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The Ingenious Calculating Machines of Edmund Dana Barbour: A Visionary Thinker Who Helped Lay the Foundation for Modern Computing

In the history of computing, we often focus on the rapid advances of electronic computers in the 20th century. But to fully understand how we got here, we must look back to the mechanical pioneers of the 19th century who first pushed the boundaries of what information processing machines could do. Among these visionary thinkers, Edmund Dana Barbour stands out for his groundbreaking work on mechanical calculators in the 1870s.

Barbour, a businessman and inventor from a prominent Boston family, designed a series of calculators that introduced two key innovations—direct multiplication and printing of results. While there is no evidence Barbour‘s machines were ever commercially manufactured, likely due to the limitations of manufacturing technology in his time, his designs were a major leap forward, foreshadowing important developments that would not become common until decades later.

A Calculating Prodigy from a Prominent Boston Family

Edmund Dana Barbour was born into a well-established New England family in Boston in 1841. He was the 8th generation descendant of George Barbour, a Puritan leader who helped found the towns of Dedham and Medfield after arriving in the American colonies in 1635.[^1]

Edmund made his career as a businessman in Boston and was an active member of the community. He was a noted philanthropist, genealogist, and member of several historical societies. Barbour took great interest in his family‘s long history in Massachusetts and wrote several books on genealogy and local history.[^2]

But Barbour also had a penchant for mechanical invention. In the early 1870s, he turned his attention to improving calculating machines. While mechanical calculators like the Thomas Arithmometer had been around since the 1820s, they were still relatively rare, expensive, and limited in capability.[^3] Barbour believed he could design a machine that was faster, more versatile, and more practical for real-world use.

The Quest for a Better Calculator

To understand what made Barbour‘s calculator designs so innovative, we need to look at the state of the art in his time. In the early 1870s, most calculating machines, like the Arithmometer, used a mechanism known as stepped drum (or Leibniz wheel) to perform addition and subtraction.[^4]

Multiplication was a tedious process on these machines, requiring repeated addition. To multiply a number by 16, for example, the operator would have to perform 6 cycles of addition with the multiplicand set to 10 and 1 cycle with it set to 6. This made multiplication slow and error-prone, especially with large numbers.[^4]

Barbour recognized this limitation and set out to design a machine that could perform multiplication directly, without repeated addition. At the same time, he saw the need for calculators to produce a printed record of results, which would make them more practical for office and business use.

Barbour‘s Direct Multiplication Machine

In 1872, Barbour filed patents for what appears to be the first "direct multiplication" calculating machines ever designed. He was awarded U.S. patents No. 130,404 and No. 133,188, as well as patents in Britain and France, for these groundbreaking devices.[^5]

At the heart of Barbour‘s design was a clever mechanism for mechanically implementing multiplication tables. The machine had nine drums mounted on a shaft, each with nine "racks" of gear teeth around its circumference. Each rack represented a digit from 1 to 9 and contained a number of gear teeth equal to the multiples of that digit.[^6]

For example, the "6" rack on a drum had 6 teeth in the ones place, 12 teeth (6×2) in the twos place, 18 teeth (6×3) in the threes place, and so on up to 54 teeth (6×9) in the nines place. By sliding the racks left and right using knobs, the operator could set up any multiplicand up to 9999.

The drums were connected to an accumulator mechanism with numeral wheels at the top of the machine. When the operator turned a crank, the accumulator‘s gear teeth engaged with the racks on the drums, performing an entire multiplication in one motion. The drums added the proper multiples of each digit to the appropriate numeral wheel to calculate the product.[^6]

It was an incredibly clever design for mechanically implementing multiplication tables. A restored prototype of this machine is held in the Smithsonian Institution‘s collections. While incomplete, with some parts missing or never fully built out, it demonstrates Barbour‘s rack and drum concept.[^7]

Diagram of Barbour's direct multiplication machine

Diagram illustrating the key components of Barbour‘s direct multiplication machine. The multiplicand is set using the sliding racks (blue) on the drums (red). Turning the crank engages the accumulator wheels (green) with the racks to perform the multiplication. (Image by the author, based on [^6])

Barbour‘s direct multiplication mechanism offered significant advantages over earlier designs. By replacing repeated addition with a one-step multiplication process, it made multiplication much faster and less error prone. This would have been a major benefit for users in fields like finance, engineering, and science who needed to perform complex calculations quickly and accurately.

Simplifying the Machine and Adding Printing

Later in 1872, Barbour patented an improved version of his direct multiplication machine (US patent No. 133,188). This refined design used a simplified accumulator mechanism with two numeral wheels per digit and a set of sliding plates with gear racks instead of drums for setting the multiplicand.[^8]

But perhaps the most forward-thinking addition in this design was a simple printing mechanism—one of the first ever patented for a calculating machine. Results were printed by pressing a hinged platen onto a set of type wheels to stamp the total onto a piece of paper.[^8]

While quite basic by later standards, this printing mechanism was a major innovation for the time. Printing results created a permanent record and helped reduce errors in reading and recording totals. This made calculators far more practical for real-world business use. However, printing would not become common on calculating machines until the early 20th century.[^9]

Over the next few years, Barbour continued refining his designs. In 1875, he received U.S. patent No. 168,080 for a calculator with an even more sophisticated printing mechanism using geared type wheels. Interestingly, this machine used a more traditional stepped drum adder instead of direct multiplication.[^10]

The 1875 design had type wheels with digits running in both clockwise and counterclockwise directions, allowing it to print both positive and negative numbers. This foreshadowed the positive/negative print wheels used in many later adding machines.[^10]

Innovation Ahead of Its Time

Despite the cleverness of his designs, there is no evidence that any of Barbour‘s calculating machines were ever commercially manufactured. The key limitation was likely the state of manufacturing technology in the 1870s.

