§1. 



In two previous papers I gave results of the analysis of the auroral 

 spectra, and came to the conclusion that Nitrogen had to be the predominant 

 gas to the ver}- limit of the atmosphere. To explain the great density of 

 Nitrogen that had to be present at a height of 500 — 600 km. and at the 

 same time give an explanation to the singular type of Nitrogen spectrum 

 excited b}- electric rays in the auroral region, I was lead to the hypothesis 

 that the Nitrogen of the highest strata, at any rate to a considerable extent, 

 existed as positive ions. 



This hypothesis introduces the very interesting problem of finding how 

 the density of an electrified atmosphere will vary with the height as we 

 pass upwards from the neutral part of the atmosphere. 



From the phenomenon of electric wind we are familiar with the idea 

 that an electrically charged gas in an electric field is exposed to the action 

 of a mechanical force, and already in the first paper I assumed that the 

 variation of pressure was given by the equation: 



dp = — iog— o F) (ir (1) 



where p is the pressure, o the density, o the electric charge per unit volume 

 of the gas, F the electric force and r the distance from the centre of the 

 earth to the point considered. 



From this equation we see that the electric charge will have the effect 

 of diminishing the rate of decrease of the density as we pass upwards. — 

 If we try to calculate the distribution of matter more accurately, we shall 

 soon find that the problem is a somewhat complicated one. 



It is my intention in this paper to show that under certain assumptions 

 we can find a differential equation for the variation of density with the 

 height, and to draw some conclusions from our hypothesis of an electrically 

 charged upper layer. 



Let us suppose the earth to be a perfect sphere and that o and o are 

 functions of r only. We apply the Theorem of Gauss on a spherical sur- 

 face through the point P at a distance r from the centre of the earth. Then: 



Anr-F =- AriEr 



1~ 



