230 HISTORY OF MAGNETISM. 



thcmatical artifices for deducing the values of V and its differentials 

 in converging series, Lie is able to derive the coefficients of these series 

 from the observed magnetic elements at certain places, and hence, to 

 calculate them for all places. The comparison of the calculation with 

 the observed results is, of course, the test of the truth of the theory. 



The degree of convergence of the series depends upon the unknown 

 distribution of magnetism within the earth. " If we could venture to 

 assume," says M. Gauss, " that the members have a sensible influence 

 only as far as the fourth order, complete observations from eight points 

 would be sufficient, theoretically considered, for the determination of 

 the coefficients." And under certain limitations, making this assump- 

 tion, as the best we can do at present, M. Gauss obtains from eight 

 places, 24 coefficients (each supplying three elements), and hence cal- 

 culates the magnetic elements (intensity, variation and dip) at 91 

 places in all parts of the earth. He finds his calculations approach 

 the observed values with a degree of exactness which appears to be 

 quite convincing as to the general truth of his results; especially 

 taking into account how entirely unlimited is his original hypothesis. 



It is one of the most curious results of this investigation that 



O 



according to the most simple meaning which we can give to the term 

 "pole" the earth has only two magnetic poles; that is, two points 

 where the direction of the magnetic force is vertical. And thus the 

 isogonal curves may be looked upon as deformations of the curves 

 deduced by Euler from the supposition of two poles, the deformation 

 arising from this, that the earth does not contain a single definite 

 magnet, but irregularly diffused magnetical elements, which still have 

 collectivelv a distinct resemblance to a single magnet. And instead 



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of Hansteen's Siberian pole, we have a Siberian region in which the 

 needles converge ; but if the apparent convergence be pursued it no- 

 where comes to a point; and the like is the case in the Antarctic 

 region. "When the 24 Gaussian elements at any time are known the 

 magnetic condition of the globe is known, just as the mechanical con 

 dition of the solar system is known, \vhcn we know the elements 01 

 the orbits of the satellites and planets and the mass of each. And 

 the comparison of this magnetic condition of the globe at distant 

 periods of time cannot fail to supply materials for future researches 

 and speculations with regard to the agencies by which the condition 

 of the earth is determined. The condition of which we here speak 

 must necessarily be its mechanico-chcmical condition, being expressed, as 

 it will be, in terms of the mechanico-chemical sciences. The in'-^ti- 



