18G C. F. GAUSS ON THE GENERAL THEORY OF 



tween these two poles called the magnetic equator, the dip is 

 = and the intensity is half as gi-eat as at the poles ; between 

 the magnetic equator and either pole, both the dip and the in- 

 tensity depend on the distance from the said equator (which 

 distance is termed the magnetic latitude) in such manner, that 

 the tangent of the dip is equal to twice the tangent of the mag- 

 netic latitude. Lastly, the direction of the horizontal needle 

 must everywhere coincide mth the direction of a gi'eat circle 

 dra^Ti through the northern magnetic pole. 



There is in nature only a rude approximation to all these ne- 

 cessary consequences of the above hypothesis. In reality the 

 line of no dip is not a great circle, but a line of double flexure ; 

 equal intensities do not correspond to equal dips ; the directions 

 of the horizontal needle are far from all converging to one point ; 

 and so on. A very slight consideration is sufficient therefore to 

 show the inadmissibility of this hypothesis. 



One of the above propositions is however still employed as an 

 approximation in deducing the hne of no dip from observations 

 of dips of small amount made at some little distance from it. 



About eighty years ago, Tobias Mayer used a similar hypo- 

 thesis, but with this modification ; that instead of supposing the 

 infinitely small magnet at the centre of the earth, he placed it 

 at about the seventh part of the earth's radius from the centre ; 

 at the same time (probably in order to avoid greater complica- 

 tion in the calculations) he retained the wholly arbitrary suppo- 

 sition, of the plane perpendicular to the axis of the magnet pass- 

 ing through the centre of the earth. In this manner, on a com- 

 parison of the obsei'ved variations and dips, at a very small num- 

 ber of places it is true, he found them agree very well with his 

 calculation. A more extended comparison would have shown 

 that this hypothesis did not afford a much better representa- 

 tion than the first-mentioned one, of the whole phaenomena of the 

 dip and declination. No observations of the intensity had been 

 at that time made, at least as far as we know. 



Hansteen went a step further, by the endeavour to represent 

 the phaenomena on the hypothesis of two infinitely small eccen- 

 tric magnets of unequal strength. The decisive test of an hypo- 

 thesis must always be the comparison of its results with those 

 of experiment. Hansteen compared his with observations at 

 forty-eight different places, amongst which however there were 

 only twelve at which the intensity had been determined, and 



