1923. No. 10. DISTRIBUTION OF MATTER IN THK ATMOSPHERE. 9 



fj' is the ratio between the number of charged molecules to the total number 

 in unit volume, p" ma}' vary with r — and thus be different from fi, 

 which is an average for the region above a certain level. To get an 

 estimate we will put ß' = ß . 



Inserting the expressions for — and 7^. the condition (9) takes the form : 



o 



2 



s>^^:-ß% 



Now 



^= 1,07 lO'^ and finally 



4 .T ß- // <C 1 ~ gram 



If each molecule carried a charge c, ß = 1 and 4 .t /( = 10 ""^ gram. 

 This would mean that practically no charged matter could exist above the 

 zero-sphere. Underneath the zero-sphere, however, the electric force is 

 directed downwards, and the electric charge could not explain that the 

 density of Nitrogen diminished so slowh' as would be wanted to explain 

 the very long auroral ray-streamers. 



If the upper strata of the atmosphere should be in an electrically 

 charged state, we should have to assume that ß is ver\' small. But at the 

 very low densities it is rather doubtful that an individual ion of molecular 

 dimensions will impart to the other molecules a mechanical force as if the 

 electric charge had been equally divided on all molecules. 



If we are to adhere to the hypothesis that Nitrogen maintains a notice- 

 able density to heights of 500 — 600 km. through the effect of electric 

 forces, we should probably have to assume that the charged particles form 

 clusters or drops of a very small size. If the temperature is extremely 

 low, it seems possible that Nitrogen might condense round the ions. 

 We know that the freezing point of Nitrogen is about 60 Abs. and, if the 

 temperature was still lower. Nitrogen might be present in the form og 

 minute crystals — or fine, solid dust. 



If the diameters of the drops or dust particles were of the same 



S 



order of magnitude as the wave-length of light, there might be 10 mole- 

 cules in each drop containing one elementary charge. This would mean 

 that ß should be of the order 10 and the quantity // should be less 

 than 10 ^ gram, which is of quite a reasonable order of magnitude. 



Our calculations are based on the assumption that the matter is in a 

 state of statistical equilibrium, but, as a matter of fact, there must be a 

 continual motion up and down. — Some particles will become so highly 

 charged that they are moving upwurds through the electric force. Then 

 they may lose some of their charge by collision with electrons, and fall 

 down asrain and so on. 



