362 Prof. E. Edlund on Atmospheric Electricity 



is at most equal to the half of that radius. The squares of 

 the distances of the two poles from the point m will therefore 

 be respectively 



r 2 + p 2 — 2rp sin / and r 2 + p 2 + 2rp sin I. 



The intensity of the current is proportional to the velocity 

 with which the molecule m moves in its parallel circle ; and 

 that velocity is, in its turn, proportional to the distance from 

 the rotation-axis, consequently to r cos /. Designating the 

 intensity of the magnetic poles by M, and by k a constant, we 

 shall have, for the force with which the south pole tends to 

 direct the molecule along m p, the expression 



fcMr cos / 

 r 2 -)-p 2 -2rpsml' 



and, for the action of the north pole upon the same molecule 

 along the line mq } 



JeMr cos I 

 r 2 + p 2 + 2rp sin t 



Taking the sum of the components of these forces along the 

 earth's radius drawn through the point m, we get 



IcMrp cos 2 / JcMrp cos 2 / , A x 



■ ■+■ . . . {J\) 



(f + p 2 - 2rp sin I)* (r 2 + p 2 + 2rp sin t)i 



This sum, which we will name the vertical component, de- 

 notes the force with which the magnet tends to direct the 

 aether (the electropositive fluid) upward in a vertical direction. 

 (If we assume also an electronegative fluid, this will be urged 

 by the same force in the opposite direction.) 



If now we consider an electric molecule which is situated 

 in the atmosphere or at the surface of the earth, for which, 

 therefore, r is >2/o, we see that formula (A) will be equal to 

 zero at the polar point, and will possess a relatively minimal 

 value in the vicinity of that point. Consequently the force 

 tending to carry the electric molecule vertically upwards is 

 nil at the pole, and a minimum in the polar region. It follows 

 of course, and is besides proved by the formula, that the sum 

 is equal for the same latitudes in both hemispheres. 



Taking the component of these forces in a direction making 

 a right angle with the earth's radius (the tangential compo- 

 nent), we obtain the force with which the electric molecules 

 are urged along the tangent of the circle the radius of which 

 is r. We have thus : — 



IcM.r(r— p sin Z) cos I _ kM.r(r + p sin /) cos I m^ 



(r 2 + p 2 -2rpsmiy2 (r 2 + p 2 + 2rp sin l)i ' 



