William Austin (1754–1793) was a physician and mathematician of extensive practice and the author of "A treatise on the stone", a Goulstonian Lecture .
After receiving a classical education at the local grammar school he was admitted, in 1773, a commoner of Wadham College, Oxford.
After giving some lectures on Arabic, Austin in 1779 came to London and began his medical studies at St. Bartholomew's Hospital.
In the same year, and after he had begun to practice as a physician at Oxford, he lectured on mathematics during the absence of John Smith, the Savilian Professor of Geometry.
The Goulstonian Lectures are printed as A Treatise on the Origin and Component Parts of the Stone in the Urinary Bladder (London, 1791).
Their erroneous result is "that the stone is formed generally in very small part, and often in no degree whatever, from the urine as secreted by the kidneys, but chiefly from the mucus produced from the sides of the different cavities through which the urine passes"; and this led the author to a melancholy conclusion as to a common form of the affection: The imperfect chemistry of his time was sufficient to lead Austin to one accurate conclusion, the variety of composition of hard concretions found throughout the body; and he also points out correctly that the hard matter found in the arteries of old people is calcareous, while the white substance covering the surface of gouty joints is not so.
[1] His last remark as to lithotomy led his surgical colleague, James Earle, to write a defence of the operation, in which he states that Austin afterwards modified his gloomy views as to the treatment of stone.