Barlow was born in Norwich. In 1806 he was appointed mathematical master in the Royal Military Academy in Woolwich, south-east London, and he filled that post for 41 years. In 1823 he was made a fellow of the Royal Society, and two years later received the Copley medal. Steam locomotion received much attention at his hands, and he sat on the railway commissions of 1836, 1839, 1842 and 1845.

His sons Peter W. Barlow and William Henry Barlow became notable civil engineers of the 19th century.

He received many distinctions from British and foreign scientific societies. Barlow’s principal works are:

*Elementary Investigation of the Theory of Numbers*(1811)*New Mathematical and Philosophical Dictionary*(1814)*Essay on Magnetic Attractions*(1820).