l6 KR. BIRKELAND. M.-N. Kl. 



If each particle carries a charge of e elecrostatic units, we have for 

 the current intensity /: 



And thus 



^=|x io9/-'^ z;2. 

 2 e 



If the C. G. S. system be employed, we obtain \V expressed in ergs 

 per second. This energy of the current will chiefly depend upon the kind 

 of rays that form the current. In our case the rays are very stiff, and 

 we have found for rays descending into the auroral zone //•(> = 3 • 10''. 



I think we may here introduce for m the expression for the longi- 

 tudinal mass given by Lorentz ^ 



m = \\ — \ — \ \ • niQ 



where ifiQ is the mass of a slow electron and c the velocity of light. 



In the extreme case we have before us, with rays of such hitherto 

 unknown stiffness, it is possible of course that the formulae of Lorentz 

 are not strictly applicable, but we have to make a choice, and 1 think this 

 is the best we can do. 



For slowly moving electrons we have (see Theory of Electrons): 



£: = 540 X loi'^ 



niQ 



whence W = ~-y^ 10'^ • t • t^ — • v- ergs per second. 



2 ^ 540 X 10^^ * ^ 



Now V is here so very nearly equal to c, the velocity of light, that 



we may write c~ for the last t'^ in our expression. 



Corresponding to our helio-cathode rays I have already calculated 



the expression: 



1 



^(i — (-)'] ' = 1.82 X io3 (»A. P.« p. 596) 



whence IV = x io^'~ • / ergs per second. 



* Lorentz, Theory of Electrons, p. 212. 



