in- 

 duced magnetism is, by hypothesis, equal to 



k being an unknown constant ; and when this is of the same 

 name as the permanent magnetism, the intensity of the act- 

 ing force, at the unit of distance, is 



Ay -}- M. 



Accordingly, the moment of this force to turn the suspended 

 magnet is {Uy + m) wircosM, u being the angle of deflection, 

 and r a constant depending on the distance ; or, making, for 

 abridgment, kr — p, Mr = q, 



(pY -|- q) m cos ti. 



But this deflecting force is resisted by the earth's horizontal 

 force, the moment of which to turn the magnet is 



\m sin u ; 



