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Charles Babbage’s Calculating Machines

Charles Babbage’s Calculating Machines

Charles Babbage was a pioneer of computer engineering and one of the earliest exponents of science as a career path. Born in 1791, Babbage attended Trinity College at Cambridge University, where he was one of the founders of the Cambridge Analytical Society. Babbage was acquainted and worked closely with many of the most prominent mathematicians of his day and took part in seminal discoveries in the fields of engineering, mathematics, and astronomy. After graduation, he went on to work as an industrialist and lecturer, though he devoted most of his time to scientific study. He was elected as a member of England’s most prestigious scientific organization, the Royal Society, in 1816 and was one of the founders of the Royal Astronomical Society in 1820.

In an effort to address the inaccuracy of mathematical calculations due to human error, Babbage began working on a way to mechanically process mathematical functions. In 1822, Babbage received funding from the Royal Astronomical Society to begin constructing a difference engine, a machine intended to aid in the construction of astronomical and mathematical tables. He was awarded the Gold Medal of the Royal Astronomical Society in 1824 for his design.

Babbage began work on the difference engine in 1825 but the deaths of his wife, father, and son in 1827 postponed his progress. After a sabbatical, Babbage had difficulty securing additional funding to complete the project. Economic concerns and disagreements with his engineering staff eventually brought progress to a standstill. The Astronomical Society abandoned the project in 1842, due primarily to political disagreements between Babbage and opponents who argued that the machine would offer no practical benefit.

While he struggled to complete the difference engine, Babbage also began designing his analytical engine, a similar machine with expanded capability to handle any equation, whereas the difference engine could only calculate polynomial equations. The analytical engine is often considered the first computer design ever produced. Babbage envisioned the machine using punch cards to transfer information between the “mill,” where calculations take place, and the “store,” where information waits to be processed. Babbage produced thousands of sketches and detailed plans for constructing the machine, which would have been fifteen feet tall and more than six feet in diameter. In the 1840s, a series of papers were published on the analytical engine as imagined by Babbage. Mathematical prodigy Augusta Ada King, Countess of Lovelace, collaborated with Babbage to write operations for the analytical engine. Their correspondence and projects are considered the first technical descriptions of computer programming.

Babbage never fully realized his calculating mac-hines, but a reproduction of the difference engine was constructed in the early 1990s, using Babbage’s original plans and specifications. The machine functioned as Babbage envisioned, thus confirming the depth of his engineering vision. Babbage also published widely in support of state and government funding for science and argued that science should be considered a career rather than a pastime for the educated elite. In this way, Babbage and likeminded associates helped to establish the modern function of science in society and its primacy in fostering societal development.


Great Lives from History: Scientists and Science

Charles Babbage

by John Pearson

English mathematician and inventor

Charles Babbage is best remembered for developing an early steam-driven mechanical calculator known as the difference engine, as well as for a later design similar to the modern programmable computer that he called the analytical engine. Although neither device directly influenced eventual electronic computer designs, Babbage is often called the “father of computing.”

Born: December 26, 1791; London, England

Died: October 18, 1871; London, England

Primary field: Mathematics

Specialties: Algebra; geometry; logic

Early Life

Charles Babbage was born on December 26, 1791, in London, England. He was one of four siblings, two of whom died in infancy. His parents were Benjamin Babbage and Elizabeth Plumleigh Teape; his father worked as a banker. The family moved from London to Teignmouth, Devon, in 1808. Charles’s grandfather had been the mayor of nearby Totnes, Devon.

Babbage received a good education, beginning with a private church school in Alphington. He attended secondary school at Totnes Grammar School and at another religious academy for boys in Middlesex, where he began to study mathematics. Babbage entered Trinity College at the University of Cambridge in 1810. He often studied independently, and as a result, his mathematical ability became more advanced than his course work. He spent much of his time in college discussing mathematics with fellow students John Herschel and George Peacock. He read the works of other contemporary mathematicians in the Cambridge library.

In the early nineteenth century, England was mathematically isolated from continental Europe, with most instruction largely following the geometric methods advanced by Cambridge professor Sir Isaac Newton nearly a century earlier. In the interim, using notation pioneered by German mathematician Gottfried Leibniz, mathematicians such as France’s Sylvestre Lacroix (born 1765) had further advanced Newton’s work in differential and integral calculus.

