PART III. EARTH CURRENTS AND EARTH MAGNETISM. CHAP. I. 779 



In the first extreme case therefore, the effect of the earth-current will be relatively greatest at 

 some distance from the storm-centre; in the second extreme case, on the other hand, this distance will 

 have less significance in this respect. 



At Kaafjord we found that the greatest effect of the earth-currents amounted to about '/ of the 

 greatest effect of the outer system in the horizontal components for storms of about 2 hours' duration. 



As we shall see in the next chapter, we can make a similar estimate for southern latitudes, 

 whereby it will be possible to draw a comparison between observation and calculation, and also, by 

 this relation, to obtain certain information concerning the earth's conductivity, although here too the 

 uncertainty will be very great. We shall return to this later. 



Finally, the condition of the vertical intensity also gives information that might afford indications 

 of the conductivity, but here the uncertainty will be still greater. 



Upon the basis of the figures that might be determined in this way, the most suitable value of y. 

 might be sought. In the first place, however, such a calculation will be rather complicated, especially 

 as one would have to include comparatively many terms of the series developments, as the systems in 

 operation come very near to the earth. In the second place, the result of such a calculation would be 

 a priori very uncertain. 



It may however be mentioned in this connection that the requirement for having conditions answer- 

 ing to the first extreme case in the terms of higher order will be fulfilled for greater values of \k\.R 

 than in the lower terms, the requirement being that 



k z R* 



i \ on 



shall be a small quantity. The importance of the higher terms will thus cause the approach of the 

 conditions to the first extreme case. Vice versa, in the higher terms | k \ R must be comparatively 

 greater, in order to satisfy the conditions for the second extreme case, than in the lower, as we have 

 here set aside terms of the order 



J2L 



\k\. q 



The condition of the vertical intensity might also be employed to separate inner and outer mag- 

 netic forces during the perturbations, but I think the result of such an investigation would not be nearly 

 so certain as the method here employed of comparing synchronous serrations, as all deflections occurring 

 in this component are very slight, and the earth's permeability certainly has a great influence here. 



CURRENTS THAT ARE INDUCED BY ROTATION OR REMOVAL OF THE SYSTEMS. 



155. In the preceding pages we have frequently pointed out that the systems of perturbation 

 may be moved, especially along the auroral zone. A removal such as this will also induce currents 

 in the earth, and it will be interesting to study the course of these currents. 



As the movement takes place approximately along a small circle, the same currents will be in- 

 duced as would be, supposing the system were fixed in space and the sphere rotated in relation to it 

 about an axis perpendicular to the plane of the small circle. For this case HERTZ has deduced special 

 formulae ('), but these are already contained in the expression given in the preceding article. 



We can choose the Z-axis perpendicular to the plane of the small circle. If we then designate 

 the angular velocity with which the system moves, or the corresponding rotation-velocity, as w, and 



(') Cf. HERTZ, Gesammelte Werke, Vol. I, p. 37. 



