and Nature of the Cosmic Electric Rays. 11 



at any height for which r is finite, provided a is sufficiently 

 near 90°. 



The variation of the air equivalent with the height is 

 given in PL II. fig. 7. From this curve we can immediately 

 take out the height to which a ray of a given penetrating 

 power will descend, and also the penetrating power (and 

 velocity) it possesses at any point of its path. A given 

 initial range is represented on the figure by a vertical line 

 through the point on the r axis for which r is equal to 

 the initial range of the ray. This curve will cut one of the 

 hydrogen curves c at the point the height of which gives us 

 the height to which this particular ray would descend if 

 only hydrogen were present. The point where it cuts the 

 sum curve should give the height of complete absorption 

 when all gases were present. Lines corresponding to a rays 

 from a number of radioactive substances have been dra^n 

 on the figure. 



If the assumptions on which our calculations are based 

 are right, we see from the figure that above 90 km. the 

 predominant part of the air equivalent is due to hydrogen. 

 This result, however, can hardly be brought into accordance 

 with observed facts. The greater part of the luminosity 

 produced by aurorae will be found in an interval between 

 100-125 km. (see fig. 7) ; but in this interval the atmo- 

 sphere according to our calculations should consist of nearly 

 pure hydrogen, and we should expect the hydrogen lines to 

 be predominant in the auroral spectrum, contrary to obser- 

 vations. Apart from the strong green line, the origin of 

 which is yet unknown, the principal lines of the hvdrogen 

 spectrum are shown to be identical with the principal negative 

 bands of nitrogen *. Thus, even at an interval of maximum 

 light-emission 100-125 kin. the nitrogen must form an 

 essential part of the atmosphere, and thus the assumption 

 of Wegener in the case of hydrogen must be fundamentally 

 wrong. It is not allowable, from the traces of hydrogen in the 

 atmosphere near the ground to draw conclusions, as Wegener 

 has done, as to the quantity of hydrogen contained in the 

 higher strata in the atmosphere. It is quite possible that 

 the hydrogen is confined to the lower strata of the atmo- 

 sphere, and there may be a continual production of free 

 hydrogen counteracted by an oxidation process in the 

 atmosphere, caused for instance by atmospheric electricity, 

 and we cannot apply the equilibrium conditions in the case 



* L. Vegard, " Photogr. Aufnahme des Nordlichtspectrums mil einem 

 Spectrographen von grosser Dispersion," Phys. Zeitschr. xiv. (1913). 



