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XI. Geometrical Investigations concerning the Phenomena of Terrestrial Mafrnetism. 

 iBy Thomas Stephens Davies, Esq. F.R.S. Lond. and Ed. F.R.A.S. Royal Military 

 Academy, Woolwich. 



Received December 18th, 1834, — Read February 5th and 12th, 1835. 



X HOUGH the experiments of Michel and Coulomb have satisfactorily determined 

 the law according to which magnetic forces vary as the distance of the needle acted 

 on is made to vary, yet, so far as I know, no one has attempted to deduce from that 

 law any method of accounting for the phenomena of terrestrial magnetism. Till that 

 is done, however, we cannot assure ourselves whether the poles (I use the term to 

 designate the centres from which the forces emanate,) be two or more ; nor even 

 whether it be necessary to consider them infinite in number and distributed over the 

 whole surface or through the whole mass of the magnet. The agreement of the re- 

 sults as to quantity with the actual phenomena would be decisive in favour of any 

 hypothesis. The necessary consequences have not, however, yet been deduced from 

 any one hypothesis whatever : and even had it been otherwise, there is so much un- 

 certainty attached to magnetical observations, and so many anomalous and unac- 

 countable discrepancies and disturbances continually mingling in the registered 

 results, that it is not possible, in the present state of the mimerical data, to bring any 

 hypothesis fairly to the trial, however complete the mathematical development of its 

 consequences may be. 



Notwithstanding the great difficulty of conducting a series of observations in a per- 

 fectly unexceptionable manner, and the utter impossibility, with our present know- 

 ledge, of properly determining the correction to be made at any given place and 

 period with any given instrument, there are yet several features in the phenomena 

 which are of too decided a character to be overlooked in comparing the results of 

 any theory with observation. We may not, indeed, be able to avoid considerable 

 discrepancies in our comparison, but still there should at least be a general tendency 

 towards agreement, and in no case a direct reversal of the phenomena presenting 

 itself as the result of any hypothesis which prefers its claims to our adoption. In 

 respect to terrestrial magnetism, no direct attempt has, however, been made to em- 

 body the results of any hypothesis in a series of appropriate formulae ; and hence the 

 conjectures which have been made respecting such agreements have been made from 

 extremely vague and inconclusive considerations. 



The duality of the terrestrial magnetic poles is the oldest hypothesis, and perhaps 

 that whose consequences will be found most easy to examine. The hasty comparisons 



