i)&0 Prof. F. A. Lindemann on the 



Using Jeans's value of 2l/i=1(V' 9 at 10 6 cm. and assuming 

 isothermal equilibrium (T = 220°) from there upwards, one 

 finds that particles penetrating to 10 7 cm. should have passed 

 through the equivalent of 13*1 cm. o£ H 2 , 0*6 cm. of He, 

 -025 cm. of: !N" 2 , and 0*01 cm. of 2 at standard temperature 

 and pressure. This corresponds to a range in air of about 

 3"6 cm. or an a. particle of: velocity 1*7. 10° cm./sec, a mode- 

 rately slow ray. It is clear that the hydrogen ions should be 

 stopped very much higher up if: the above method of calcu- 

 lation is correct. There seem, however, to be some very 

 doubtful assumptions involved : firstly that the air contains 

 hydrogen to the extent of! one part in 10 5 at ground-level, 

 and secondly that the isothermal region extends indefinitely 

 from 10° cm. on upwards. 



A number of! estimates of the proportion of H 2 in air are 

 given by various observers ranging from nothing at all to 

 one part in 1() 4 . Now the hydrogen molecules in the outer 

 layers of the atmosphere would certainly predominate if 

 there were more than one part in 4.10 6 at sea-level, and 

 it seems strange if this is so that no hydrogen lines have 

 been identified in spectra of the aurora. The hydrogen lines 

 are some of the easiest to produce spectroscopically, and 

 their total absence leads one to infer that there is very little 

 hydrogen present above 10 7 cm., and therefore say less than 

 one part in 10 8 at sea-level. If this is admitted, helium is 

 the predominant gas in auroral regions with a small ad- 

 mixture of nitrogen, and this is apparently in good accord 

 with spectroscopic results. 



The second assumption is more important and probably 

 more doubtful. If x is the absorption coefficient of unit 

 mass of gas of molecular weight A, then the energy absorbed 

 by a gramme-molecule of gas at temperature T is of the 

 form AF(<r, T), which is made up of the difference between 

 the energy absorbed from the layers at a higher temperature 

 T' and the energy emitted at temperature T. If a gramme- 

 molecule rises at velocitv -,- = V, therefore 

 " at 



r 7T , AFQ, T)dh 



or since p v — RT and — = — Vttft dh , 

 1 p ±\I 



dT _ 7 -l Ay/ FQ%T) \ 

 dk~ y R \ gV / 



