Charles Babbage proposes the difference engine

Background. A difference engine is an automatic mechanical calculator designed to tabulate polynomial functions. The name derives from the method of finite differences, which interpolates functions using polynomial coefficients. Babbage began constructing a small prototype in c. 1819, completing it by 1822. This device could compute useful tables for engineering, science, and navigation by approximating logarithmic and trigonometric functions.

Proposal and Announcement. Babbage formulated his idea for mechanical computation in 1821 or 1822. He announced his invention on 14 June 1822 in a paper to the Royal Astronomical Society. The paper, titled "Note on the application of machinery to the computation of astronomical and mathematical tables," outlined the engine's purpose. Babbage had previously founded the Royal Astronomical Society in 1820.

Government Sponsorship. The British government became interested in the project because producing tables was time-consuming and expensive. In 1823, the government granted Babbage £1700 to start work. Joseph Clement was brought in to implement the design. However, the project faced difficulties, and by 1842, the government abandoned it after Babbage had spent over £17,000 without achieving a working engine.