162 BELL SYSTEM TECLINICAL JOURNAL 



The condition that these add giving a field 



E = {ex + e2) sin 2Tr Ft 



is that, d\ — d-i={a. whole number) (2) 



that is, the difiference in length of the two paths must be an exact 

 whole number of wave lengths. The condition that the two waves 

 cancel each other giving a field 



E = {61 — 62) sin 2TvFt 



is that, ^1 — <i2=(a whole number)+^ (3) 



that is, the difference in length of path must be an exact odd number 

 of half wave lengths. 



Thus if the two components ei and e^ are equal, the resultant vertical 

 field E will go through values ranging from (^1+62) down to zero 

 as the path lengths change relative to each other. If the two waves 

 do not have exactly the same amplitude, the minimum value of E 

 will be something more than zero. 



Differences in attenuation of the two waves and differences in 

 their direction of arrival will modify the relative amplitudes of ex and 

 62 but will not modify the time relations required for minima of the 

 resultant field E unless we assume that at the time of a minimum 

 neither wave has an appreciable vertical component. Since the 

 consequences of such an assumption do not accord with our experi- 

 mental data we have considered that it may be left out of account 

 in the present discussion. 



This is obviously a picture which fits in very well with the simple 

 single frequency fading records. The major maxima and minima 

 occur when the conditions of equations (2) and (3) are met and ei 

 and 62, are nearly equal. On the other hand it seems doubtful that 

 the picture can be so simple. If we suppose two wave paths w^hy 

 not three or more? Additional paths would add irregularities to 

 the fading and it would not be necessary to assume as great a degree 

 of irregularity in the changes in any one path. But with an increasing 

 number of paths the various arriving waves would tend to average 

 to a more or less constant mean value and large departures from 

 this mean would become rare. The fact that the fading signal con- 

 tinually covers a large range of amplitude, with the maximum many 

 times the minimum, definitely points toward there being but a very 

 small number of major paths, probably not more than two. 



Considering now the question of selective fading in relation to 

 wave interference we refer back to equation (2). 



