Canton was born in Middle Street Stroud, Gloucestershire, the son of a weaver John Canton (B.1687) and Esther (nee Davis.) At the age of nineteen, under the auspices of Dr Henry Miles, he was articled for five years as clerk to Samuel Watkins, the master of a school in Spital Square, London, with whom at the end of that time he entered into partnership. In 1750 he read a paper before the Royal Society on a method of making artificial magnets, which procured him election as a fellow of the society and the award of the Copley Medal. He was the first in England to verify Benjamin Franklin's hypothesis of the identity of lightning and electricity, and he made several important electrical discoveries.

In 1762 and 1764 he published experiments in refutation of the decision of the Florentine Academy, at that time generally accepted, that water is incompressible; and in 1768 he described the preparation, by calcining oyster-shell with sulphur, of the phosphorescent material known as Canton's phosphorus. His investigations were carried on without any intermission of his work as a schoolmaster. He died in London aged 53 of Dropsy.

He was the recipient of letters from Thomas Bayes which were then published by the Royal Society.

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