Swedish chemist Torbern Bergman's 1775 listing of the symbols for phlogiston and the matter of heat, categorized as two types of "earths", of which he listed 15 types, as contrasted with the acids (25), alkalis (3), and metallic calces (16). [3]

In chemistry, phlogiston, symbol ϕ (phi), from Greek, meaning "to enflame" (Leicester, 1951) or "fire of earth" (Woodcock, 2005), was a hypothetical substance supposed to be common to all combustible bodies and metals, which escaped during combustion or calcinations, but could be transferred to one body to another, and restored to the metallic calces by heating with substances rich in phlogiston (charcoal, oil, etc.); metal, for example, was produced by the following reaction: [1]

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Overview
In 1669, Johann Becher proposed the terra pinguis theory of heat.

In 1703, German chemist Georg Stahl, Becher's student, proposed the phlogiston theory.

Phlogiston theory was a precursor to French chemist Antoine Lavoisier 1787 caloric theory; which in turn was a precursor to German physicist Rudolf Clausius' entropy theory.

On a modification of Becher’s three earths theory, terra pinguis was renamed as phlogiston, from the Ancient Greek phlogios for ‘fiery’, which was said to be the “matter and principle of fire, and not fire itself” that escapes from burning bodies with a rapid whirling motion, and is contained in all combustible bodies and also in metals, which can be burnt to “calces”.

Calx is a residual substance, sometimes in the form of a fine powder, that is left when a metal or mineral combusts or is calcinated due to heat. Calx, especially of a metal, is now properly defined as an ‘oxide’, i.e. a chemical compound containing an oxygen atom and other elements. In the phlogiston theory, the calx was the true elemental substance, having lost its phlogiston in the process of combustion. The phlogiston was said to have the property that it could be restored to the original substance by supplying a replacement phlogiston from any material containing it, such as oil, wax, charcoal, or soot, which was thought to be nearly pure phlogiston.

Phlogiston was thought of as a material entity, sometimes considered as the matter of fire, sometimes as a dry earthy substance (soot), sometimes as a fatty principle, such as in sulphur, oils, fats, and resins, and sometimes as invisible particles emitted by a burning candle; contained in animal, vegetable, and mineral bodies. It could be transferred from one body to another. [2]

References
1. (a) Partington, James R. (1937). A Short History of Chemistry (The Phlogistic Period, pgs. 148-50). Dover.
(b) Woodcock, Leslie V. (2005). “Phlogiston Theory and Chemical Revolutions” (Ѻ), Bulletin of the History of Chemistry, 30(2):63-69.
(c) Leicester, Henry M. and Klickstein, Herbert S. (1951). A Source Book in Chemistry, 1400-1900 (§:Johann Joachim Becher, pgs. 55-58). Harvard University Press.
2. Thims, Libb. (2007). Human Chemistry (Volume Two) (phlogiston, pgs. 426-28), (preview), (Google books). Morrisville, NC: LuLu.
3. Bergman, Torbern. (1775). A Dissertation on Elective Attractions. London: Frank Cass & Co.

Further reading
● Higgins, William. (1789). A Comparative View of Phlogistic and Antiphlogistic Theories. J. Murray.