In 1812, Babbage, Herschel, and Peacock formed a collegiate math group named the Analytical Society. Inspired by the writings of Cambridge professor Robert Woodhouse, the group called for the adoption of “continental analysis” and differential notation. Babbage received his bachelor’s degree in 1814. That same year, he married Georgiana Whitmore in Teignmouth, Devon. The couple would have eight children, only three of whom would survive to adulthood.

The Analytical Society’s first substantial effort was an 1816 translation of Lacroix’s An Elementary Treatise on the Differential and Integral Calculus, originally published as Traité de calcul differéntiel et du calcul intégral (1797–98). Recognition of this effort earned Babbage acceptance into the Royal Society of London. This well-regarded science association had the official sanction of the English monarchy and could sway funding toward members’ experiments. In 1820, Babbage also became a member of the Royal Society of Edinburgh and cofounded the Royal Astronomical Society.

The Analytical Society’s efforts to encourage continental notation were instrumental in eventually reuniting English mathematicians, principally those at Cambridge, with broader European natural sciences efforts, as led by French and German mathematicians. The society published an original work of examples of differential and integral calculus in 1820.

Life’s Work

After earning his master’s degree from Cambridge in 1817, Babbage went to France with Herschel to meet with various continental mathematicians. He was influenced during his trip by the work of Gaspard Riche de Prony (born 1755), consisting of logarithmic and trigonometric tables of calculations of the numbers 1 through 200,000. This work was completed over the course of a decade, entirely by hand, using more than sixty untrained workers doing simple math (the method of differences), with skilled mathematicians combining the results to render increasingly complex calculations.

During this time, the Industrial Revolution was accelerating in England. Early eighteenth-century advances in steelmaking were combined with steam-powered engines to create new machines for industrial processes, particularly to replace human labor in the textile industry.

Around 1819, Babbage proposed using a machine to calculate differences in order to accurately and efficiently produce de Prony–style logarithmic tables. Over the course of about three years, he worked with toolmaker and draftsman Joseph Clement to build a small example of what he called a difference engine. This scaled-down model still contained about two thousand parts. It was formally demonstrated to the Astronomical Society in 1822.

The machine could produce the result of a relatively simple equation in about five seconds. The Astronomical Society gave Babbage an award for his invention in 1823, and, more importantly, the Royal Society successfully called for government funding of his work. A public interest also emerged in creating accurate numeric tables for cartography and ocean navigation.

Babbage’s full-scale design, capable of replicating any of the calculations in de Prony’s tables, would require as many as twenty-five thousand parts. It would be about eight feet high and seven feet long. Steam driven and made of hand-machined brass, steel, and pewter, it would weigh more than fifteen tons. Unfortunately for both Babbage and the British government, his design required a multitude of duplicate parts, the mass production of which was not feasible at the time. The expenditure of £17,500 over ten years, a huge sum at the time, led to growing political controversy. The project was halted in 1834 following an unresolved dispute between Babbage and Clement. By that time, it is estimated, Babbage had contributed £6,000 of his own money to the failed project.

Undeterred, Babbage produced plans for an even more elaborate device he called the analytical engine. His design is strikingly similar to the modern electronic computer. It divides computation between a “store” for holding results and a “mill” for computation, analogous to a hard drive or other storage and a processor. It is meant to be programmed by using punch cards, already in use at that time for various industrial machines, and calls for separate input and output sections. Unlike the difference engine, it is doubtful that the analytical engine could work as conceived, even with modern manufacturing techniques. In particular, it may not properly allow for heat buildup or possible data corruption during data transition.

In 1826, in an effort to raise additional private funds, Babbage published A Comparative View of the Various Institutions for the Assurance of Lives, a compendium of actuarial tables for use in insurance calculations. his other publications was Reflections on the Decline of Science in England (1830), which laments the lack of emphasis on the sciences in England at the time. This work encouraged the founding of the British Association for the Advancement of Science in 1831. His On the Economy of Machinery and Manufactures, published in 1832, discusses manufacturing practices and helped lay the foundations for operations research and management science. One of his findings was that a fixed-price postage stamp would be more efficient than charging by distance mailed and would generate more income. This led to the widespread adoption of uniform postal rates.

Babbage’s efforts outside the realm of mathematics include an unsuccessful run for office to represent the borough of Finsbury in 1832. He also wrote the ballet Alethes and Iris, primarily to demonstrate new designs for stage lighting, although the work was not performed due to fear of fire from the bright lights.

