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The Slide Rule: A Historical Analog Calculation Device, Study notes of Mathematics

The slide rule is a historical mechanical calculator that uses logarithmic scales for multiplication and division. Invented around 1630, it gained popularity during the 19th and 20th centuries, especially among engineers. An overview of the slide rule, its history, advantages, disadvantages, and a review of logarithms.

Typology: Study notes

2009/2010

Uploaded on 02/25/2010

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The Slide Rule
A slide rule is a mechanical analog device, consisting of two finely divided scales with a
movable inner one, and a sliding window called a curser.
The slide rule is used primarily for multiplication and division, but can also be used for
functions such as trigonometric functions, square and cube roots, exponential functions, and
logarithms. It does not do well with addition or subtraction.
Before calculators, this was the most commonly used instrument for doing mathematical
computations.
The use of the slide rule grew through the 1950s and 1960s, even as digital computing
devices were being developed. In the early to mid 1970s, however, the electronic scientific
calculator was introduced, and the slide rule quickly became obsolete.
The slide rule uses logarithmic scales to allow for quick computations. It builds on the fact
that:
log(xy) = log(x) + log(y)
log(x/y) = log(x) – log(y)
In general, mathematical calculations are performed by aligning a mark on the sliding
central strip with a mark on one of the fixed strips, and then observing the relative positions
of other marks on the strips.
The user needs to determine the location of the decimal point in the result, based on mental
estimation.
History
The slide rule was invented around 1620-1630, shortly after John Napier’s publication of the
concept of logarithm.
Edmund Gunter of Oxford developed a calculating device with a single logarithmic scale
that could be used for multiplying and dividing.
William Oughtred in 1632 combined two logarithmic scales directly opposite each other to
do calculations.
The more modern form of the slide rule was created in 1859 by French artillery lieutenant
Amedee Mannheim. It was around that time that engineering became a professional field,
and this helped spread the use of a slide rule across Europe.
They did not become common in the U.S. until 1881, when Edwin Thacher introduced the
cylindrical rule.
During the 19th century, Germany had a steel slide rule about 2 meters long that was used at
one astronomical observatory. It had a microscope attached giving it 6 decimal places of
accuracy.
Throughout the 1950s and 1960s, the slide rule became the symbol of the engineer’s
profession, in the same way that a stethoscope symbolized the medical profession.
Traditionally slide rules were made out of hard wood such as mahogany or boxwood with
cursers made out of glass and metal. Later they were made out of plastic or aluminum and
the cursers were made of acrylics.
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The Slide Rule

  • A slide rule is a mechanical analog device, consisting of two finely divided scales with a movable inner one, and a sliding window called a curser.
  • The slide rule is used primarily for multiplication and division, but can also be used for functions such as trigonometric functions, square and cube roots, exponential functions, and logarithms. It does not do well with addition or subtraction.
  • Before calculators, this was the most commonly used instrument for doing mathematical computations.
  • The use of the slide rule grew through the 1950s and 1960s, even as digital computing devices were being developed. In the early to mid 1970s, however, the electronic scientific calculator was introduced, and the slide rule quickly became obsolete.
  • The slide rule uses logarithmic scales to allow for quick computations. It builds on the fact that: log(xy) = log(x) + log(y) log(x/y) = log(x) – log(y)
  • In general, mathematical calculations are performed by aligning a mark on the sliding central strip with a mark on one of the fixed strips, and then observing the relative positions of other marks on the strips.
  • The user needs to determine the location of the decimal point in the result, based on mental estimation. History
  • The slide rule was invented around 1620 - 1630, shortly after John Napier’s publication of the concept of logarithm.
  • Edmund Gunter of Oxford developed a calculating device with a single logarithmic scale that could be used for multiplying and dividing.
  • William Oughtred in 1632 combined two logarithmic scales directly opposite each other to do calculations.
  • The more modern form of the slide rule was created in 1859 by French artillery lieutenant Amedee Mannheim. It was around that time that engineering became a professional field, and this helped spread the use of a slide rule across Europe.
  • They did not become common in the U.S. until 1881, when Edwin Thacher introduced the cylindrical rule.
  • During the 19 th century, Germany had a steel slide rule about 2 meters long that was used at one astronomical observatory. It had a microscope attached giving it 6 decimal places of accuracy.
  • Throughout the 1950s and 1960s, the slide rule became the symbol of the engineer’s profession, in the same way that a stethoscope symbolized the medical profession.
  • Traditionally slide rules were made out of hard wood such as mahogany or boxwood with cursers made out of glass and metal. Later they were made out of plastic or aluminum and the cursers were made of acrylics.

Advantages

  • A slide rule moderates the fallacy of false precision.
  • A slide rule requires a continual estimation of order of magnitude, since one needs to determine the placement of the decimal point his/herself.
  • When performing a sequence of multiplication or division by the same number, you simply need to glance at the slide rule to get multiple answers.
  • A slide rule can be easily replicated without electrical knowledge. Classroom sets can be made out of paper or cardboard.
  • They are highly standardized so you don’t have to “relearn” when you switch to a new one.
  • At the time that they were popular, they were much less expensive than current calculators. Disadvantages
  • Errors may arise from mechanical imprecision.
  • Calculations are limited in precision. They are more like estimations than calculations.
  • Depending on the calculation, calculators will sometimes be quicker. Review of Logarithms log(1) = 0 log(10) = 1 log(100) = 2 log(1000) = 3 etc. The log of any number between 1 and 10 is between 0 and 1. The log of any number between 10 and 100 is between 1 and 2. The log of any number between 100 and 1000 is between 2 and 3. Etc. Also note, log(3) = .477121… log(30) = 1.477121… log(300) = 2.477121… Guess what log(3000) is…. Also note that 3000 = 300 x 10, so log(3000) = log(300) + log(10).