The Slide Rule Essay, Research Paper
The slide rule is mechanical device used by mostly engineers and scientists for fast and accurate
multiplication, division, to find roots and powers, and other simple math problems. It consists of a fixed
section with upper and lower parts marked with different logarithmic scales, a center part that slides
between the parts of the fixed section and is also marked with scales, and a clear cursor that can be moved
to help align the scale marks. The slide rule has almost been totally eliminated because of the 1970?s
invention of the hand-held electronic calculator. Today it is mostly used by engineers and collected by
antique collectors. A basic slide rule from the 1940?s that cost thirty dollars at the time would now be
worth over two hundred dollars.
Most people think that the only type of slide rule is the one that is straight and almost resembles a
ruler. There are really three types of slide rules. The first type is the most common one, the Mannheim.
This is basically a long stick with a movable centerpiece as well as a movable window, called the center
piece, to work out math problems.
The second type is the circular slide rule. These are virtually the same as the Mannheim, but bent around in
a circle. The cursor is a pair of radial arms that move around the center or origin. The advantage of a
circular slide rule is that you can fit a longer scale within a certain area.
The third type is the cylindrical slide rule. These are the hardest kind of slide rule to come by and are very
rare today. They are also similar to the Mannheim?s, but the scales are wrapped around a cylinder. These
are the most accurate of slide rules, and also the most expensive, because they are made to be the most
precise and have the longest scales to work with.
The history of the slide rule dates back to 1614 when John Napier discovered the logarithm. This
made it possible to perform multiplication and divisions by addition and subtraction. Even though this was
a great time saver, there was still a lot of work required. The mathematician had to look up two logs, add
them together, and then look for the number whose log was the sum. Edmund Gunter soon reduced the
effort by drawing a number line in which the positions of numbers were proportional to their logs.
The scale started at one because the log of one is zero. Two numbers could be added by measuring the
distance from the beginning of the scale to one factor with a pair of dividers, then moving them to start at
the other factor and reading the number at the combined distance. In 1621, William Oughtred simplified
things further by taking two of Gunter?s lines and sliding them relative to each other which eliminated the
In the years that followed, other people refined Oughtred?s design into a sliding bar held in place
between two other bars. The first slide rule in which a sliding scale moved between two fixed sections was
made in 1654. Later on, circular and cylindrical slide rules were developed. The cursor appeared on the
earliest circular models, but appeared much later on straight versions. By the later 17th century, the slide
rule was a common instrument with many different variations. The present form of the slide rule was
developed in 1850 by a French army officer, Amedee Mannheim.
It was the math tool of choice and was used by everyone from tax collectors to Sir Isaac Newton.
By the 20th century, it was especially known as the engineers companion. In college campuses around the
world, engineering students could be recognized by the slide rules they carried in leather cases and strapped
to their belts. Yet, what commonly happens to most inventions happened to the slide rule. The once great
math tool was then almost irrelevant when Hewlett-Packard introduced the HP 35 pocket scientific
calculator in the early 1970?s. Since then you usually only find slide rules in an engineer?s desk or at an
The basic slide rule instructions start out with multiplying numbers on the slide rule. To multiply
two numbers on the typical slide rule, the user sets the left index (start of the scale) on the C scale to line up
with one factor on the D scale. The user then finds the second factor on the C scale and looks on the D for
the product. By doing this, the user effectively added the logs (lengths) of the two numbers and look up the
Multiplication with more than a single digit were carried out by making use of the smaller
graduations to represent additional digits of decreasing significance. The accuracy the slide rule gave
depended on the size of it. Also, the slide rule did not indicate the decimal point and the user usually had to
estimate. For example:
Here the answer is 7, which is changed to the hundreds to equal 700. If you multiply 42.2 and 16.6 you
will find that the answer is 700.52.
Division was performed by reversing the multiplication steps (setting the divisor on the C scale
opposite the dividend on the D scale and reading the result of the D scale under the C scale index). To
multiply multiple numbers, the user simply moved the C index to the previous product to start the next
Slide rules have drawn on them a variety of scales, depending on what one you have or need.
These scales originally went by a variety of names, but since the introduction of the Mannheim they have
been standardized as follows:
C,D- These are the basic multiplication scales.
A,B- These scales are also used as multiplication scales. More importantly they are the squares of C and D
CF,DF- These are also called the folded scales. They are constructed the same as the C and D scales, but
start and at pie (3.14).
CI, DI, CIF, DIF- These are the inverse scales. They are exactly the same as the C and D scales, but
arranged right to left. Numbers appearing on these scales are the reciprocals of the basis scale.
S, T, ST- These are the basic trigonometry scales.
K- This scale is used for finding cubes and cube roots.
L- This scale is used to find common logarithms directly.
LL0, LL1, LL2, LL3- These are called the LL scales and are used to obtain powers and roots of numbers
from 1.001 to 22,000.
Ln- This scale is used to find the natural logarithm directly.
Sh, Th- These scales are for the sine and tangent functions.
P- This is the Pythagorean scale, used in finding the base of a right triangle if the hypotenuse and heights
This picture shows a full scaled or complicated slide rule.
Even though slide rules are obsolete today, they are still around. Many collectors today trade,
buy, and sell slide rules. These collectors developed their own ?slide rule society?, called The Oughtred
Society. The Oughtred Society was formed in 1993 to serve the needs of the growing number of slide rule
collectors. Starting out with only 11 charter members in June of 1991, the society has grown to become a
worldwide organization with over 350 members. The society has established a journal, published a bi-
annual swapsheet (which is like the classified ads of slide rule collectors), and sponsored a series of popular
annual meetings and conventions of collectors. The society has become a valued network for contact and
exchange between slide rule collectors.
The slide rule was once a great invention that lasted for over three hundred years. They were
used by some of the earliest of mathematicians to help develop theories or ideas that they are now famous
for. Now, hand-held calculators are used everywhere from the classroom to a construction site. They were
a crucial part of the development of modern math and have helped in the world advance in technology.