Difference Engine

The Difference Engine was a very early purely mechanical decimal digital computing device invented by Charles Babbage in the early 1800's, following an idea originated by Johann Helfrich von Müller in 1786. It was intended to compute mathematical tables (logarithms, etc), which at that point were computed by hand, and thus often contained errors.

The basic concept is that many mathematical functions can be expressed as polynomials (of the form C₀ + C₁X + C₂X^2 + C₃X^3 ... where C₀, etc are the coefficients). Successive values of the function are fairly easy to compute by adding differences to running totals (hence the name of the machine), with addition being the only operation needed.

There were in fact two generation of his Engines; a prototype of the first was started in the 1820's, but never finished (although it did spark considerable improvements in the manufacture of advanced mechanical components).

He then became diverted into working on the Analytical Engine - but this turned out to be not without benefit to the Difference Engines. Using what he had learned in his work on the Analytical Engine, he created a new, and better, design for a Difference Engine (the 'Difference Engine No. 2') in 1847-49; his re-design resulted in reduction of the part count from 25,000 to 8,000. It also included several mechanisms included to reduce the chance of un-detected errors; its digital nature made these easier to add.

The design included both a printer, and a mechanism for creating printing plates of the tables, the latter to reduce the scope for human error (in transcription of the results).

Alas, no actual work on it was undertaken in his lifetime. The plans were preserved, though, and as memorial tribute to Babbage on the 200th anniversary of his birth, during 1985-1991 the Science Museum in London built an actual Difference Engine, using those plans. It was finished just in time for the anniversary, and actually worked quite well (thereby lending credence to his other planned, but never finished, Engines).

Further reading

• Bruce Collier, James MacLachlan, Charles Babbage: And the Engines of Perfection, Oxford University, Oxford, 1998 - has good coverage of his machines
• Doron Swade, Charles Babbage and His Calculating Engines, Science Museum, London, 1991 - exhibition catalogue
• Doron Swade, The Difference Engine: Charles Babbage and the Quest to Build the First Computer, Viking, New York, 1991 - excellent history of the Science Museum's project to build an actual Difference Engine, includes biographical content and historical context of the original

External links

• Doron Swade, The Construction of Charles Babbage’s Difference Engine No. 2, Annals of the History of Computing, Vol. 27, No. 3, July–September 2005, pp. 70-88 - covers the technical aspects of the Engine, and the construction of the contemporary one, in some detail; also covers the details and building of the printer, not covered in his book
• Bruce Collier, The Little Engines that Could've: The Calculating Machines of Charles Babbage, Harvard University, Cambridge, 1970 - has a good description of his machines
• Allan G. Bromley, Difference and Analytical Engines; Chapter Two in William Aspray (editor), Computing Before Computers, Iowa State University Press, Ames, 1990
• Babbage Difference Engine #2
  • Doron Swade, Charles Babbage's Difference Engine No. 2 Technical Description, Science Museum Papers in the History of Technology, Number 5, September 1996 - a description of the details of the Engine, prepared as it was being constructed
    • Build - "issues of construction, assembly, and setting up that arose during the engine build"
    • Appendix: Drawings
  • Barrie Holloway and Reg Crick, Instruction Manual to Operate and Maintain Charles Babbage's 2nd Difference Engine, June 1991 - actual manual for the Science Museum Engine, prepared by the engineers who built it
• The Engines
  • Principle of the Difference Engines
• Charles Babbage's Difference Engine
• What a Difference the Difference Engine Made: From Charles Babbage’s Calculator Emerged Today’s Computer