ATMOSPHERIC CARBON DIOXIDE AND RADIOCARBON: II 



123 



It is convenient to eliminate the *Nj via the identities 



R io 



C N 



10 



N i0 



(B.3) 



The preindustrial 14 C equations determine only ratios of the Rj 's. For the 

 six-reservoir model there are thus five independent equations: 



R u o = Rio + 



S X 



k ulN u o 



(RboNbo +R e oN e0 +R10N 



lo 



R 



a ab 



RlO 



bo %a 1 +(*XN bo /a b aFbo) 



+ RmoN m0 +RdoN do ) (B.4) 



(B.5) 



R 



eO 



g a b Rjo 



a ba 1 + (*XN e0 /aba F eo) 



R-mo ~ a am R lo 



^ma + 1 



'A 



am 



/ N mo + ]^do Odmkdm\ "1 

 \N a0 N a0 *X+k dm /J 



(B.6) 



(B.7) 



R _ R a dmkdm 



K do - K m0 



'mo * 



X + k d 



m 



where 



(B.8) 



, N m0 /W m 

 a dm-amg N d0 /W d (1 a mg) 



(B.9) 



In Eqs. B.7 and B.8, we have made the approximation R m o = Rmo- After 

 each equation has been divided by Ri , the relative ratios R; /Rio can be 

 evaluated in the following order: B.5, B.6, B.7, B.8, and then B.4. 



APPENDIX C: PERTURBATION EQUATIONS 



For numerical calculations, the equations of Appendix A are replaced by 

 perturbation equations in terms of changes from the preindustrial state 



nj = Nj -N i0 



(C.l) 



*n; = *Ni - *N i( 



(C.2) 



