308 Prof. E. Edlund on Atmospheric Electricity 



the rigid line drawn through the magnetic pole parallel to the 

 earth's axis. The squares of the distances between the mole- 

 cule m and the magnetic poles will be respectively 



r 2 + p 2 — 2rp (cos I sin a cos v + sin I cos a) 

 and 



r 2 -\-p 2 + 2rp (cos I sin a cos u + sin I cos a) . 



The forces with which the magnetic poles s and n act upon 

 the molecule are therefore expressed by 



and 



fcM s/ r 2 cos 2 1 + p 2 sin 2 a — 2rp cos Z sin a cos v 

 r 2 + p 2 — 2rp(cos I sin a cos v + sin / cos a) 



AMV?' 2 cos 2 / + /o 2 sin 2 a + 2rp cos / sin a cos v^ 

 r 2 + p 2 + 2r/? (cos / sin ot cos v + sin I cos a) 



The former of these forces acts in the plane which passes 

 through the molecule m and the right line drawn through the 

 magnetic pole s parallel to the axis of the earth, and the latter 

 in the plane passing through m and the right line drawn, 

 parallel to the same axis, through the magnetic pole n. It 

 w r ill suffice for our purpose to seek the expression of the com- 

 ponents of these forces in the cases in which v is equal to 90° 

 and to 0°. This calculation will show that the electric mole- 

 cule is moved further from the centre of the earth and carried 

 from lower to higher latitudes, that it is situated in the plane 

 represented by fig. 11 or in a plane making a right angle with 

 it. As this must evidently take place whatever the plane in 

 which the electric molecule is situated, the result obtained is 

 that the electric molecules are driven vertically upward and 

 at the same time from lower to higher latitudes. For the 

 highest latitudes, where cos I is a minimum, both forces, as also 

 their horizontal and vertical components, become very small ; 

 the electric density of the polar atmosphere cannot, therefore, 

 be great. Thus, although the position of the magnetic poles 

 is eccentric, the upper regions of the atmosphere from which 

 the electric fluid is precipitated upon the earth in continuous 

 currents must describe a closed annular zone about the pole. 

 But, as we shall demonstrate, this zone is not closed around 

 the astronomic pole as its centre. 



We suppose the molecule m situated in the plane passing 

 through the terrestrial axis and through the line joining the 

 poles of the magnet. By making v = in the preceding for- 

 mulae we get the following expressions for the two forces : — 



JcM(r cos l—p sin a) 

 r 2 + p 2 — 2rp sin (/ + «) 



