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There is perhaps no beguilement more insidious and dangerous than an elaborate and elegant mathematical process built upon unfortified premises." - Chamberlain 1899b:224Following the discovery of radioactivity by Becquerel (1896), the possibility of using this phenomenon as a means for determining the age of uranium-bearing minerals was demonstrated by Rutherford (1906).
One year later Boltwood (1907) developed the chemical U-Pb method. By combining Von Weizsacker’s argon abundance arguments with Kohlhorster’s observation that potassium emitted gamma-radiation, Bramley (1937) presented strong evidence that potassium underwent dual decay.
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...
As one answer to his critics, Kelvin produced a completely independent estimate -- this time for the age of the Sun.Based on these assumptions he at first suggested an age of the Earth of between 100 Ma and 500 Ma.