I'.i.iiC'iRic c/Rccrr iiir.ouv 371 



symbol, so dial (295) is entirely real. (\)rrespoiKlint;Iy the xariahlc 

 resistance will be taken as 



r{t) = ^{e'^^' + e '"') 



= y(,iM (j.^.,-^1 p^^rt) (296) 



= r cos wt. 



Here r is taken as a pure real quantity, which fixes the size of the re- 

 sistance variation. No loss of generality is involved in this, since it 

 merely involves referring the time scale to the zero of the resistance 

 variation. 



The symbolic impedance Z, as employed in the theory of alter- 

 nating currents, will depend on the frequency and is, in general, a 

 complex quantity. Its value at frequency 9,/2ir will be denoted by 



Z{ii1)=Zo 



while its value at frequency {il,-\-noci)/2T will be written as 



Z(i(fi + l?a;))=Z„. 



We now assume a series solution of (293) of the form 



/ = /o + /i + /2+ . . . 



where the terms of the series are defined by the symbolic equations 



J- I— —y- i-0. 



J _ 'V/ J 



Jh + I — ~ —ry- In 



(297) 

 r{t) 

 Z 



Substitution shows that this series formally satisfies the equation. 



Starting with the first of (297) and substituting (295) and (296) 

 we get 



h---^ (e'-'-'+e-'-'-O (/oe'^^'+/oe-'"0 



^ I J„g'("+"^' + 7„e-'«^+^)' + /o(''^"-"'' + Joe-'(«-'^)' I , (298) 



4Z ^ 



or 



A=- ' /o \ ^- + S \' (299) 



In (299) it is to be understood that the real part is alone to be retained. 



