Difference engine

A mechanical calculator that generates polynomial-function tables through repeated addition of finite differences. Charles Babbage’s designs are its best-known examples.

Finite difference: A difference between values of a function sampled at regularly spaced inputs. The engine advances a table by repeatedly adding stored finite differences.
Charles Babbage: An English mathematician and inventor who designed the difference engine and analytical engine. Babbage conceived the machine and developed successive designs for it.
Difference Engine No. 1: Babbage’s first large difference-engine design, intended to calculate and print mathematical tables. It was the ambitious original project that established the machine’s historical identity.
Analytical Engine: Babbage’s proposed general-purpose mechanical computer, designed to follow instructions using a store and a mill. Unlike the difference engine, it was intended to perform varied operations under program control.
Method of finite differences: A computational method that uses differences between successive function values to build polynomial tables. This method turns polynomial evaluation into a sequence of additions suited to gears.
Gaspard de Prony: A French engineer who organized large-scale mathematical table production during the French Revolution. His labor-saving approach to table making helped inspire Babbage’s calculating-machine project.
Science Museum Difference Engine No. 2: A working reconstruction of Babbage’s Difference Engine No. 2, completed by the Science Museum in 2002. Its operation demonstrates that Babbage’s later design can be built and used.
Jacquard machine: A loom that uses punched cards to control the patterns woven into fabric. Its punched-card control inspired a programming idea used in Babbage’s later designs, not the difference engine.
Decimal arithmetic: A positional number system in which each digit represents a power of ten. Babbage’s wheels represented decimal digits and carried values between columns.
Mathematical table: A reference listing numerical values of mathematical functions for specified inputs. The engine was intended to automate the production of printed tables.

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