I know a joke isn’t funny after you explain it, but at least after reading this you might find phlogiston humorous (and also, I just made a pun).
Phlogiston isn’t real, but Early Modern scientists thought it was. They used it as a way to explain the ash or calx (for metals) residue after something burns. As the German scientist Johann Becher wrote in 1669, all materials were made of one of three types of earth elements — terra lapidea (stony earth), terra fluida (liquid earth), or terra pinguis (oily earth). Terra pinguis, eventually called “phlogiston,” made things combustible. When flames came out of an object, it was a sign that the phlogiston was leaving it. The residue ash or calx is much less dense, which scientists thought was a sign that the phlogiston had left it.
Not until the 18th-century Frenchman Antoine Lavoisier (later executed by political extremists in the Revolution’s Reign of Terror) ran rigorous experiments was phlogiston formally disproved — he showed that the burned substances actually *gained* weight (this was oxygen) in the process of combustion.
Thus, the woman being burned as a witch in this cartoon did not perish because her phlogiston was taken away.
Sources: @ Royal Society of Chemistry, Education in Chemistry, “The logic of phlogiston,” Mike Tingle, 6 Jan 2014