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Now, the fuller that barrel gets the more water is going to leak out the thoroughly perforated sides, just as more carbon-14 will decay if you have more of it around.
Finally, when the water reaches a certain level in the barrel, the amount of water going into the barrel is equal to the amount leaking out the perforated sides.
That is, we can use carbon-14 dating on a given tree-ring (the 8000-year sequence having been assembled from the overlapping tree-ring patterns of living and dead trees) and compare the resulting age with the tree-ring date.
A study of the deviations from the accurate tree-ring dating sequence shows that the earth's magnetic field has an important effect on carbon-14 production.
That is, the equilibrium point should have long since been reached given the present rate of carbon-14 production and the old age of the earth.