Charles Babbage’s Difference Engines and the Science Museum

Charles Babbage (1791-1871) was an English mathematician, philosopher and polymath. A prolific inventor and political economist, he pioneered lighthouse signalling, designed a cow-catcher for the front end of railway locomotives, multi-coloured theatre lighting and ciphers. But Babbage is best known for his calculating machines, the Difference Engines and Analytical Engine, which are among the most celebrated icons in the prehistory of computing. Although never built in his lifetime, experimental pieces, engine plans and notebooks are some of the treasures of the Science Museum’s collection.  

In the early nineteenth century mathematicians, navigators, engineers, surveyors and bankers relied on printed mathematical tables to perform calculations requiring more than a few figures of accuracy. The production of tables was not only tedious but prone to error by the human computers who compiled them. Mistakes were known to occur in transcription as well as calculation, typesetting and printing. While hard to quantify, Babbage cited that these errors had lost the government £2-3 million and caused ships to run aground.  

Frustrated by numerous miscalculations within printed mathematical tables, Babbage declared in 1821 in a meeting with his friend John Herschel, “I wish to God these calculations had been executed by steam”. The task that seized Babbage and was to occupy him on and off for the rest of his life, was to design and build mechanical calculating engines to mechanise the production of tables.  

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Charles Babbage first announced the invention of the Difference Engine, his first calculating machine, in a paper read at the Royal Astronomical Society on 14 June 1822, as A note respecting the application of machinery to the calculation of astronomical tables.  

This section of Babbage’s Different Engine No. 1, with about 2,000 parts, was built by his engineer and master toolmaker Joseph Clement and completed in 1832. This ‘finished portion of the unfinished engine’ represents one-seventh of the complete design and was demonstrated by Babbage to some acclaim.  

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Unlike contemporary calculators, the Difference Engine was not designed to perform ordinary day-to-day arithmetic but to calculate a series of numerical values and automatically print the results, a milestone in the history of computing. Babbage used the principle of finite differences – used by human computers at the time when preparing mathematical tables. This involves addition and subtraction only, which were much easier to mechanise than multiplication.   

One of the finest examples of precision engineering of the time the Difference Engine consisted entirely of mechanical components — brass gear wheels, rods, ratchets, pinions, etc. Numbers were represented in the decimal system by the positions of 10-toothed metal wheels mounted in columns. The intricate shapes required special jigs and tools, and the need for hundreds of near-identical precision parts challenged an engineering culture somewhere between craft and mass production traditions. Babbage made cardboard cut-outs of parts to visualise and verify their operation and experimented incessantly with small trial mechanisms to test and simplify his ideas. 

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Work was abruptly halted in 1833 following a dispute with Clement and the engine was never built. For the British Government that had bankrolled the venture, the project was a costly failure. When the final bills were paid the Treasury had spent £17,500 - the cost of twenty-two brand new steam locomotives from Robert Stephenson's factory in 1831 - a formidable sum. 

In 1834, with the Difference Engine project stalled, Babbage conceived of a more ambitious and technically more demanding machine. The Analytical Engine was designed to perform any calculation set before it and to have even higher powers of analysis than the original Difference Engine. It is considered the first fully automatic calculating machine. 

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The concept of the engine and the detail of its design embody many features of modern electronic computers. The engine was programable using punched cards – a technique used in the Jacquard loom to control the patterns woven with thread. It had a store where numbers and intermediate results were held, and a separate mill where the arithmetic processing was performed. The separation of the store and mill is a fundamental feature of the internal organisation of modern computers. Convinced of its utility, he worked on it for the rest of his life but, despite designing several different versions, funding never materialised. 

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If built the Analytical Engine would have been the size of a small locomotive and powered by steam. This trial piece, under construction at the time of Babbage’s death in 1871, is the physical legacy of a remarkable intellectual achievement of the nineteenth century. 

Ada Lovelace (1815-1852) met Babbage at a party in June 1833 when she was seventeen and was entranced when he later demonstrated the small working section of the Difference Engine to her. They started a lifelong friendship based around their shared passion for mathematics, Babbage referred to her as the ‘Enchantress of numbers’. Lovelace played a key role in interpreting and publicising Babbage’s Analytical Engine. 

