On Eapid Periodic Variations of Terrestrial Magnetism. Q( 



to consider tliat the difficulties met with in the preceding 

 paragraph witli regard to tlie phase relation may partly be 

 accounted lor hy a similar combination of the motion and the 

 variation in the intensity of the current. Such a combination 

 is quite i^roliable in view of tlie reciprocal action of the magnetic 

 field on the conducting layer carrying the current. Though these 

 points seem to suggest many interesting problems worth in- 

 vestigation, it will at present be rather too far fetched to introduce 

 any further liypothesis.'-' 



25. The fact described in n^ 5, (/) that two trains of waves 

 with different periods sometimes appear simultaneouslj' in the X- 

 and Y-components respectively, may probably be explained 

 by the combination of fluctuations in the direction as well as 

 in the intensit^^ of the current. Take the simplest case, when 

 a linear current at a distance d from the point of observation A. 

 in its mean position, is fluctuating in its intensity as given by 



/z=/„ cos pt, 



while it is osciUating statioiiarily about the position of equilibrium, 

 in sucli a manner that it were always tangential to a string 

 vibrating in a horizontal plane with its node at the foot of the 

 perpendicular from A to its mean position. If the angle made 

 by the current to its mean position at the time t be «. then tg « 

 will vary as Ccos(qf-\-(f), where C is the tangent of the maximum 

 angle of inclination. If the mean position of the current be 

 perpendicular to the meridian, tlie periodic variation of X and 

 Y will be given by 



JX=— - cos pt, 



i C 

 Jr=— ^* — cos 2)t cos(qt + <f)- 

 d 



Thus a "combination tone " will arise in the component parallel 

 to the mean direction of the current. The effect of the induced 

 current will probably enhance the "summation tone" in 

 comparison with the "difference tone." If the oscillation is the 



1) These points will be touched upon again later in § 28. 



