Inventor and industrialist. Neilson was born in Shettleston (Glasgow), the son of an engineer at the Govan Colliery. He studied at the Andersonian Institution and obtained a position in Glasgow's first Gas Works around 1814. He rose to become manager and chief engineer of the company and was able to design several improvements to the gas manufacturing process. He also invented the "swallow-tail" gas burner, which was widely used.
In 1828, Neilson invented the hot blast furnace, which was a great advance in the iron industry. His process reduced the amount of coal needed to produce iron, and greatly increased efficiency to satisfy the demands of the railway and shipbuilding industries. Neilson had to vigorously defend his patent in the courts, but was able to licence his invention and grew wealthy on the proceeds.
He died on his estate at Queenshill, near Kirkcudbright. His eldest son, Walter Montgomerie Neilson (1819-89), became a noted builder of locomotives in Glasgow.