Page:Scientific Memoirs, Vol. 2 (1841).djvu/198

 186 these two poles called the magnetic equator, the dip is $$= 0$$ and the intensity is half as gi-eat as at the poles; between the magnetic equator and either pole, both the dip and the intensity 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 magnetic latitude. Lastly, the direction of the horizontal needle must everywhere coincide with the direction of a great circle drawn through the northern magnetic pole.

There is in nature only a rude approximation to all these necessary 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 line 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 hypothesis, 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 complication in the calculations) he retained the wholly arbitrary supposition, of the plane perpendicular to the axis of the magnet passing through the centre of the earth. In this manner, on a comparison of the observed variations and dips, at a very small number 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 representation than the first-mentioned one, of the whole phænomena 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 phænomena on the hypothesis of two infinitely small eccentric magnets of unequal strength. The decisive test of an hypothesis 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