In 1837, Babbage published The Ninth Bridgewater Treatise. The title refers to the eight chapters of the Bridgewater Treatises, an 1833 compendium of Victorian natural theology. Babbage’s ninth chapter reconciles Christianity and the origin of the species with his ideas of machine logic, explaining such miracles as new species as the natural result of God’s complex programming.

As the railroad expanded in England in the 1830s, Babbage argued for wide-gauge track, which later became standard railroad gauge, and in 1838 he developed a “cow catcher,” or pilot, that was placed on the front of steam locomotives to help clear the track. In 1834, Babbage helped found the Royal Statistical Society. An avid cryptographer, he broke several “indecipherable” ciphers of the time.

In the late 1840s, Babbage redesigned the difference engine using refinements conceived during his work on the analytical engine. This model was much more efficient, calling for only about four thousand parts and weighing less than three tons. He complemented it with a printer design that included variable column and row width and automatic line wrapping. Babbage was denied public funding for this new design. However, Swedish inventor George Scheutz managed to construct a simple difference engine in 1843 and then a full-scale version in 1853. This first machine was seldom used, but a second version procured by the British government saw extensive use.

Impact

In 1828, Babbage was awarded the Lucasian Chair of Mathematics at Cambridge University, a prestigious post once held by Sir Isaac Newton. However, Babbage was so engrossed with the construction of his engine that he never actually taught at Cambridge. Apart from occasional recognitions such as this, Babbage’s work met predominantly with rejection. By the time of his death on October 18, 1871, he was embittered by his lack of success and his popular reputation as an eccentric who had misused public funds.

Babbage’s son Henry Prevost attempted to further his father’s work, but with little success. One of Babbage’s most famous supporters was Countess Augusta Ada Lovelace, the daughter of Lord Byron. An avid mathematician, she developed programs to be transferred to the analytical engine’s punch cards.

Just over a century after his death, Babbage’s second difference engine was recreated in the late 1980s as an exhibit piece for the London Science Museum. Completed in 1991, it worked as intended and returned accurate results. In 1990, William Gibson and Bruce Sterling published the novel The Difference Engine, a fictionalized account of the world in which they explore the presumed impact of Babbage’s work on twentieth-century technology and society, had he succeeded in introducing a steam-powered computer age one hundred years prior to the introduction of the electronic computer.

Further examples of the posthumous recognition Babbage received include the founding of the Charles Babbage Foundation in 1977. The foundation is dedicated to preserving Babbage’s contributions to the history of information technology. Additionally, a lunar crater was named in Babbage’s honor.

Further Reading

1 

Campbell-Kelly, Martin, and William Aspray. Computer: A History of the Information Machine. Boulder, CO: Westview, 2004. Print. Features an analysis of Babbage’s contributions to the earliest developments in the history and practice of computer science.

2 

Snyder, Laura J. The Philosophical Breakfast Club: Four Remarkable Friends Who Transformed Science and Changed the World. New York: Broadway, 2011. Print. Explores the significance of weekly meetings held by Babbage and three of his friends, who discussed the state of nineteenth-century science and had mutually beneficial effects on each other’s work.

3 

Swade, Doron. The Difference Engine: Charles Babbage and the Quest to Build the First Computer. New York: Viking, 2001. Print. A study of Babbage’s life’s work, noting the technical limitations of the nineteenth century, Babbage’s difficulties in securing funding for his projects, and the author’s attempt to recreate a working model of Babbage’s difference engine.

4 

Warrick, Patricia S. Charles Babbage and the Countess. Bloomington, IN: AuthorHouse, 2007. Print. A dual biography of Babbage and Ada Lovelace, arranged in a narrative format.

Citation Types

Type
Format
MLA 9th
Pearson, John. "Charles Babbage." Great Lives from History: Scientists and Science, edited by Joseph L. Spradley, Salem Press, 2012. Salem Online, online.salempress.com/articleDetails.do?articleName=GLSS_0018.
APA 7th
Pearson, J. (2012). Charles Babbage. In J. L. Spradley (Ed.), Great Lives from History: Scientists and Science. Salem Press. online.salempress.com.
CMOS 17th
Pearson, John. "Charles Babbage." Edited by Joseph L. Spradley. Great Lives from History: Scientists and Science. Hackensack: Salem Press, 2012. Accessed December 14, 2025. online.salempress.com.