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Potassium - Argon and Argon - Argon dating are based on the current understanding that radioactive Potassium-40 decays to the stable form, Argon-40 with a half-life of approximately 1.25 billion years.
There are some circumstances that can affect this rate such as magnetic fluctuations etc...
Based on these assumptions he at first suggested an age of the Earth of between 100 Ma and 500 Ma.
Most sedimentary rocks such as sandstone, limestone, and shale (which do contain fossils) are related to the radiometric time scale by bracketing them within time zones that are determined by dating appropriately selected igneous rocks in lava flows, or weathered from lava flows.
These two independent and agreeing dating methods for of the age of two primary members of the solar system formed a strong case for the correctness of his answer within the scientific community.
This just goes to show that just because independent estimates of age seem to agree with each other doesn't mean that they're correct - despite the fact that this particular argument is the very same one used to support the validity of radiometric dating today.
Later, after radioactivity had been proven to be a significant source of the Earth's internal heat, he did privately admit that he might have been in error.
What is especially telling about this whole story is the conclusion of the absolute truth of the conclusion based on premises that are weak, or at least not adequately demonstrated.