312 BIRKELAND. THE NORWEGIAN AURORA POLARIS EXPEDITION, 1902 1903. 



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



f . 



- fl - amperes 



and thus 



3 X 10 



W = 3 io ' '' 



2 



If the C.G.S. system be employed, we obtain IV expressed in ergs per second. 



The energy of the current will chiefly depend upon the kind of rays that form the current. It is 

 evident, however, from the magnetic storms previously described, that the corpuscular rays here referred 

 to must be very "stiff" magnetically. 



Leaving the question of the particular nature of these rays for the present undecided, we will make 

 the calculation for two types. 



(i) For cathode rays, whose velocity is small in proportion to the velocity of light, we have, when 

 e is calculated in electrostatic units, 



15 



sec. 



" 1 



- = 510 x IC> cm - g r - 

 P* 



For rays where v = 0.7 X IC)10 > we thus find that 



W = -X loi) ' 35 z -44 X iQ 11 ' er g s P e r second, 



or 



W = 19.6 /' h.-p. 

 (2) For rays with velocities of 



v = 2.59 x r 10 cm - sec." 1 , 

 we have, by Kaufmanns determinations, 



Corresponding to this, 



= 255 x Iolr ' cm - * g r - 2 sec - 



W = 3.94 X Io12 ' er g s P er second, 



or 



W = 535 ' h.-p. 



The energy in each separate case can then be calculated according to these expressions. 

 For i = 1,000,000 amperes, we obtain in the first case 



W = 19.6 x I0< ' h.-p., 

 in the second case 



^ = 535 X io 6 h.-p., 



or 100 times more than the maximal amount of force that all the waterfalls of Norway together could 

 deliver by a perfect regulation of all water-courses. 



There is much that seems to favour the idea that the rays that come to the earth are very "stiff", 

 and may possibly have considerably more energy than the here assumed /? rays. We recollect that the 

 apparent mass increases comparatively quickly when the velocity of the corpuscles approaches that of 

 light. We know of /? rays whose velocity is only 5 per cent, less than that of light, and whose apparent 

 mass is 50 per cent, greater than that of the /? rays assumed above. 



We have moreover, in the preceding pages, during powerful magnetic storms, calculated current- 

 strengths greater than a million amperes, which is the amount here taken as the basis. 



(') The values are calculated from those given in Sir J. J. Thomson's "Corpuscular Theory of Matter"; London, 1907. 



