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Babbage's Difference Engine No. 1 is Designed to Calculate and Typeset Mathematical Tables

Babbage engraved portrait
Creative Commons LicenseJeremy Norman Collection of Images - Creative Commons

About 1820 mathematician Charles Babbage started building a model of his first Difference Engine, a special-purpose machine that linked adding and subtracting mechanisms to one another to calculate the values of more complex mathematical functions. Frustrated by “the intolerable labour and fatiguing monotony of a continued repetition of similar arithmetical calculations”, Babbage came up with the plan of designing a machine capable of performing various mathematical functions. The immediate purpose of the machine was to improve the accuracy of printed mathematical tables—especially the Nautical Almanac. These printed tables were the most widely used calculating devices of the time.

By 1822 Babbage had constructed a model of his Difference Engine No. 1, a special-purpose calculating machine far more complex than any that had previously been conceived, designed to compute mathematical tables by the method of finite differences and to print the results. In the design of his machine Babbage was influenced by the division of labor employed in the celebrated manuscript tables of de Prony, which Babbage had seen in 1819. The division of labor, both physical and mental, became central themes of Babbage’s economic thought later developed in his Economy of Machinery and Manufactures.

Babbage was convinced of the “great utility” of his machine, but knew that constructing a larger version would entail “very considerable expense,” and would also leave him no time to pursue his studies in pure mathematics. On July 3, 1822, as a means of testing the waters, Babbage wrote an open letter to Sir Humphry Davy, president of the Royal Society, in which he presented a detailed description of his Difference Engine. He had his letter published as a pamphlet, and sent it to people he deemed influential:

A Letter to Sir Humphry Davy, Bart. . . . on the Application of Machinery to the Purpose of Calculating and Printing Mathematical Tables (London, 1822).

This was Babbage's first public statement of his plans for his calculating engine, and his first publication on his project for developing calculating engines, on which he would devote most of his creative energy for the remainder of his life. A copy of the pamphlet reached the Lords of the Treasury, who referred it back to the Royal Society on April 1, 1823, with a letter requesting the Society’s opinion of Babbage’s machine. One month later, on May 1, the Royal Society responded to the Treasury as follows:

"That it appears to the Committee, that Mr. Babbage has displayed great talents and ingenuity in the construction of his machine for computation, which the Committee think fully adequate to the attainment of the objects proposed by the Inventor, and that they consider Mr. Babbage as highly deserving of public encouragement in the prosecution of his arduous undertaking" (Great Britain. Parliament. House of Commons. Sessional Papers [1823], p. 6).

This favorable report gained Babbage his first national funding of £1000 toward his construction of the Difference Engine. The project tested the limits of precision obtainable by machine tool makers at the time; it also ended up being far more costly than expected, claiming £17,000 of the government’s money over the next decade before foundering in 1833, largely due to contractual disputes between Babbage and Joseph Clement, the engineer hired to construct Babbage’s machine. By this time Babbage had begun to turn his attention to the Analytical Engine, a far more complex and powerful calculating machine whose design would occupy Babbage for most of the rest of his scientific career.

Remarkably the printing feature of Babbage's Difference Engine No. 1 became known to printers through Thomas Hansard's Typographia, an Historical Sketch of the Origin and Progress of the Art of Printing (1825). In January 2015 when I was reading what Hansard had to say about the highly advanced typesetting and printing inventions of William Church, about which Hansard was incredulous, I came across these remarks of Hansard on p. 689-90:

"But surely this [Church's inventions], wonderful as it may seem, is far exceeded by the proposed application of machinery to the work of the head as well as of the hands?—See what follows!


"Charles Babbage, Esq. F.R.S., London and Edinburgh &c. in a letter addressed to Sir Humphry Davy, president of the Royal Society of London, has announced to the world, that he has invented various machines, by which some of the most complicated processes of arithmetical calculation may be performed with certainty and dispatch; and in order to avoid the errors which might be produced in copying and printing the numbers in the common way, the ingenious inventor states, that he has contrived means by which the machines shall take, from several boxes containing type, the numbers which they calculate, and place them side by side; thus becoming at once a substitute for the computer [i.e. a human computer] and the compositor.

 "The scheme of Mr. Babbage is, however, much more within the scope of probability than that of Dr. Church. He does not go to the casting-type process— his authorship and composing go no further than the ten figures— and his object is, to effect accuracy where it is of great consequence, so that it may, perhaps be of general benefit."

Hook & Norman, Origins of Cyberspace (2002) No. 29. 


Timeline Themes

Related Entries

Nautical Almanac:

Economy of Machinery and Manufactures:

Analytical Engine:

William Church: