Shady Char­ac­ters advent calendar 2023: the E-6B

Welcome to day eight of the first ever Shady Characters advent calendar! I’m counting down to Christmas by way of a collection of beautiful, clever, important, and/or outright odd calculators and calculating devices. Some come from the pages of Empire of the Sum, some are part of my Calculator of the Day series, and some will be new to the blog. I won’t manage twenty-four posts, but I do plan to hit at least one every other day. I hope you enjoy the series!

Most slide rules are rectangular. (If you’ve never seen one before, there’s a good example of a rectangular slide rule belonging to the US astronaut Sally Ride in a previous post here at Shady Characters.) We won’t go into the mechanics of it all here,* but, in essence, a slide rule helps its user to multiply numbers simply by reading off a pair of distances, as on a conventional ruler. One distance plus another distance is a third, and all three can be read off a pair of logarithmic scales lined up next to each other. Really, a rectangle is all you need.

An E6-B flight computer, as owned by Sally Ride, the first female American astronaut. (CC0 image courtesy of the National Air and Space Museum.)
An E-6B flight computer, as owned by Sally Ride, the first female American astronaut. (CC0 image courtesy of the National Air and Space Museum.)

Yet in some cases, a circle is better. You can stretch a longer scale around the circumference of a circle than you can fit across its diameter, and a longer scale means more accurate measurements and more accurate multiplications.1 As such, the discerning slide rule enthusiast appreciates the accuracy of the circular slide rule as much as the portability of the rectangular version. And accuracy, it turns out, is very handy when navigating an aircraft. That’s where this slide rule, the Dalton E-6B dead reckoning computer, comes in.

Designed in the 1930s by an American naval pilot named Philip Dalton, the E-6B combined a circular slide rule with a “wind triangle” computer — a clever analogue mechanism for figuring out how the direction of an aircraft flying at a particular speed will be affected by the wind.2,3 The slide rule portion allowed a practiced pilot or navigator to compute air speed given a distance travelled and a time taken (or, indeed, to compute any one of those quantities given the other two); to calculate fuel burn rates; to convert between nautical miles and kilometres; to estimate how far off course an aircraft may have travelled; and to correct observed air pressure for the outside air temperature.2,3 Or even — *gasp* — to simply multiply or divide a pair of numbers.

The E-6B went on to become a standard part of the average US aviator’s training and tools, and although today it has been largely replaced by specialized electronic navigation computers (many of which look a lot like pocket calculators), the FAA’s own Weight and Balance Handbook still makes reference to the E-6B in its chapter on computing aircraft weight and balance.4

So useful was the E-6B in its day, in fact, that the professional prognosticators of the 1960s imagined that it would still be in use in the 23rd century: Mr Spock, science officer of the USS Enterprise, is shown with an E-6B in hand in two separate Star Trek episodes.5 And if it’s good enough for Mr Spock, who am I to argue?

1.
Bruderer, Herbert. “How Does One Calculate With A Circular Slide Rule?”.

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2.
National Museum of American History. “Dalton E-6B Dead Reckoning Computer by Jeppesen”. Accessed December 2, 2023.

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3.
Safetech E-6B Computer Manual. Newtown, PA: Safetech, n.d.

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4.
Weight & Balance Handbook. Federal Aviation Administration, 2016.

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5.
Valerio, Pablo. “E6B Computer: Celebrating 75 Years Of Flight”. InformationWeek.

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*
…but you can buy my book to learn more! ↢

Shady Char­ac­ters advent calendar 2023: the addiator

Welcome to day seven of the first ever Shady Characters advent calendar! I’m counting down to Christmas by way of a collection of beautiful, clever, important, and/or outright odd calculators and calculating devices. Some come from the pages of Empire of the Sum, some are part of my Calculator of the Day series, and some will be new to the blog. I won’t manage twenty-four posts, but I do plan to hit at least one every other day. I hope you enjoy the series!

Not all mechanical calculators were as sophisticated as the arithmometer or as intuitive as the Comptometer — or as large as either of them. Some, like the addiator, were very simple and very small indeed.

