He is remembered for his calculation of the density of the earth from Nevil Maskelyne's observations on Schiehallion.
He was assisted in the task by mathematician Charles Hutton, who devised a graphical system to represent large volumes of surveyed heights, later known as contour lines.
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As it also happened, Henry Atkinson, of Newcastle, devised a similar approximation scheme in 1809; he had consulted his fellow Geordie, Charles Hutton, another specialist and a senior colleague of Barlow at the Royal Military Academy, Woolwich, only to be advised that, while his work was publishable, it was unlikely to have much impact.