14 I- VEGARD. M.-N. Kl. 



Nitrogen pressure at a height of 400 km. should have the extremely small 

 value of 4,4.10 -' dyn, cm-. 



In this respect it does not help much to assume a somewhat higher 

 temperature. With a temperature of 300 " obs. the same low pressure 

 would exist at a height of 542 km., which is also inside the auroral 

 region. 



If we at all are allowed to speak of a pressure of this order of 

 magnetude it would mean that at a height of 400 — 600 km., where the 

 pressure is of the order 10"-' dyn/ cm-, there should only be one molecule 

 in a volume of 10 cubic meters. This, again, would mean that the density 

 of the electric radiation had to be enormously great to produce the light- 

 intensity actually observed. 



If e. g., we assume that the aurorae are prodused by cathode rays of 

 a certain velocity, v = /)' c, we can estimate the density of radiation by a 

 comparison with the light produced when Nitrogen is bombarded by a 

 stream of cathode rays in a vacuum tube. 



We suppose the sources of light to be placed before the slit of a 

 spectroscope at distances R and r from the slit. The effective come of 

 the instrument with a solide angle co cuts the sources in areas 5 and s. 

 Let the intensity of light pr. unit area of the northlight and the vacuum 

 tube be Ja and /;.. The quantity of light passing through the instrument 

 in unit time will be proportional to 



(/'S Ja , q s Jv 



for the aurorae and the vacuum tube respectively ; q is the area of the 

 slit and : 



5 s 



If the two sources shall produce the same effect in the instrument we get 



Ja = Jv. (3 a) 



Now the intensity pr. unit area is equal to the intensity pr. unit volume 

 multiplied by the thickness of the layer, because there is practically no 

 absorption in the layer at any rate in the visible part of the spectrum. 

 The condition of equal photographic effect then will be : 



iala = ivlv. (3 b) 



/ is the intensity per unit volume, / is the thickness of the layer. The quantity 

 / is roughly proportional to the number of collissions made by the cathode 

 particles per unit volume in unit time or proportional to r/>, where v is 



