PART I. ON MAGNETIC STORMS. CHAP. II. IOI 



If we assume the two other portions of the current to be perfectly vertical, they will only give rise 

 to a magnetic force that is perpendicular to them, and thus everywhere horizontal, if the earth is con- 

 sidered as a homogeneous sphere. 



In the storm-centre and its immediate surroundings, these vertical currents will counteract the hori- 

 zontal portion of the current. Farther out along the transverse axis, we shall reach two points situated 

 symmetrically in relation to the principal axis, at which the effect of the horizontal portion in a hori- 

 zontal direction will be neutralised by those of the vertical currents. These two points then, answer to 

 those that we have previously designated as the points of convergence and divergence. Still farther 

 away from the storm-centre, from the moment of passing the points of tangency already mentioned, the 

 horizontal and the resultant of the two vertical portions will act in the same direction, and thus strengthen 

 one another. 



From the points of convergence and divergence then, P t will increase rapidly; at a certain dis- 

 tance it will attain a maximum, and then once more decrease. 



With regard to P v , we find that it is only the horizontal portion that can produce a force such 

 as this. One would expect, moreover, to find the vertical components strongest along the transverse 

 axis, at two points situated one on each side of the principal axis, and not far from the storm-centre. 

 At the point of convergence, P, should be directed upwards, at the point of divergence downwards. 



Along the principal axis, it will be chiefly the horizontal current that acts, at any rate in the district 

 that comes between the two vertical currents. In this district, the vertical currents will act contrary to 

 the horizontal. As we pass the points in which the vertical currents produced will meet the principal 

 axis, the nearest vertical portion will act in the same direction as the horizontal. 



In the quadrants enclosed between these axes, the effect of the nearest vertical portion at rather 

 greater distances will predominate ; and the distribution of force will be as shown in fig. 40. 



We have thus seen that the chief features of the form of the field in such a system, answer com- 

 pletely to those that are typical of an elementary polar storm. 



We cannot, however, without more ado, draw any conclusion as to the distribution of intensity; 

 it is possible that these fields corresponded only qualitatively, not quantitatively. I have therefore made 

 a calculation of the effect along the transverse axis of some systems such as this. This is sufficient, as 

 the form of the field is thereby given accurately enough. The actual current-conditions do not answer 

 so exactly to these assumed linear currents with two vertical portions and one horizontal, as to make 

 it worth while going into details. 



If we consider, in the first place, the magnetic effect of an infinitely narrow rectilinear piece of 



current on a magnetic mass i cm* g* sec , we find that 



f / tis . i f 



K == I - sin a = - 

 Jio /- 10) 



b 



yds 



a 



b 



y being the distance from the point under consideration to the current, and r and a respectively the 

 distance of the point from the current-element under consideration, and the angle made by the element 

 with the direction to the pole. The direction of the force is found by Ampere's rule, and as limits, 

 must be inserted the distances of the terminal points from the perpendicular that can be dropped from 

 the point under consideration to the current-line. 



