74 Prof. L.Vegard: Results of Northliglit Investigations 



Numerical calculations regarding the range of a-rays in 

 the atmosphere have also been carried out by R. Swinne *. 



I shall here briefly mention the mode of procedure and 

 some of the results which have a bearing on the present 

 problem f. 



Let the gas considered have the atomic weight A, and let 

 the ray at the point considered have traversed a mass of the 

 gas which per unit area is equal to m. Then the absorption 

 suffered by the ray is equivalent to the absorption suffered 

 by traversing a distance r in air at 0° G. and 760 mm. 

 pressure, where 



V 3-81 m. 

 r = = 



and where D is the density of air at 0° and 760 mm. 

 pressure. 



Let the partial pressure be p dyne/cm. 2 , or B cm. Hg. 

 Then 



/IOC 



9 Jh 



where s is the density of Hg, and H is the height of the 

 point above the surface of the earth. 



If we know the composition of the atmosphere, which 

 means that we know the partial pressure of each constituent 

 gas as a function of the height H, we can find the air equi- 

 valent of each gas as a function of H, and the resultant 

 air equivalent is found as the sum of those of the various 

 components. 



Hence we at once can find the height to which a ray of a 

 given initial penetrating power will descend, as also— if 

 wanted — the velocity at any point of the path. If the 

 initial range of the ray is given by the air equivalent ?' , 

 then the height H at which the ray is stopped is the one 

 which gives an atmospheric air equivalent equal to r . If 

 the atmospheric air equivalent at the height H is r, then, 

 according to the well-known relation between velocity and 

 range, the velocity at the height H will be 



3 / " 



where v is the initial velocity. 



* Physik. Zeitschr. xvii. p. 529 (1916). 



t See L. Yegard, "Bericht iiber die neueren Untersucliimgen am 

 Nordlicht." Jahrburh dcr Had. u. Elektrtnik, xiv. p. 455. 



