ATMOSPHERIC CARBON DIOXIDE AND RADIOCARBON: I 85 



Finally, since the perturbation in each reservoir grows in sympathy with the 

 source after lapse times long enough that a calculation using Z(r) is valid, a direct 

 method of extracting the partitioning in all reservoirs is to substitute 



nj(t) = Zj(r)e rt (B.8) 



directly into the B.l equations, cancel out the common factor of e rt in each 

 equation, and then solve simultaneously the resulting algebraic linear equations 

 for the various Z;(r). This method is algebraically equivalent to the harmonic 

 analysis used to form the *Zj(co) and indeed employs the same fundamentally 

 more general Fourier or Laplace transforms of the n; and *n;, as discussed by 

 Keeling. 28 



Our present method of analyzing reservoir models has the simplicity that the 

 roots of the determinantal equations D(U) = need not be found explicitly. It 

 must be known, however, that they are all real positive numbers (one may be 

 zero) before the transfer functions can be proved to lead to stable results over 

 long time periods. This has been verified for all cases presented in this paper. 





