In reality, all mechanical calculators are cool. Many are triumphs of human ingenuity, but there are some that deserve especial note due to their … let’s say “elegance” for want of a better word. In fact, one could easily fill a book on these little scamps without trying, but then we would never manage to get to any other interesting stuff, so we’ll restrain ourselves to consider only two rather cunning types …

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Louis Troncet and the Arithmographe
Several people experimented with versions of simple mechanical calculators that involved strips of metal with numbers marked on them mounted in a frame, where a stylus was used to slide these strips up and down. A few names that usually rise to the top of the pile in this regard are Claude Perrot (1613 - 1688), who invented an early form of this class of device sometime around the mid 1660s, and the Frenchman Caze, who created his version around 1720. One problem with Caze’s machine was that it wasn’t possible to perform carries from one column to another. This niggle was solved around 1845 by the Prussian-German mathematician Ernst Eduard Kummer (1810-1893).

In 1889, a Frenchman named Louis Troncet created his version of this type of calculator, which he called the Arithmographe. Troncet's invention became so popular that the term “Troncet-type” is often used to refer to this class of device.




 
Addiator Gesellschaft and the Addiator
One of the most popular versions of the Troncet-type calculator was the Addiator, which was created in Germany by Addiator Gesellschaft. Introduced in 1920, over 100,000 units were sold in the first year, and versions of this device remained in production as late as 1982.

Featuring a novel carry mechanism, the Addiator could be used to add or subtract, but addition and subtraction required two different control panels. In early versions of these devices, the two panels were provided by flipping an overlay on the front or by having the addition function on the front and the subtraction function on the back (later models had two separate panels on the front).

Addiator

One cool thing about this sort of calculator is that it could be adapted to accommodate non-decimal measurements such as length in feet and inches or British currency in pounds, shillings, and pence as shown in the photo above.




 
Pounds, Shillings, and Pence
With regard to the previous topic, the picture shown is of an Addiator intended for use with the British currency system of "pounds, shillings, and pence." This is also written as LSD, where the "L" comes from the Latin word libra and the "D" comes from the Latin word denarius, which was a type of coin in Roman times.

The way in which this worked was that there were 12 pennies in a shilling (also called a bob) and 20 shillings (240 pennies) in a pound. It’s easy to see the problems involved with such a scheme; for example, let’s assume that something in a shop was priced at 1 pound, 8 shillings, and 9 pence ... how much would it cost for three of the little rascals?

And in fact, things were a tad more complicated than the brief overview above might lead you to believe, because there were a variety of other coins. For example, there was a farthing (a quarter of a penny) and a halfpenny that was pronounced hapenny or haypeni [prior to the reign of Edward 1 (1272-1307), halfpennies and farthings were made by cutting a real penny into two or four pieces, respectively.]

There was also a twopenny piece (although admittedly this was only made in 1797) and a threepenny piece that was referred to as a threpney bit (or threpeni, thripeni, or thrupeni – the actual pronunciation depended on where in the UK one lived). The threepenny piece was made in 0.500 fine silver up to and including 1944. In 1937, the government also started minting dodecagonal nickel-brass versions (both types were minted during the intervening years, and the silver versions remained in circulation long after they had stopped being minted).

Then there was the groat, which was worth four pennies and was made from 1836 to 1888. Also the sixpence (worth six pennies), which was known as a tanner, and the shilling (worth twelve pennies), which was known as the bob. But wait, there’s more! There was also the florin, half-crown, double-florin, crown, half-sovereign, sovereign, and guinea.

These coins are discussed in more detail in The History of Calculators, Computers, and Other Stuff document provided on the CD-ROM accompanying our book How Computers Do Math.) Suffice it to say for the moment that in February 1971, Great Britain retired the concept of pounds, shillings, and pence and officially adopted a decimal system in which a pound equaled 100 pennies (they were called "new pennies" at the time), much like the American dollar equals 100 cents. Strange as it may seem, however, the majority of British citizens fought this move toward decimalization tooth-and-nail claiming that the new scheme was far too complicated and would never catch on!




 
Curt Herzstark and the Curta
One of the most famous mechanical calculators of all time is the Curta, which was invented by Curt Herzstark (1902-1988). Looking something like a coffee or pepper grinder, this incredible high-precision unit fit in the palm of one hand and could perform addition, subtraction, multiplication, and division.

The Curta had sliding levers on the side that were used to set digits and an operating handle on the top that was turned clockwise. Values were displayed in small openings on the top of the device above each lever. The photos below show a Curta with the value "12345789" set on the levers on the side and the crank turned once, as reflected by the "1" appearing in the white "counter" area on the top. This has added "12345789" to the value shown in the black "accumulator" area on the top. Turning the crank another revolution would increment the counter to "2" and add another "12345789" to the accumulator. The ring is used to clear both the accumulator and counter.

Curta

The story behind the invention of the Curta is as amazing as the device itself. Curt's father, Samuel Herzstark (1867-1937), was the founder of an Austrian company that manufactured Thomas-based Arithmometers augmented with Herzstark’s own patented inventions. Following an apprenticeship as a precision mechanic and toolmaker in his father's factory, Curt was eventually made responsible for sales. While making sales trips and talking to his customers, Curt got the idea for the construction of a unique four-function pocket calculator. After years of experimentation, the first prototype was built in the winter of 1937/38.

And then came the Second World War. In 1943, Curt was arrested and sent to the infamous SS-run Pankraz prison in Prague. From there, he was transported to the notorious Buchenwald concentration camp, where the camp commander ordered him to make drawings of his calculator (apparently he wanted to give one as a present to Adolf Hitler). Thus, Curt gained access to a small drawing board and managed to re-create the drawings from memory.

By this strange series of events, Curt was in possession of a complete set of drawings for his calculator – which he called the Curta – when the Americans eventually liberated Buchenwald on 11 April, 1945. In 1946, the Prince of Liechtenstein invited Curt to establish a factory to manufacture Curtas in the Principality of Liechtenstein. In 1949, the Curta I was presented to the market with the Curta II following sometime later. The Curta stayed in production until the early 1970s, at which point electronic pocket calculators started to take over the market. Having said this, the Curta's accuracy of 11 or 15 positions (depending on the model) meant that this device was actually more accurate than most of its early electronic pocket counterparts.



Note: The material presented here was abstracted and condensed from The History of Calculators, Computers, and Other Stuff document provided on the CD-ROM accompanying our book How Computers Do Math (ISBN: 0471732788).