On Rapid Periodic Variations of Toircstrial Magnetism. 59 



waves, when kn increases from to x , tlie retardât ion will vary 



from 4r to -7r+--r <>i' ""^^ while in the ease of retrui;Tade waves, 

 '2 2 4 4 _ _ 



it may l^e considered as negative and \'aries from — ^ to ~ r- 



Now, retnrning to the actual case, Ave will tiy to examine 

 if either of these h^'pothetical waves could be reconciled with 

 the observed facts regarding the relations between the horizontal 

 and vertical components of magnetic pulsations. 



If the stationary waves alone were concerned, we would 

 have to assume that the distance of the observing station from 

 the node of the electric current was in any case greater than 

 -5- but less than -f^, in order to explain the fact that the ratio 



o 4 



AZjàX,,, was always less than unity, at least in the case of the 

 slow oscillations where ajA in (11) is nearly equal to unity and 

 cotg ax may become less than unity only when o.x or — ,— is greater 

 than -7-. This will be a rather awkward, though not impossible 



assumption, if the wave length were small in comparison with 

 the earth's quadrant, since Ave must then also assume that the 

 location of the current is always limited to a rather narroAV range 

 favorable to the above relation. TJie only plausible hypothesis 

 reconcilable with this assumption is that the Avave length of 

 the current producing the sIoav waves is of the order of magnitude 

 of the earth's meridian, and also that the station lies ahvays 

 not far apart from the loop of the current. In such a case, 

 hoAvever, either of our assumption as to the planeness of tlie 

 earth's surface and the existence of the infinite train of Avaves, 

 Avill fail to apply; but the case Avill ratiier approach that Avliich 

 Avas discussed in the preceding paragraph. The present result 

 may be interpreted as merel}' indicating that the effect of 

 the induced current has the tendency to retard the vertical 

 component Avith respect to the horizontal one. For such a case, 

 the mathematical calculation giA'en by Lamb^^ for spherical 

 conductors Avill directly apply, which also shoAVS the retardation 

 tending to -^ for the large A'alue of kn. At auA^ rate, the observed 



(1) H. Lamb, Phil. Trans., 1883, p. 52Ü ; ihid. ISO, 1880, p. 513. 



