In 10 years, your
computer will be in
the landfill, but
your slide rule will be
operating just as fast as
it did in 1700. As an
engineer from the
1970s, I have a nostalgic
place in my heart for
■ FIGURE 1. Simple Linear Slide Rule.
■ TABLE 1. Approximations to “e.”
What is a Slide Rule?
The slide rule (often called a
“slipstick”) is a mechanical analog
computer, consisting of at least two
finely divided scales (rules), most
often a fixed outer pair and a movable inner one, with a sliding window called the cursor. Before the
advent of the pocket calculator, it
was the most commonly used calculation tool in science and engineering. The use of slide rules continued
to grow through the 1950s and
1960s even as digital computing
devices were being gradually introduced; but in the early 1970s, the
pocket electronic calculator made
slide rules largely obsolete and most
suppliers exited the business.
Simple Slide Rule
Let’s look at the simplest example of a slide rule. We will make a
simple adding slide rule from two
12 inch rulers marked in millimeters.
If we line the rulers up as shown
in Figure 1, we can add small
numbers. From the ruler, we see
that 5 + 6 = 11. While the linear rule
is useful as an example for addition
or subtraction, the real break for
slide rules occurred in 1614 when
John Napier — a Scottish scholar —
invented the logarithm.
In order to understand how slide
rules can multiply and divide, we
must investigate logarithms. A logarithm is just an exponent. For example, the logarithm of a number x to a
base b is just the exponent you put
onto b to make the result equal x.
For instance, since 32 = 9, we know
that 2 (the power) is the logarithm of
9 to base 3. Symbolically, log3( 9) = 2.
More generically, if x = by, then we
say that y is “the logarithm of x to the
base b.” In symbols, y = logb(x).
Every exponential equation can be
rewritten as a logarithmic equation,
and vice versa, just by interchanging
the x and y in this way. Commonly
used bases are 10 and e. Logarithms
that use e as the base are known as
“natural” logarithms and are written
as ln. Base 10 logarithms are written
as log. For the natural logarithm, we
can write the relationship ex = y and
x = ln(y).
But what is this “e?” Numerically,
e is about 2.7182818284; “e” (like pi)
crops up in all sorts of places.
Perhaps its first use was in the
computation of compound interest.
Babylonian tablets from 1700 BC ask
Savings = Principal(1+Interest Rate/Compounding Period)