L. VEGARD. 



M.-N. Kl. 



§3. 



If the gas in the auroral region should exist in a highly electrified 

 state, it would indeed seem very likely that the density of matter above 

 the sphere of zero potential is very small. We suppose a cylinder of unit 

 cross section placed radially, and with one end at the surface of the zero- 

 sphere and the other reaching outside the atmosphere. Let the mass con- 

 tained in this cylinder be // and the number of molecules n. Then : 



f.1 = n M . 



Let us suppose that a fraction ß of these molecules carry an elementary 

 charge c. The total charge er in the cylinder would then be: 



er ^ ß 11 c 

 Hence: 



' /* (8) 



ß M 



As the length of the cylinder is small as compared with the radius 

 of the earth, the total electric charge carried by the earth above the zero- 

 sphere should be : • 



E = A n r^ er 



and just at the limit of the atmosphere the electric force should be: 



/* = ^ or approximately : 



F= A7ier = Ajiß^fi. (9) 



If at the outer limit of the atmosphere the action of gravitation on 

 unit volume shall be greater than the mechanical force due to the electric 

 charge, we must have: 



Qg>oF (10) 



Let the number of molecules in unit volume be //' then: 



Q = Mf/ and 

 o = ß' n' c Hence 



^ = ß'^ 

 Q ^ M 



