Francis Bashforth (8 January 1819, in Thurnscoe, Yorkshire – 12 February 1912, in Woodhall Spa, Lincolnshire) was a British applied mathematician who studied ballistics.
Bashforth studied mathematics at the University of Cambridge, where he was Second Wrangler (second highest-scoring candidate) in the 1843 Tripos examination. Later he was a fellow at St. John's College, Cambridge. He was ordained in the Anglican Church. From 1857 until 1892, he was the school rector at Minting in Lincolnshire.
Between 1864 and 1880 he undertook some systematic ballistics experiments that studied the resistance of air. He invented a ballistic chronograph. He received an award from the British government in the amount of 2000 pounds. At times, he was also a professor of mathematics at the Royal Military Academy, Woolwich.
He also studied liquid drops and surface tension.
The Adams–Bashforth method (a numerical integration method) is named after John Couch Adams (who was the 1847 Senior Wrangler) and Bashforth. They used the method to study drop formation in 1883.
Bashforth, Francis (1866), Description of a Chronograph adapted for measuring the varying velocity of a body in motion through the air and for other purposes, London: Bell and Daldy
Bashforth, Francis (1873), A mathematical treatise on the motion of Projectiles founded chiefly on the results of experiments made with the author's chronograph, London: Asher and Company
Bashforth, Francis; Adams, John Couch (1883), An attempt to test the theories of capillary action by comparing the theoretical and measured forms of drops of fluid, with an explanation of the method of integration employed in constructing the tables which give the theoretical forms of such drops, University Press
Bashforth, Francis (1890), Revised account of the experiments made with the Bashforth Chronograph, to find the resistance of the air to the motion of projectiles, with the application of the results to the calculation of trajectories according to J. Bernoulli's method, Cambridge University Press
Bashforth, Francis (1895), Supplement to a revised account of the experiments made with the Bashforth ..., Cambridge: University Press
Bashforth, Francis (1903), A Historical Sketch of the Experimental Determination of the Resistance of the Air to the Motion of Projectiles, Cambridge University Press
Bashforth, Francis (1907), Ballistic experiments from 1864 to 1880, Cambridge University Press
