Willard Libby and a group of chemists at the University of Chicago were responsible for the development of radiocarbon dating. He wrote two papers on the history of the subject.
History of Radiocarbon Dating, 1967 (.pdf)
Radiocarbon Dating, Memories and Hopes, 1972 (.pdf)
The first paper is more detailed. He talks about the production of Carbon-14 by cosmic rays, the neutron absorption cross section, the equilibrium concentration of C-14, and mentions the relative amounts in the oceans in the form of carbonates and dissolved, on land and in the air. His group was responsible for the development of early detectors which proved the existence of C-14 in nature. One of his students showed that elemental carbon obtained from natural sources produced about 15 decays per minute per gram of carbon. It was also shown from the characteristic decay length on passing its radiation through matter that the natural radioactive carbon behaved like that produced by atomic reactors.
The radiocarbon dates showed some variation from the known historical dates and the possibility that cosmic rays varied with time was considered. Libby mentions the increase in atmospheric C-14 due to nuclear testing does not appear to be aware of the relaxation time or the derived connection between the production rate and the equilibrium amount.
To understand the absorption of radiation by matter a 1902 paper by Rutherford and Brooks might prove useful.
Supplemental (21 Jul): In fairness to Libby I would have to say that he appeared to be working with a model involving carbon sinks. It would have been premature to discuss a work in progress prior to publication. At the time his histories were published he may not have had a good value for a relaxation rate and the subject would have gone beyond the bounds of a history of radiocarbon dating. It would seem more appropriate to treat it as a multidisciplinary study.