On Rapi«! Periodic Variations of Terrestrial Magnetism. 53 



In the following, we will recapitulate some of the most 

 remarkable results of tlie statistical investigations and try to 

 revie-sv them in the light of the different hypothetical atmospheric 

 currents. 



21, First, take the relation between X- and Z-components 

 which show such an intimate connection as regards their 

 amplitudes and phases, as desci'ibed fully in previous |)aragraphs. 

 We will proceed to consider the influences of different possible 

 ideal systems of atmospheric currents separately, and compare 

 the results with the observed facts by way of seeking a most 

 plausiljle explanation. 



Since the disturbances ^vith tlie short periods here in 

 question most probably extend to a limited portion of the 

 earth's surface, as may l)e judged from their remarkable 

 dependency on the hours of the day, it will be allowed for a 

 first approximation to consider both the surface t^f the earth and 

 the atmospheric layer carrying the current as a plane. 



'22. a) Consider an infinite linear current / running per- 

 pendicular to the meridian at a height A from the earth's surface 

 considered plane, and at a horizontal distance x from the point 

 of observation A. Then the X- und Z-components will ]je given l)y 



jX=_plL__ ^ jz = -^^ (1) 



x' + lr xr + lv 



If the intensity of the current fluctuates in any manner, while 

 its position remains unchanged with respect to the earth, the 

 two components w^ill follow the fluctuation simultaneously, 

 provided that the variation is slow enough for neglecting the 

 effect of the induced current. The ratio of the amplitudes being 



JX h ' 



it may assume any value when x varies from — :o to +00. 

 Besides, AZ will be of opposite phase on both sides of the current. 

 h) If the above current moves perpendicular to itself from 

 x= — -jD to +x, X-component at A evidently attains a maximum 

 at x=0, while JZ is zero at ^-=0 and has a maximum and 



