Boundary values are estimated for the long-term rate of exchange of carbon dioxide between the atmosphere and the ocean, based on the analyses of the experimentally determined shapes of 'wiggles' in the atmospheric 14C/12C ratios, for which accurate tree ring data are available for the past 8 millenia. It is shown that the high frequency wiggles (characteristic period of about 200 years) can be explained as entirely due to temporal variations in the global production rate of 14C (estimated maximum range: ¿25%) arising from solar modulation of galactic cosmic ray flux provided the mean residence time of carbon dioxide in the atmosphere lies in the range (3--25) years. These calculations are based on a four-box model for the carbon cycle, with a wide range of parameters for the mixed layer of the ocean to simulate the carbon dioxide exchange.