William Small (1734-1775) was a British physician and a member of the Lunar Society.

He was born in Forfarshire, Scotland, the son of a Presbyterian minister. He attended Marischal College, Aberdeen and was awarded his M.D. in 1765. In 1758, he was appointed Professor of Natural Philosophy at William and Mary College, Virginia, then one of Britain’s American colonies.

One of his students, Thomas Jefferson, described him as "a man profound in most of the useful branches of science, with a happy talent of communication, correct and gentlemanly manners, and a large and liberal mind... from his conversation I got my first views of the expansion of science and of the system of things in which we are placed."

In 1764 he returned to Britain, with a letter of introduction to Matthew Boulton from Benjamin Franklin. He established a medical practice in Birmingham, and shared a house with Dr. John Ash.

Between 1765 and 1775, Small was Boulton's doctor and became a close friend of Erasmus Darwin, Thomas Day, James Keir, James Watt, Anna Seward and others connected with the Lunar Society.

He helped to bring the Theatre Royal to Birmingham in 1774.

William Watson Small (October 19, 1909 - January 18, 1978) was a British MP for Glasgow Scotstoun (1959-1974) and Glasgow Garscadden (1974-1978).