762 



I5IRKELAND. THE NORWEGIAN AURORA POLARIS EXPEDITION. 1902 1903. 



_,. 



-JL- V n = V n f V n dQ 



n + i <> ) 







n V* _ i Cdgf i C \ 



, I r I " I ' n n o i 



+!+ VeJVeV <?J / 



Here the summation with regard to can be made direct, and we can therefore in this case write 



o o 



In the second extreme case, where j k j . R is very large, Q = R is simpler, 



n 



= H*) - ^ f v 



If we now look at the conditions on the earth during the magnetic storms, we can assume 

 earth-current conditions as a whole exhibit a greater or less resemblance to the idealised case that \\x 

 have here studied. Whether the conditions followed either of the two extreme cases, and if so, \\huh 

 of them, would mainly depend upon the specific resistance and the length of period. If they agreed 

 with neither case, it might still be assumed that they will answer to something intermediate betuvm 

 the two. 



If we assume the length of period to be 2 hours, i. e. p = -^^ , then 



8 7 r 2 />/? 2 = 4.5 X io 15 . 



For sea- water we may put x = about io 10 , 



for rain-water about 6 X io 13 , 



and for purest distilled water about io lr> . 



The corresponding values of k | . R are 



7 X io 2 , 9, 



The specific resistance in the outermost strata of the earth may probably now be assumed to have an 

 order of magnitude corresponding to these figures. It should therefore be assumed that the earth-current 

 conditions answer to something between the two extreme cases. 



In order to obtain a general view of the course of the earth-currents during a polar elementary 

 storm, we will determine the course of the induction-currents at the surface for the current-system pre- 

 viously employed in Art. 91, answering to the first and second extreme cases, assuming that the positimi 

 of the system is fixed in relation to the earth, and that the strength of the current, i , varies. We have 

 previously found for the potential of this system [see equation (28), p. 428], 



