New exhibition at the Arithmeum in Bonn How alcohol accelerated the triumphal march of the slide rule

Bonn · A new exhibition at the Arithmeum in Bonn reveals how alcohol and tax on spirits accelerated the triumph of the slide rule. Their use was by no means trivial.

High-percentage mathematics: the brass ball that Ina Prinz drops into the rum is weighed out so that it floats on top at 57 percent by volume. Patrick Rocca supervises the process as an 18th-century "exciseman" (tax official).

High-percentage mathematics: the brass ball that Ina Prinz drops into the rum is weighed out so that it floats on top at 57 percent by volume. Patrick Rocca supervises the process as an 18th-century "exciseman" (tax official).

Foto: Martin Wein

Calculating while intoxicated is challenging. Nevertheless, it was alcoholic beverages, especially high-proof whisky and gin, that advanced modern mathematics a great deal. This is the conclusion of a current exhibition with the sober title "Slide Rules and Alcohol", which is on show at the Arithmeum in Bonn until 26 February.

Incidentally, it was these same spirits to which we today owe a large part of the poems of the Scottish national poet Robert Burns (1759-1796), who in turn paid bitterly for it with his early death in the year. It should not go unmentioned that a milkmaid named Mary Campbell also played a not inconsiderable part in Burns' success, although the young lady had none of it.

Until the early modern era, there were no suitable aids for multiplication and division. It was not until 1614 that the mathematician John Napier in Scotland published his concept of "ratios", which he translated as logarithms. The logarithm denotes how many times you have to multiply a number (the "base") by itself to get a desired result. This idea was to make tedious calculations easier for many future generations. For with the addition or subtraction of logarithms, multiplication and division can be done much more easily.

Logarithms brought the breakthrough

Ten years after Napier's discovery, the English theologian and mathematician Edmund Gunter was the first to write logarithmic scales on a rod, which still had to be read with a compass. By the middle of the century, however, there were already straight slide rules with a fixed and a movable scale. The addition of two distances on both scales corresponded to the multiplication of the two read values (how this works: see the picture above using the example of a slide rule from the middle of the 20th century).

"One of the first important applications in practical use was for the correct calculation of barrel contents," reports Professor Ina Prinz, director of the Arithmeum. If the British subjects regularly drank liquor and were subsequently useless, the crown at least wanted to collect its share in the form of taxes - but first had to have the tax amount calculated.

A poet as tax official

"There are several ways of approaching this question if one wants to deduce its contents from the barrel," Prinz explains. "The most pragmatic is to open the barrel and taste the contents until the barrel is emptied." But since in such a case there would be nothing left to tax, another method had to be found, which in short can be reduced to the formula: Cask volume minus missing contents times alcohol content (supplemented by the factor "corruptibility of the official").

These officials were called "excisemen" in 18th century Britain. One of them was the aforementioned poet Robert Burns. After the farmer's son had gone bankrupt due to several bad harvests and an economic crisis and had also failed in flax processing, he was already planning to emigrate to Jamaica when the milkmaid Mary Campbell persuaded him to stay.

How to calculate the contents of a barrel

Burns had dedicated a few passionate songs to this young woman from his neighbourhood. Published in an anthology, they made him famous and also brought him a net profit of 20 pounds sterling (about 3500 euros in today's purchasing power). Incidentally, if Mary had deliberately made eyes at Robert, this was a milkmaid's calculation, for she received no share of the royalties. Burns' ambition, on the other hand, was aroused, and his Jamaica idea remained a fluff piece. But because poetry wasn't enough to live on, a short time later, sponsored by friends, he started working as a salaried tax officer with distillers - and used the long journeys to write poetry.

It was quite a lucrative job, but not an easy one, as Professor Patrick Rocca demonstrated with a practical exercise in Burns' garb on the day of the exhibition opening. Using yardsticks, Rocca first measured the diameter of a sample barrel at the rim and in the bulbous centre of the barrel and formed an average. Half the diameter, i.e. the radius, squared and multiplied by the circle number Pi and the barrel height gives the barrel volume. In the test, the result (192.5 litres) was still 2.5 litres away from the barrel manufacturer's specification. Like a student of magic, Rocca used various calculating rods for the individual calculation steps, then measured the actual fill level with a sighting rod as if checking the oil level.

Corrupted with high-proof alcohol

Since the tax was calculated according to the alcohol content of the contents, a test glass also had to be drained. Ina Prinz dropped a brass ball into it. In the 18th century, this was sized so that it floated on top at 57 percent alcohol by volume and a defined temperature. With the addition or removal of weights, it was easy to determine a tax-lowering "underproof" (weaker content) or a tax-increasing "overproof" (stronger content).

However, there were also plenty of opportunities to go wrong when measuring (just out of clumsiness, of course!). "Because the contents of the glass were not supposed to go to waste and one wanted to make the excisemen feel positive, they were probably often offered something," Prinz suspects. With consequences: Many of them were dismissed alternately for drunkenness or corruptibility. Robert Burns also became addicted to alcohol and died at the age of 37. The poet saw the evil coming: Before his death, he wrote a poem with the theme "The devil take the Exciseman".

It was not until the 1970s that the pocket calculator made the slide rule superfluous.

Nevertheless, his work paid off, at least in monetary terms, as Ina Prinz has calculated. The fee of 10 pounds sterling paid to the Crown for taking office was offset by 365 pounds in pensions that Burns' widow received from the state after his death (today that would be around 63,000 euros).

In the meantime, the slide rule became popular all over the world (even if in Germany it was 50 years late) and became an indispensable tool, especially for calculating mechanical, hydraulic, electrical, static, process engineering and thermodynamic components and systems. The first astronauts also had them on board their space capsules. Only the pocket calculator made them superfluous in the 1970s. Some pilots are still said to take small ones on board, reports the film accompanying the exhibition. Just in case the on-board computer goes on strike.


Multiplying a number so-and-so times by itself is called exponentiation: 10 x 10 (written 102) = 100. 10 x 10 x 10 (written 103) = 1000. The logarithm is the inverse of this calculation: 2 is called the "logarithm to the base 10 (tens logarithm) of 100", 3 is the tens logarithm of 1000 and so on. The advantage is that a) this also works for all values "in between" (for example, the logarithm of the tens of 500 is 2.69897, that of 750 is 2.87506) and b) the addition of two logarithms corresponds to the multiplication of the initial values: the sum of the logarithms mentioned (5.57403) is the logarithm of their product 375 000. Having all the logarithms available (for example, on a slide rule) therefore makes multiplication and division of even "crooked" numbers much easier. piw

Original text: Martin Wein

Translation: Mareike Graepel

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