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The barrel represents the earth's atmosphere in which the carbon-14 accumulates.
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.Figure 19.5, curve C, shows the dipole field strength calculated from measurements of magnetism of lava flows and of artifacts such as pottery and bricks, whose age can be determined.The curve is roughly fitted to mean values determined about every 500 to 1,000 years...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.We stick the garden hose in and turn it on full blast.
The water coming out of the hose is analogous to the continuous production of carbon-14 atoms in the upper atmosphere.
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.
The next step in Henry Morris' argument was to show that the water level in our barrel analogy was not in equilibrium, that considerably more water was coming in than leaking out.
To that end, he quoted some authorities, including Richard Lingenfelter.
Having accomplished that, Morris concluded that the barrel was still in the process of being filled up and that, given the present rate of water coming in and leaking out, the filling process began only 10,000 years ago.
This nullifies the carbon-14 method as well as demonstrating that the earth is less than 10,000 years old. One suspects that the scientific world would not be using the carbon-14 method if it were so obviously flawed.