[1] When geology was at its beginnings, a major problem for stratigraphers was to find a reliable method for the measurement of time.
The longer estimate came from Charles Darwin, who probably went closer to the truth because he had clear in mind that the evolution of life must have required a lot of time to take place.
[3] Today, the determination of the age of the Earth is not a primary scope of geochronometry anymore, and most efforts are rather aimed at obtaining increasingly precise radiometric datings.
[5] Other methods of radiometric dating are also available, that are based on slightly or largely different principles, but always rely on the phenomenon of radioactive decay.
The greater efforts of geochronometry today are aimed at retrieving accurate ages of major events in the Earth's history and of stage/age boundaries.