I'Koi'.iG.irtos or i.u.ciKic ir.irns o\er tiii: earth 2i\ 

 '->>■■ .. ,'" 



al)sori)ti<iii .IS hrlorc, ii.iiiu'l\- x- "■' .. .mil tin- hIIht r.iv wliosi- cdiii- 



* ■ O .\ ft 



pli-\ iiiili'X cif rcfr.utioii is «i— " has the .ihsorptioii coiistiml J (/fri + ztj) 



ill whirh k\ and kt are the abs<irpti()n constants j^Im-ii aliove for 

 prop.iij.uion alons a nuiKnetic meridian. 



.\l llu- rritir.il freqiieniA we tind, tlierefore, lli.it tlie absorption 



constant is abnorm.ili\' hiuh and equal U^ ,' . ■ . which is one-half 



4 «„- / 



that obtained for the first ray of case 2. 



One very striking fact is brought to light by these equations. Thus, 

 referring to the two values of absorption constants for transmission 

 along the magnetic field, we find that for \ery long waves (for which 

 (ji is large) the ionic absorption is very much less with a magnetic 

 field present than without it. This means that in this case and in 

 the next the presence of a magnetic field assists in the propagation of 

 an electromagnetic wave by decreasing the absorption. This reduc- 

 tion in absorption may amount to a rather large amount, as may be 

 seen from an inspection of the formula for ^i. For example, if in 

 this case ui is 20, corresponding to 4,000 meter w'aves, we find 

 that under corresponding conditions the absorption due to electrons 

 only is reduced by the magnetic field to 1 /400th the value it 

 would have for no magnetic field. Of course, these cases are not 

 directly comparable because the path chosen by the wave would be 

 different in the two cases. It is plausible, however, that the propaga- 

 tion of long waxes along the magnetic field ma>' go on with much 

 less attenuation than propagation from Kast to West omt ,i region 

 in which the magnetic field is nearly vertical, in which case the effect 

 of the magnetic field is largely absent. This conclusion, however, 

 cannot be made in general since a number of other causes are influen- 

 tial in determining the propagation, for example, the bending of the 

 rays, so that it is not certain that transmission oN^er a region in which 

 the magnetic field is vertical is always more difficult than in the 

 other cases. 



The reason for the decreased absoriitioii of long wa\es wlien the 

 magnetic field can operate (that is, in all cases in which the electric 

 vector is not parallel to the field) is that the velocities acc|uired by 

 the free electrons are much less for small \alues of // wiien the magnetic 

 field is present. 



Fading. By this is meant a variation with time of the strength of 

 a received signal at a given point. It is clear that a wave starting 



