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Johann Becher
Becher published Physica subterranea in which he proposed the first version of what would become the phlogiston theory. Here is where the first instance of the word "Phlogiston" being used can be found. Becher takes the older theory of elements, which consisted of earth, air, water, and fire and eliminates everything but earth. He proposes three kinds of earth, one of which is identified with Phlogiston. -
Georg Stahl
Stahl elaborates on the phlogiston theory and uses it to explain the calcination of metals. Stalls version of the Phlogiston theory would be the predominant mechanism used in chemistry to explain combustion based experiments. Elaboration of the theory as proposed by Stahl can be found at https://youtu.be/DZTD-vYhwj4. -
J. H. Pott
Pott, a student of Stahl, publishes a version of the Phlogistion theory which is more approachable than that of Stahl and is used by others. -
Joseph Priestly
Priestly isolates what we now know as Oxygen in a pneumatic experiment. At the time, using the phlogiston theory, he identifies it as Dephlogisticated Air. Working under the Phlogiston theory, Priestly is credited with discovering around 20 different gases.
Further reading on Priestly and his eventual defense of the Phlogiston they're can be found at http://www.scs.illinois.edu/~mainzv/HIST/bulletin_open_access/v30-2/v30-2%20p63-69.pdf -
Antoine Lavoisier
Lavoisier proposes a new theory which opposes the Phlogiston theory, citing the increase in mass in going from metal to metal calx as evidence against the theory. Under his new theory, he labels Priestly's dephlogisticated air as "Oxygen". A VERY through discussion of the evidence Lavoisier used to argue against the Phlogiston theory can be found at https://youtu.be/HahAGmMewLU.