SEl.r.CTiri- CIRCUITS .iXD ST.iTIC ISTERFERF.NCE 275 



.line 4), (/), aiul P tlu- nu-aii power absorln-d from tlu- angrcRatc 

 ili>turl)aiu-e. r (ui) is ileliiifil by formula (21)) .iiid is the mean spec- 

 trum of (he a!ii;ren.ile dislurbaiice, lluis 



rM = 1 .V V \frM {■ = K(o>),.\. (26) 



We are now in a [wsition to discuss more precisely ilie ai)pro\ima- 

 lions, fundanu'iUal lo formulas (D) (14), 



•'0 





\Z{iw)[-" "^-""\/„ \Z(io>)-\ 



riie approximation involved in this formula consists in idenlif\ing 

 u'm, 2 ir with the "mid-frequency" of the selective circuit, and is based 

 on tile hypotiiesis tiiat over tlie range of frequencies, which includes 

 the important contribution to the integral (22), the fluctuation of 

 R (u)) may be ignored. 



Now it is evident from formulas (21) -(22) thai the theoretically 

 complete solution of the problem requires that R (oj) be specified 

 over the entire frequency range from oi = o to co = ^. Obviously, the 

 required information cannot be deduced without making some addi- 

 tional hypothesis regarding the character of the interference or the 

 mechanism in which it originates. On the other hand, the mere 

 assumption that the individual elementary disturbances <^i . . . 0j, 

 tlifTer among themselves substantially in wave form and duration, or 

 that the maxima of the corresponding spectra |/r(a)) | are distributed 

 over a considerable frequency range, is sufificient to establish the 

 conclusion that the individual fluctuations are smoothed out in the 

 aggregate and that consequently r (oi) and hence R (oj) would have 

 negligible fluctuations, or curvature with respect to oi, over any 

 limited range of frequencies comparable to a signaling range. 



It is admitted, of course, that the foregoing statements are purely 

 qualitative, as they must be in the absence of any precise information 

 regarding the wave forms of the elementary disturbances constituting 

 random interference. On the other hand, the fact that static is en- 

 countered at all frequencies without any sharp changes in its intensity 

 as the frequency is varied, and that the assumption of a systematic 

 wave form for the elementary disturbances would be physically 

 imreasonable, constitute strong inferential support of the hypothesis 

 underlying equation (27). Watt and Appleton (Proc. Roy. Soc, 

 -April 3, 1923) supply the only e.xperimental data regarding the wave 

 forms of the elemcntarj' disturbances which they found to be classifi- 

 able under general types with rather widely variable amplitudes and 



