Harvey was based in Plymouth, where he tutored William Yolland in mathematics. Later he became a lecturer in mathematics at the Royal Military Academy, Woolwich. Around 1826 his name was mentioned in correspondence about a professorial post at the University of Virginia, between Francis Walker Gilmer and Peter Barlow.
The chair went in the end to Charles Bonnycastle.
Harvey became a Fellow of the Royal Society of Edinburgh in 1824. Next year he became Fellow of the Royal Society of London.
He was a Fellow also of the Astronomical Society, Geological Society and Linnaean Society.