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Mercedes Euklid

Mercedes Euklid model 16

The Mercedes Euklid 16 is a manually driven, full keyboard calculator which has automatic division. It was made in Germany from 1927 till 1935.

The keyboard has 13 columns of keys. This is the first model to use an innovative modular design that would remain in use for all models for the next 25 years or so. Each key column is a single replacable module, and has keys with cubical keytops with no space between the keys. In each column only one key can be pressed down at a time, and if you press a second key then the first will pop up again. A small window at the front displays the currently entered digit of the column. The case of the machine is shaped around the keyboard to make it an integral part whereas on previous models the keyboard was more obviously a separate block bolted onto the non-keyboard version of the calculator.

At the front is a carriage with a 16-digit register, and an 8-digit counter. There are two sliding levers on the front of the carriage with which you can reset the counter and the main register to zero. The carriage is attached to an internal spring that pulls it to the left. You can push the carriage to the right manually to the most significant digit of your multiplication or division, and then it can shift to the left digit by digit automatically (during division) or by pressing the tab at the front of the carriage (during multiplication). The carriage shift tab can also be activated by knobs to the right and left of the keyboard. The round metal button at the left of the carriage fully releases the carriage so you can shift it to its home position quickly.

The crank on the right can be attached in two ways - sticking up almost vertically, or forwards toward the user. It can only be turned clockwise, and if you do an anti-clockwise turn nothing happens as the crank then simply does not engage with the rest of the mechanism. A clockwise turn will cause the input to be added or subtracted from the main register, and the counter will be increased or decreased. Which action is performed depends on the settings of the control buttons.

The controls are all buttons, whereas older models also used levers. To the right of the keyboard is an L button which clears any input on the keyboard (Löschen). The button marked A (Addieren) can be latched down to engage the automatic clearing of the keyboard for use in a series of additions or subtractions, whereby the keyboard is cleared at the end of each turn of the crank.

To the left of the keyboard are two pairs of radio buttons. The left pair determines whether to add (+×) or subtract (-) the input from the register. The right pair determines whether the counter is incremented (N) or decremented (C). There is also a button marked D which can be latched down to activate the automatic division. In this mode the other buttons are set automatically for each step in the division. The automatic division is explained in more detail below.

There is an innovative automatic decimal point marker system. There is a small hole to the right of every digit in the input display register. With the lever on the left hand side of the machine you can place a marker after any one of the last 8 digits of the input register, visible through the small hole. Above the counter is an arrow pointer that can be slid to mark the decimal point in the counter. Above the register is a row of holes through which one shows a white marker. This marker is automatically placed at a distance that is the sum of the other two markers. In this way the decimal point will automatically be correctly set during a multiplication.

The serial number of my machine is 14545, which means it was made in about 1929. Almost every part of the machine has the serial number stamped or scratched on it, sometimes only the last three digits. The easiest way to find the number is to move the carriage to the right so that the number becomes visible on the front edge of the base.

The principle of proportional levers is unique to the Mercedes Euklid series of calculators. The basic version used in the first models used sliders for inputting a number, one for each digit. These would shift a gear along its axle, but instead of engaging with a stepped drum, it engaged with one of ten parallel toothed racks shared by all the input digits. These toothed racks are pivoted to an arm, and when one end of that arm swings out, the racks move different amounts, varying from 0 to 9 units. The register wheels move in one direction only, so when the arm has moved back and the racks have returned to their starting position then the input has been added to the register. For subtraction the other end of the arm is moved so that complementary digits are added.

When a keyboard was used for input instead of sliders, each axle was given five gears that can slide along it, normally resting in a position inbetween two of the racks. When a key is pressed, one of the gears moves slightly up or down to engage with a rack. In this way only one gear is active at any one time, and only a small movement is needed to make it active.

Video

Below is a video I made that demonstrates the Mercedes Euklid model 16.

Mercedes Euklid model 29

The Mercedes Euklid 29 is a manually driven, full keyboard calculator which has automatic division. It was made in (East) Germany from 1934 until 1953. It can be considered the successor to the model 12 above, as it has about the same functionality, and was the only manually driven Euklid model remaining (all the others were electric).

The keyboard has 7 columns of keys. There is a carriage with a 12-digit register, and a 6-digit counter. The carriage is at the back, angled towards the user to make the registers earier to read.