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In 1843, Lovelace published an account of the Analytical Engine in which she set out its possibilities as a mechanical general-purpose device. In her description, Lovelace speculated that the engine could be used beyond numerical calculations and, in principle, manipulate quantities other than numbers such as symbols, letters and musical notes. This conceptual leap marks the prehistory of the computer age and was not fully appreciated until the advent of electronic computing a century later. 

Between 1847 and 1849 Babbage designed a new engine, Difference Engine No. 2, which benefitted from the techniques developed for the more demanding Analytical Engine. The design was more efficient, requiring one third the number of parts of the first Difference Engine.  

Babbage made no attempt to construct the machine, but his dream came to fruition in 1991 when the Science Museum completed the first phase of the construction of Difference Engine 2, to coincide with an exhibition marking the bicentenary of his birth. This work was led by its then curator of computing, Doron Swade. The planning and construction of Difference Engine No.2 had commenced in 1985 and drew upon the surviving Babbage models and components in the museum’s collections and the museum’s Babbage archive, which contains almost the entire surviving technical material relating to his automatic calculating machines. Difference Engine No.2 was finally completed in 2002 with the addition of the printing mechanism.  Since then, it has been demonstrated to researchers, for filming and at special events. It is powered not by steam, but by turning a hand crank. Only one other Difference Engine No.2 was made by the museum and for many years it was displayed in the Computer History Museum in California.   

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The creation and display of Difference Engine No.2 helped to propel Babbage into the public consciousness, and Swade has continued to promote his importance since leaving the museum in 2002. He has also completed the user manual and documentation that explains the construction and working of Difference Engine No.2 in detail.

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By 2011 Swade had joined with others to form the Plan 28 Project, set up to build a working prototype of the Analytical Engine. The museum then digitised the archive and made it available to the Project under license. The Archive was also completely re-catalogued to ensure that the digital copies could be linked to the correct archive entry. Since then, these entries have been improved following feedback from Plan 28. A separate project, led by Royal Holloway University of London also gained licensed access to the images and built a simplified version of Difference Engine No.2, powered by steam.

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The archive catalogue remained inaccessible to the public until 2016 when it was launched on the web and later the same year it became accessible on the museum’s Collections Online portal together with over 7,700 digitised images.  This remains one of our most popular archives accessed online, despite its technical nature, which is surely a testament to the continued fascination with Babbage and his remarkable machines.  

Online Content 

• Joseph Clement: the man who built the difference engine: https://www.youtube.com/watch?v=1BgAvE6DqQk  
• Plan 28 Project Blog: https://blog.plan28.org/  
• The Royal Holloway Project: steam powered simplified DE2: https://www.youtube.com/watch?v=t8aYkow-Fv8  
• Science Museum: The Babbage Papers: https://collection.sciencemuseumgroup.org.uk/documents/aa110000003/the-babbage-papers  
• Difference Engine No.2 Technical Description
• Difference Engine No.2 User Manual

Despite the author’s and the museum’s best efforts,  we are unable to make these PDF documents fully screen reader accessible.

BOOKS AND JOURNALS 

• Swade, Doron. Charles Babbage and his calculating engines. Science Museum, 1991. 
• Swade, Doron. "Calculation and Tabulation in the 19th Century: George Biddell Airy Versus Charles Babbage." PhD. University College London, 2003. https://discovery.ucl.ac.uk/id/eprint/10102065/
• Swade, Doron. The cogwheel brain: Charles Babbage and the quest to build the first computer. Abacus, 2001. 
• Swade, Doron. "The Construction of Charles Babbage's Difference Engine No. 2." IEEE Annals of the History of Computing 27.3 (2005): 70-88. This is a peer-reviewed summary of construction of DE2 and its implications.
• Wyatt, Nicholas. Digitising Charles Babbage at the Science Museum, London: managing expectations, enabling access in Circumscribere: international journal for the history of science. Vol. 22 (2018):  https://revistas.pucsp.br/circumhc/article/view/36680