Peter Barlow (17761862) was a practitioner and teacher of applied mathematics. He taught at the Royal Military Academy, Woolwich, where engineers and artillery officers were trained between 1741 and 1939. In addition to compiling useful mathematical handbooks containing cube roots etc., he worked out the load-bearing capacities of various substances used in Woolwich Dockyard, and published his findings in 1817. These were so useful for structural engineers that he was much in demand for validating the mathematics used in many of the great Victorian construction projects such as railways and suspension bridges. He also applied his mathematical skills to optics, electricity and navigation: when ships' compasses ceased to work owing to the increasing amount of iron used in shipbuilding, he invented a device to correct them, for which he was elected a fellow of scientific academies in Russia, America, France and Belgium. This ghostly portrait of him, a lithograph on grey prepared paper, is extremely unusual in showing a profile view of the sitter: he has an intense expression, as he carries out in his head some complicated mathematical calculation. Of the artist, J.S. Hooke, nothing seems to be known.