On Atmospheric Electricity and the Aurora Borealis. 361 



making a certain angle with the axis of rotation. The said 

 action is too irregular for such an explanation to be admissible. 

 Nevertheless the total intensity of the magnetic force is ascer- 

 tained to increase in a sufficiently regular manner as we re- 

 cede from the magnetic equator towards the magnetic poles. 

 If we join the points of the terrestrial surface where the mag- 

 netic dip has the same value, we obtain curves which, though 

 not forming true circles encompassing the earth and parallel 

 to one another, may yet be regarded as parallel circles drawn 

 at the surface of the earth, and having their centres on the 

 right line which joins the earth's magnetic poles. If from 

 the equator we proceed continually in the direction indicated 

 by the declination-needle (not in such a direction that the 

 angle of declination remains constantly the same), we obtain 

 magnetic meridians converging towards the magnetic poles ; 

 these meridians are not great circles, but yet bear a certain re- 

 semblance to them*. In general, and on a large scale, it is 

 therefore permissible to regard the earth as a magnet the axis 

 of which makes a certain angle with the terrestrial axis of ro- 

 tation. There is no need of a more exact idea of the magnetic 

 condition of the earth for the exposition which follows. 



Let abed (fig. 9) be a section passing through the axis of 

 rotation of the earth (which we will suppose to constitute a 

 perfect sphere) ; ac is its rotation-axis, bd its equator, and o its 

 centre. To simplify the question, we will at first suppose that 

 the two magnetic poles are on the rotation-axis, the south pole 

 in s, and the north pole in n. abod will consequently repre- 

 sent the northern hemisphere ; and we will designate by 

 a'b'c'd' the upper limit of the atmosphere. While the earth 

 is turning from west to east about its axis, an electric mole- 

 cule situated in m describes in the same direction a circle pa- 

 rallel to the equator, and therefore forms a current which is 

 acted upon by the two poles of the magnet. If now we pass 

 planes through the circuit-element situated in m and through 

 the two poles of the magnet, these planes will cut the figure 

 along the right lines sm and nm; and if in the same planes we 

 draw the right lines mp and mq respectively perpendicular to 

 ms and mn, we shall get the directions in which the magnetic 

 poles tend to direct the positive electric molecule (the aether). 

 Let r denote the distance from the centre of the earth to m, 

 p the distance from each of the poles of the magnet to the 

 same centre, and I the latitude of the point m. We remark 

 at starting that the magnetic phenomena presented by the 

 earth indicate that at least p cannot exceed in length the half 

 of the earth's radius ; and, in consequence, we assume that p 

 * Becquerel, TraiU complet du Magnetisme (Paris, 1846), p. 428. 