An addiator manufactured around 1930. (CC0 image courtesy of Volkskunde- und Freilichtmuseum Roscheider Hof & Rainer Blazejewicz.)
A pocket-sized addiator manufactured around 1930, accompanied by a stylus to moves its numeric sliders. (CC0 image courtesy of Volkskunde- und Freilichtmuseum Roscheider Hof & Rainer Blazejewicz.)

Technically speaking, “addiator” is a trade name often used to refer to a class of small adding machines more properly called slide adders. (They were also sometimes called “Troncets”, after another early manufacturer.) Slide adders comprised a number of parallel, toothed metal strips sandwiched between two boards. Each slide was visible through a slot cut in the board above it — and sometimes the one below it, too, in order to handle subtraction as well as addition. Users moved the sliders up or down in their slots using a stylus, following simple rules to handle carries from one column to the next.1,2,3

For me, the addiator is a fascinating device, and that’s at least partly because I don’t know very much about it. It hovered around the periphery of the more “mainstream”, computer-adjacent calculators that populate Empire of the Sum, but I could never quite make the case to myself that it should be included with them. There were a number of sticking points.

First, setting aside the pioneering idea that an adding machine could fit in a pocket, the addiator was essentially a dead end: neither its internal mechanisms nor its “user interface” seem to have inspired any later devices. As such, very little was written about it at the time.

Equally, despite many modern sources calling the addiator a popular device, there isn’t much data to back up that assertion. The only sales figures I’ve seen suggest that the “Arithma”, a West German model imported to the USA between 1957 and 1973, sold around 2.5 million copies.4 That’s a lot — more than 150 thousand per year — but by way of comparison, Victor, an American firm that made Comptometers and other desktop calculators, churned out twice as many devices in 1968, each one of which would have cost far more than an addiator.5.

Finally, I’m just not sure that I detect the fondness for the addiator that I do for the slide rule or the many different mechanical calculators that came after it. There are many slide rule and calculator collectors; there are far fewer addiator collectors.

And so for Empire at least, the addiator ended up on the cutting room floor. A shame, because this pocketable gadget was nothing if not ingenious in its simplicity.

1.
Wolff, John. “Slide Adding Machines”. John Wolff’s Web Museum.

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2.
Tout, Nigel. “’Addiator’ Type Calculators”. Vintage Calculators Web Museum. Accessed December 13, 2023.

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3.
Scriven, John. “Addiators”. A Collection of Mechanical Calculators (blog).

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4.
Parsons, F. “Addiator Arithma”. American Stationer (blog).

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5.
Darby, Edwin. It all adds up; the growth of Victor Comptometer Corporation. Chicago: Victor Comptometer Corporation, 1968.

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Shady Char­ac­ters advent calendar 2023: the Comptometer

Welcome to day six of the first ever Shady Characters advent calendar! I’m counting down to Christmas by way of a collection of beautiful, clever, important, and/or outright odd calculators and calculating devices. Some come from the pages of Empire of the Sum, some are part of my Calculator of the Day series, and some will be new to the blog. I won’t manage twenty-four posts, but I do plan to hit at least one every other day. I hope you enjoy the series!

This monster, this typewriter-adjacent behemoth, is a Comptometer. It was the brainchild of a Wisconsinite named Dorr E. Felt, and it was born in a macaroni box.1

A Comptometer dating to around 1887.
A Comptometer dating to around 1887. (CC0 image courtesy of Cooper Hewitt, Smithsonian Design Museum.)

