68 



EKDAHL AND KEELING 



where to is the angular frequency, i = \J—l,*y(oo) is the (time-invariant) 

 amplitude of the oscillation in radiocarbon source at frequency to, and *n a (to) is 

 a (time-invariant) complex factor that contains the amplitude and phase shift of 

 the atmospheric 14 C variation, *n a (t). Substituting Eqs. 8 and 9 in Eq. 7 and 

 solving for *n a ( to) yields 



-l 



n a (to) = (ico + *k e ff) *7(w) 



(10) 



Dividing Eq. 10 by the steady-state solution (see Eq. 6) 



>N 



1 



yields 



: n a (co) 



e N 



ao 



aO * k 



eff 



ICO 



keff \ 



+ *k eff ; 



'T(co) 



*r 



(ii) 



(12) 



The transfer function we identify as 



Z a (co) = (ico + *k eff ) 



-l 



(13) 



The ratio 



Z a (co) 

 Z a (0) 



Z a (co) 

 Z a (0) 



e'id = 



*k 



eff 



ico + *k e ff 



(14) 



relates, as a complex number, the fractional variations of the source to those of 

 C in the atmosphere. The attenuation at any frequencv is given by the 

 modulus 



Z a (co) 

 Z a (0) 



\/i + (co/*k eff r 



(15) 



and the shift in phase by 



0(w) 



-, / co \ 



-tan 



\*keff/ 



(16) 



If we evaluate Eqs. 15 and 16 with Grey and Damon's 5 preferred value of 100 

 years for *T e ff, the 85-year component in the observed sunspot spectrum is 

 predicted to appear in the atmosphere attenuated by a factor of 7.5 and the 

 11-year component by a factor of 57. As we will now show, these attenuations 



