On Rapid Periodic Variations of Terrestrial Magnetism. (33 



As for the phase retardation of AZ after AX, the serious 

 difficulty against the hypothesis of the progressive waves is that, 

 in the theoretical result, the phase angle must be included within 

 the range 90° to 135° or —45° to —00°, wliile in the observed 

 results, it crowds most densely within tlie limit 45° to 90°. 

 At present we are at a loss to judge whether the difficulty may 

 be evaded by assuming the presence of more conducting layer 

 below the earth's crust, as argued by Schuster to explain a 

 similar discrepancy in the case of the diurnal wave. 



On the other hand, if we once admit in the case of the 

 stationary wave that cotg ox is somehow of the order of unity, 

 the ratio of amplitude JZJjX,^ is just the same as in the case of 

 the progressive waves, and the aljove calculations generally 

 apply also to this case, except that part concerning the velocity 

 of propagation which is zero in this case. The general mode of 

 dependency of the ratio on the periods is equally favourable for 

 the stationary waves, and we see no strong reason for preferring 

 the theory of progressive waves, as far as the amplitude ratio is 

 concerned. If we take cotgaa;=l or 0'8 and k=10~'^^ the wave 

 length estimated seems, however, too small. 



At any rate too much weight must not be laid on the 

 numerical results of the above calculations, since they have no 

 claim to accuracy of the quantitative results, if we remember 

 the utmost simplicity of tlie assumptions on which they are 

 based, even if they may be legitimate in essential features. 



24. Next, consider the ideal case where an atmospheric 

 current is subject to a rotatory oscillation remaining parallel to 

 itself. Taking the simplest case of a constant linear current 

 running parallel to the 7/-axis and oscillating about the mean 

 position, given by its elevation h^ above the surface of the earth 

 and the horizontal distance ^o from the point of observation taken 

 as the origin. Let the position of the current I be given by 



x=Xq+x^co^ nt, 



Ä = 7^0 + /jjCOS {7lt — (f). 



We may obtain, neglecting the efïect of induction 



I '■' 