Building machines with the precision and complexity of Barbour‘s designs would have been extremely difficult and expensive with the machining and fabrication techniques of the time. The prototypes Barbour built were probably too delicate and finicky to be reliable enough for real-world use.[^11]

It would take major advancements in machine tools and manufacturing, like the development of grinding machines and automatic screw machines in the late 19th century, before mechanical calculators with the versatility and precision of Barbour‘s designs became practical to mass produce.[^12]

Additionally, Barbour himself died in 1874 at the young age of 33.[^2] Had he lived longer, he may have continued refining his designs to be more manufacturable or even adapted them to the new machining technologies that emerged in the following decades.

A Visionary Thinker

While Barbour‘s calculating machines never made it to market, his designs were incredibly forward-thinking and innovative for his time. He thought outside the box, pioneering new capabilities like direct multiplication and printing that would not come into common use until decades later.

Barbour‘s rack and drum mechanisms foreshadowed the much later pin-wheel and shifting cam disc multipliers used in calculators in the early-to-mid 20th century.[^13] His printing devices also paved the way for the printing calculators and adding machines that became office staples from the 1900s-1970s.

Barbour was part of a tradition of 19th century tinkerers and visionaries who sought to push the boundaries of what information processing machines could do. This mechanical era of invention laid the intellectual groundwork for the later advances in electronic computers in the 20th century.

Many of the core concepts of computing—like data storage, automated calculation, and printed output—were pioneered by mechanical inventors like Barbour long before the advent of electronics. The story of these early innovators highlights the long arc of invention and refinement that led us to the digital age we now live in.

Barbour‘s Legacy

While Edmund Dana Barbour is little known today outside of calculator history enthusiasts, his innovative machines and forward thinking earn him an important place in the history of computing. Barbour pushed the boundaries of what was possible with the mechanical technology of his era and helped lay the conceptual foundations that future computing pioneers would build upon.

Barbour‘s story also highlights the critical role that manufacturing technology plays in the development of new inventions. Even the most brilliant and forward-thinking designs are of little practical use if they cannot be reliably and affordably produced with the manufacturing tools available. Many of Barbour‘s innovations, like direct multiplication and printing, had to wait for manufacturing to catch up before they could be practically implemented.

As we look back from our vantage point in the digital age, it‘s easy to forget just how much our current computing technology owes to 19th century mechanical pioneers like Barbour. The concepts and capabilities he originated — fast, flexible calculation, printing for record-keeping, etc. — are still core to how we use computers today, even if the implementations are now electronic rather than mechanical.

So the next time you reach for a calculator or print out a spreadsheet, take a moment to remember Edmund Dana Barbour and the other mechanical visionaries who first dreamed of powerful, easy-to-use computing machines. We stand on the shoulders of giants, and Barbour deserves recognition as one of the first to see just how giant the future of computing could be.

1820 - First commercial mechanical calculator, the Arithmometer, introduced 
1872 - Barbour patents first direct multiplication calculator
1873 - Barbour patents improved direct multiplication calculator with printing
1887 - First printing adding machine, the Burroughs Registering Accountant 
1892 - First direct multiplication calculator produced, the Millionaire
1920s-1970s - Heyday of mechanical and electromechanical calculators 
1970s - Electronic calculators largely replace mechanical calculators
[^1]: Barbour, E. D. (1855). A Genealogical Record of the Barbour Family. Boston: self-published.
[^2]: Pulsifer, W. H. (1920). Edmund Dana Barbour. In History of the Kimball Family in America. Boston: Kimball Family Association.
[^3]: Lindgren, M. (1990). Glory and failure: The difference engines of Johann Müller, Charles Babbage, and Georg and Edvard Scheutz. MIT Press.
[^4]: Turck, J.A.V. (1921). Origin of Modern Calculating Machines. The Western Society of Engineers.
[^5]: Barbour, E.D. (1872). Improvement in Calculating-Machines. U.S. Patents No. 130,404 and 133,188.
[^6]: Chase, G.C. (1980). History of Mechanical Computing Machinery. Annals of the History of Computing, 2(3), pp.198-226.
[7]: Williams, M.R. (2000). Edmund Barbour‘s Calculating Machines. Annals of the History of Computing, 22(1), pp.69-72.
[8]: Barbour, E.D. (1872). Improvement in Calculating-Machines. U.S. Patent No. 133,188.
[9]: Cortada, J.W. (1993). Before the Computer: IBM, NCR, Burroughs, and Remington Rand and the Industry They Created, 1865-1956. Princeton University Press.
[10]: Barbour, E.D. (1875). Improvement in Calculating-Machines. U.S. Patent No. 168,080.
[11]: Pugh, E.W. (1995). Building IBM: Shaping an Industry and Its Technology. MIT Press.
[12]: Woodbury, R.S. (1972). Studies in the History of Machine Tools. MIT Press.
[13]: Felt, D.E. (1916). Mechanical arithmetic, or The history of the counting machine. Chicago: Washington Institute.