Born in 1862, Felt had left school at 14 to apprentice in a local machine shop before moving to Chicago six years later.1 He found work there in a “rolling mill”, a factory which rolls metal into different thicknesses and shapes.2 And it in was there, in 1884, that he had the idea to build an adding machine.3

Felt had been using a tool that relied on a series of notches to control its movement, and he wondered if he could use a similar mechanism to drive an adding machine. First, he told himself: “I will make such a machine.” Then, he told a friend: “In ninety days every office in the United States will be doing its calculation by machinery.” A grand ambition, but it would start more humbly. To build a prototype, Felt bought a macaroni box at a grocer’s shop, skewers at a butcher, staples at a hardware store and elastic bands at a bookshop. He worked on his device on Thanksgiving, Christmas Day and New Year’s Day, but it was still nowhere near complete.4

In the event, it would take Felt most of his ninety days just to finish a working prototype. A more functional metal version followed early in 1885; a production-ready machine in the autumn of 1886; and a partnership with a Chicago factory owner in 1887.3

Although the first Comptometer was an adding machine rather than a true calculator, its voluminous keyboard was the key (sorry) to its success. Each digit was handled by a column of keys labelled from 0 to 9, and pressing a key immediately added its value to the running total. There was no crank to turn or lever to pull, and a skilled operator could add an entire multi-digit number by pressing multiple keys at once.5

The keyboard, in fact, was the Comptometer’s chief legacy: many other mechanical calculators adopted it, despite using different internal mechanisms, purely for its familiarity to users. Even the Sumlock Anita, the first electronic calculator, would do the same. The Comptometer cast a long shadow.

1.
Holman, Alfred L. (Alfred Lyman), and Dorr Eugene Felt. A register of the ancestors of Dorr Eugene Felt and Agnes (McNulty) Felt. Chicago, Priv. print. for D. E. Felt, 1921.

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2.
Papers in Illinois history and transactions. Springfield, 1921.

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3.
Turck, J. A. V. Origin of modern calculating machines; a chronicle of the evolution of the principles that form the generic make up of the modern calculating machine. Chicago, The Western society of engineers, 1921.

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4.
Felt, D. E. Mechanical Arithmetic, Or, The History of the Counting Machine. Lectures on Business, Ed. By T. H. Russell. Chicago: Washington institute, 1916.

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5.
Methods of Operating the Comptometer.

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Shady Char­ac­ters advent calendar 2023: the arithmometer

Welcome to day five of the first ever Shady Characters advent calendar! I’m counting down to Christmas by way of a collection of beautiful, clever, important, and/or outright odd calculators and calculating devices. Some come from the pages of Empire of the Sum, some are part of my Calculator of the Day series, and some will be new to the blog. I won’t manage twenty-four posts, but I do plan to hit at least one every other day. I hope you enjoy the series!

The machine that belatedly claimed the crown of first practical mechanical calculator, after the failure of Wilhelm Schickard’s Rechenuhr and many other pretenders, was this one: the arithmometer designed by Charles Xavier Thomas de Colmar, administrator in Napoleon’s army, insurance pioneer, and Chevalier of the Légion d’Honneur.1 It was a long time coming.

An arithmometer in a protective wooden case, circa 1863. (<a href="http://doi.org/10.21264/ethz-a-000000326">Public domain image courtesy of Sammlung wissenschaftlicher Instrumente und Lehrmittel, ETH-Bibliothek, ETH Zürich</a>.)
An arithmometer in a protective wooden case, circa 1863. (Public domain image courtesy of Sammlung wissenschaftlicher Instrumente und Lehrmittel, ETH-Bibliothek, ETH Zürich.)

As with Napier, Schickard, and others before him, Thomas wanted to reduce the mental labour required in everyday arithmetic. No-one had yet succeeded, as an American publication called The Manufacturer and Builder explained in 1872:

[Some calculators] were so complicated that it would take an engineer to run them, and a watch-maker to keep them in order, while others were evidently designed by men who knew nothing, practically, of the working of machinery […] Finally, every machine was out of order, and gave arithmetical results that would bankrupt the most successful business man in two turns of the handle.2

Thomas, finally, would break the impasse. He worked on the arithmometer for much of his life, obtaining an initial patent in 1820 and then refining his machine on and off for the next fifty years. The result was a robust, sophisticated machine that could add, subtract, carry, and even, with some clever manipulation, multiply and divide — and it could do so over and over again with impressive consistency. It was not cheap, exactly (Henry Brunel, an English engineer, paid the equivalent of almost $2,000 in today’s money for a single arithmometer), but it worked, and it worked well, inaugurating features such as sliders to set inputs, a sliding “carriage” to record the running total, and a crank to enact each addition or subtraction, that would go on to be used in many similar devices.1 The arithmometer was the shape of things to come.*

1.
Johnston, Stephen. “Making the Arithmometer Count”. Bulletin of the Scientific Instrument Society, 1997, 12-21.

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2.
The Manufacturer and builder : a practical journal of industrial progress. “Calculating Machine.”

