A Difference Engine is an automatic, mechanical calculator designed to tabulate polynomial functions. Both logarithmic and trigonometric functions can be approximated by polynomials, so a difference engine can compute many useful sets of numbers.
J. H. Müller, an engineer in the Hessian army conceived the idea in a book published in 1786, but failed to find funding to progress this further.
In 1822, Charles Babbage proposed the use of such a machine in a paper to the Royal Astronomical Society on 14 June entitled “Note on the application of machinery to the computation of astronomical and mathematical tables”. This machine used the decimal number system and was powered by cranking a handle. The British government initially financed the project, but withdrew funding when it became apparent that the machine would cost much more than originally anticipated. Babbage went on to design his much more general analytical engine but later produced an improved difference engine design (his “Difference Engine No. 2”) between 1847 and 1849. Inspired by Babbage’s difference engine plans, Per Georg Scheutz built several Difference Engines from 1855 onwards; one was sold to the British government in 1859. Martin Wiberg improved Scheutz’s construction but used his device only for producing and publishing printed logarithmic tables.
Based on Babbage’s original plans, the London Science Museum constructed a working Difference Engine No. 2 from 1989 to 1991, under Doron Swade, the then Curator of Computing. This was to celebrate the 200th anniversary of Babbage’s birth. In 2000, the printer which Babbage originally designed for the difference engine was also completed. The conversion of the original design drawings into drawings suitable for engineering manufacturers’ use revealed some minor errors in Babbage’s design, which had to be corrected. Once completed, both the engine and its printer worked flawlessly, and still do. The difference engine and printer were constructed to tolerances achievable with 19th century technology, resolving a long-standing debate whether Babbage’s design would actually have worked. (One of the reasons formerly advanced for the non-completion of Babbage’s engines had been that engineering methods were insufficiently developed in the Victorian era.)
Although the “printer” is here referred to as such, its primary purpose is to produce stereotype plates for use in printing presses; Babbage’s intention being that the Engine’s results be conveyed directly to mass printing, rather than through a fallible human typesetter. The printer’s paper output is mainly a means of checking the Engine’s performance.