The crank on the right is angled towards the front. It can only be turned clockwise. There are two switches to the left of the keyboard. One selects whether a turn of the crank will perform an addition or a subtraction. The other selects whether the counter is incremented or decremented. To the right of the keyboard is a black button which clears the input from the keyboard. Normally this button is marked L for Löschen, but on my machine the button is blank. The other button is marked Add, and when it is pushed down and locked in place, the keyboard will be automatically cleared after every turn of the crank. The button on the left marked Div selects automatic division, and that is explained in more detail below.

It uses the same proportional lever mechanism as the model 16 above. The main difference is that the carriage is at the rear with the keyboard in front.

The serial number of my machine is 48967, which means it was made in about 1941. The serial number can be found on various places on the mechanism, but from the the outside can only be seen on the underside of the carriage when it is shifted to the right.

Video

Below is a video I made that demonstrates the Mercedes Euklid model 29.

In this video I show the proportional lever mechanism in action.

Automatic Division

Automatic division is quite easy to perform. Once it is set up, all you have to do is turn the crank until it finishes the calculation. Here are the steps you would do to set up the division 355/113.

1. Shift the carriage to the right as far as possible.
2. Enter the dividend into the main register, in this example 355. You could do this by entering it on the keyboard and adding it, but you can also use the setting knobs of the register to enter it directly.
3. Reset the counter if necessary. This is important to remember if you used an addition in the previous step as that would have incremented the counter.
4. Enter the divisor into the keyboard, in this example 113.
5. Push down the Division button, latching it down. This should set the control buttons correctly - subtraction from the register, the counter set to increment, and the automatic keyboard clearing disabled.
6. Repeatedly turn the crank until the division is completed. At the end of the calculation the crank should either lock up or disengage the mechanism.
7. To restore normal functioning, nudge the carriage to the right until it clicks, which restores function of the crank, and also unlatch the Division button to regain manual control of the other buttons.

The division works by repeatedly subtracting until the register underflows (becomes negative). The carriage then shifts to the next digit, and the control buttons switch over so that the machine now adds repeatedly until the register overflows (becomes positive again). The carriage shifts again if possible, and the process repeats. As the counter has an even number of digits, the division ends in addition mode with a positive remainder.

Here is an example division of 123/17:

Register Counter 012300000 000000 -17 Subtract, increment counter 010600000 100000 008900000 200000 007200000 300000 005500000 400000 003800000 500000 002100000 600000 000400000 700000 998700000 800000 +17 Add, decrement counter 998870000 790000 999040000 780000 999210000 770000 999380000 760000 999550000 750000 999720000 740000 999890000 730000 000060000 720000 -17 Subtract, increment counter 000043000 721000 000026000 722000 000009000 723000 999992000 724000 +17 Add, decrement counter 999993700 723900 999995400 723800 999997100 723700 999998800 723600 000000500 723500 -17 Subtract, increment counter 000000330 723510 000000160 723520 999999990 723530 +17 Add, decrement counter 000000007 723529

History

Christel Hamann (1870-1946) was a highly prolific and inventive designer of calculating machines. He founded his own company in 1896, at which his first machines were made. The full range of his lesser known early work is somewhat unclear. It is possible that he started with troncet adders and pinwheel machines, as his name has been linked to the Trick (troncet adder) and the Berolina (pinwheel machine) due to some of his patents. His first proper machine design was called the Gauss, and was a cylindrical machine with number wheels arranged around it. Instead of a single stepped drum in the centre, he used a disc with circular tracks that have varying numbers of teeth. He patented this in 1902. The cylindrical design with a shared stepped drum had been used by Philipp Matthäus Hahn in the 1770s to make a handful of machines, but the Gauss was slightly simpler, and maybe about a thousand were made. The culmination of the cylindrical design was the Curta calculator from 1946 by Curt Herzstark.

In 1904 hamann made a prototype calculator called the Gauss 4. It looked like a standard Arithmometer type of machine with sliders. However, instead of each slider moving a gear that engages with its own stepped drum, in this machine the stepped drums were replaced by a single ridged plate that was like an unrolled stepped drum, or a straightened version of the Gauss's disc, and when the crank was turned this plate was pulled past all the input gears. By 1905 this had developed further into an entirely new principle, proportional levers. Now in place of the ridged plate there were a set of ten parallel toothed racks, again shared by all the input digits. These toothed racks are pivoted to an arm, and when one end of that arm swings out, the racks move different amounts, varying from 0 to 9 units. The register wheels move in one direction only, so when the racks have returned to their starting position the input has been added to the register. For subtraction the other end of the arm is moved so that complementary digits are added. Hamann called this machine the Euklid.