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*
Ironically, the arithmometer itself would eventually come in a different shape, but we’ll get to that story another time soon. ↢

Shady Char­ac­ters advent calendar 2023: Wilhelm Schickard’s Rechenuhr

Welcome to day four of the first ever Shady Characters advent calendar! I’m counting down to Christmas by way of a collection of beautiful, clever, important, and/or outright odd calculators and calculating devices. Some come from the pages of Empire of the Sum, some are part of my Calculator of the Day series, and some will be new to the blog. I won’t manage twenty-four posts, but I do plan to hit at least one every other day. I hope you enjoy the series!

Wilhelm Schickard’s life overlapped that of John Napier, inventor of logarithms and Napier’s bones, by a quarter century. Born in 1592, Schickard’s birthplace of Herrenberg and his alma mater of nearby Tübingen, both now in Germany, put him in the midst of a clockwork revolution: the surrounding area was famed for its clockmakers, and the technology of mechanical clocks was advancing by leaps and bounds.1,2,3

Schickard himself studied languages and theology, though he was also an excellent engraver in wood and copper and a keen mathematician. Those latter two talents combined to win him commissions for illustrations and mathematical tables from Johannes Kepler, one of the most prominent and influential astronomers of the day.1

A modern reproduction of Wilhelm Schickard's <i>Rechenuhr</i>, or "calculating clock". At top is a set of Napier's bones to help with large multiplications, while the dials at the bottom drove an adding mechanism.
A modern reproduction of Wilhelm Schickard’s Rechenuhr, or “calculating clock”. At top is a set of Napier’s bones to help with large multiplications, while the dials at the bottom drove an adding mechanism. (CC-BY 4.0 image courtesy of Stadtmuseum Tübingen.)

All of this came together in Schickard’s invention, in 1623, of a device he described in a letter to Kepler and that he called the Rechenuhr, or “calculating clock.” It was, in essence, the first ever practical mechanical calculator.

Schickard’s ungainly machine placed a set of Napier’s bones atop a mechanical adding machine. A set of six small windows in the lower part showed a running total, to which the user added or subtracted units, tens, hundreds, and so on by turning one of six associated dials in either one direction or the other. Napier’s rods were there to help with multiplications, since Schickard’s mechanism could only add or subtract.

It was groundbreaking, and, well, it was not very good. Mechanical calculators, it turns out, live or die by how well their “carry” mechanisms work: whether an addition causes ‘9’ to tick over to ‘10’, or ‘99999’ to ‘100000’, the machine must be able to handle it. Schickard’s machine supported only six digit-numbers precisely because its carry mechanism was too fragile for any more than that.4

In the event, the Rechenuhr’s ability to carry tens did not much matter. A prototype that Schickard made for Kepler was lost in a fire, and its makers ambitions with it. The Rechenuhr forfeited the race to become the first successful mechanical calculator before it ever got started — but on that note, come back next time to learn about the machine that would claim the crown two centuries later!

1.
O’Connor, J. J., and E. F. Robertson. “Wilhelm Schickard”. MacTutor.

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2.
Friedman, Alan J. “The Clockwork Universe”. Technology and Culture 25, no. 2 (1984): 280-286.

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3.
Bedini, Silvio A. “The Role of Automata in the History of Technology”. Technology and Culture 5, no. 1 (1964): 24-42.

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4.
Lee, J. A. N. “Wilhelm Schickard”. Computer Pioneers.

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