1923- No. 8. THE ATRORAL 5PECTRLM AND THE ATMOSPHERE. l^ 



the number of electrons crossing unit area in unit time. Let w be the 

 number of cathode particles which at any moment is present in 1 cnr^; then 



// =^ — . 



V 



Assuming the same ray-velocity, the intensity of light emission per unit 

 volume will be proportional to up, and our condition for equal spectro- 

 scopic action takes the form : 



141 Napa la = ": />; /;•• 



For the vacuum tube we assume /;. = 1 cm., pi- = 100 dyn cm-. The 

 corpuscular current which would produce the same spectroscopic action as 

 that of the upper part of an auroral ray can be estimated to about lO"'' 

 ampere when the velocity of the rays is about ' 2 c, where c is the 

 velocity of light. 



This would give: 



n,eß = 10"'. 



Putting ß = '^ 2 and c = 4.8. IQ"'*', 



//;. ^^ 4 • 10-. Hence : 



ftapa/a = 4 • 10", 



/a is of the order of 10^ cm., and 



ftapa = 4- 10--. 



If, now, pa shoule be equal to 4,10 -^ it would follow hat 

 (5) fia = 10-'^. 



At any moment there should be about as many electrons (ray -carriers) 

 present in each cm^ as there are molecules in 1 cm"^ of gas 0" C and 

 atmospheric pressure. Such as density of electric radiation cannot be assumed. 

 The electrostatic forces would prevent a ray bandle of such a density 

 to be formed. 



If Nitrogen is the predominant gas to the very limit of the atmosphere, 

 it must at the height of 400 — 600 km. possess a density of a much higher 

 order of magnitude than that previously calculated. 



Quite formally we could get a sufficient pressure and density of 

 Nitrogen at a height of 600 km. by a proper assumption with regard to 

 the temperature of the upper strata of the atmosphere. 



If, as before, for the sake of simplicity, we suppose the temperature to 

 be constant above 10 km. from the ground, we can easely find the tempera- 