In 1907 Hamann's company became part of Mercedes Büromaschinen-Werke. This small company had been founded only the year before by Gustav Metz and made typewriters, and presumably wanted to expand into making calculators as well. They made a few dozen Mercedes Gauss machines as well as similar amounts of the Mercedes Plus which was an adding machine that Hamann designed, but it was mainly the Mercedes-Euklid machines that became successful and were developed further. The company grew and moved from Berlin to Mehlis (now Zella-Mehlis) in Thüringen, which is where Walther were also based. By the time of the first world war, 8 models had been produced. Development and production were affected by the war, and in about 1922 Hamann left the company and moved back to Berlin to join Deutsche Telephonwerke GmbH where the Hamann calculators were made.

Many more Mercedes-Euklid models were developed in subsequent years, all based on the same principle. When Germany was split up after the second world war the company was in East Germany, where it was allowed to grow, though it soon was producing its machines only for the Eastern Bloc countries. The casing of the machines was changed from green to light grey, and the letter R was added to the model designations. In about 1963 Mercedes became Cellatron, and the machines were rebranded accordingly. Mercedes and then Cellatron produced about 10,000 calculators per year until either 1969 or 1975 (sources disagree on the end date). In 1977 the company became part of the state-owned Robotron Elektronik, and in 1990 this was split up into smaller companies that were bought up by various others after the Iron Curtain had fallen.

Models

The Mercedes-Euklid models are generally split into four series. Below is a table listing most of the models.

Model: Model number.
Years: Years of production. Sources are often contradictory, for example model 8 is sometimes placed as 1918 and model 29 as 1936, while adverts show them in existence in 1915 and 1934 respectively.
Capacity: Number of digits in the input×counter×result registers.
Elec.: N means manually driven, Y means electrically driven.
Keyb.: N means input via sliders, Y means input via keyboard.
Stor.: N means no extra register, T means it has an extra totaliser register, M means it has a memory storage register.
Div.: N means no special division capabilities, S means it has stop division, F means fully automatic division.
Mult.: N means no special multiplication capabilities, S means semi-automatic, K means it has multiplication keys, F means fully automatic multiplication.

Mercedes used consecutive serial numbers, shared by all their calculators except for the Trick troncet adder. So not only were these numbers used for the Mercedes Euklid, but also for the few dozen Gauss and Mercedes Plus machines, and for the approximately 4000 Mercedes A adding listing machines made between 1938 and 1945. These numbers can therefore be used to fairly accurately date when the machine was made, but not how many there are of each model. Below is a list of years and the final serial number reached in that year. After 1943 the numbers are based on very rough production estimates, so I have rounded the serial numbers to the nearest 1000 to avoid the appearance of accuracy. There is so much uncertainty that one source even claims that there is a large gap where the serial numbers jumped to 100,000. It is also unclear whether production stopped around 1969 or 1975.

Promotional material

This is a flyer that promotes the models 7 to 12. It is in French, has a stamp from a Belgian retailer, and probably dates from 1925 or 1926.

Articles and Advertisements

Here is an extract from Mathematische Instrumente by Andreas Galle from 1912:

Here is an extract from Modern Instruments and Methods Of Calculation, a Handbook Of the Napier Tercentenary Exhibition, from 1915:

Here is the entry in the Orga-Handbuch erprobter Büromaschinen of 1921 by Ludwig Brauner and Victor Vogt:

Here is the entry in Ernst Martin's 1925 book Die Rechenmaschinen:

Here is part of an article by F. Zernike which appeared in the Dutch magazine Euclides, in the first issue of the year 1942.

Here are a few other small articles from books, newspapers and magazines.

Lastly, here are some advertisements. The first one is for the Gauss, before Mercedes got involved.

Patents

Links

• Rechnerlexikon has a page about Mercedes, with links to various models, also a history of Mercedes-Euklid, and some material about Christel Hamann.
• Rechenmaschinen-Illustrated has a page about the Mercedes Euklid, and also tables of models and production years. Note however that several models appear in adverts some years before what is shown in these tables.
• Computer Timeline has a biography page for Christel Hamann
• Cris Vande Velde has a Model 1 and a Model 29
• Christian Hamann has a Mercedes-Euklid model 22, model 29, and a model 38MS.
• Detlev Bölter has a page about the Gauss 4 prototype, and a more in depth article.
• The National Museum of American History has in its collection a model 1, a model 8, a model 12, and a model 38MS.
• zella-mehlis-geschichte.de has a page about the history of Mercedes company.

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