What is a slide rule?

Date: 07/27/97 at 14:59:59
From: Cherie
Subject: What is a slide rule?

Hi,

My parents once showed me this funny slidey thing called a "slide 
rule."  It looked really confusing to me. What does a slide rule do 
and how does it work?

Cherie

Date: 07/29/97 at 13:09:42
From: Doctor Rob
Subject: Re: What is a slide rule?

The slide rule was what engineers and scientists used to do 
calculations before the invention of the electronic pocket calculator.

The main feature of the slide rule is two scales, one on the fixed 
part of the object, the other on the sliding part, each marked with 
little tick marks and numbers from 1 to 10. The marks are not evenly 
placed, as they would be on a ruler. Instead, they are placed in such 
a way that their distance from the 1 mark is the common logarithm of 
the number they represent. In other words, the mark for 3 is located 
about 0.4771 units from the mark for 1, because 3 = 10^(0.4771), 
approximately. The unit here is the distance from the 1 mark to the 
10 mark, which is the length of the entire scale. Similarly the mark 
for 2 is located about 0.3010 units from the mark for 1, because 
2 = 10^(0.3010), approximately.

To use the slide rule to multiply numbers, find the tick mark on the
fixed scale representing one of the numbers. Slide the slide so that
the "1" mark on the slide lines up exactly with that mark. Then find
the tick mark on the sliding scale which represents the other number.
Directly opposite it on the fixed scale is a new tick mark, which
represents a third number. That third number is the product of the
first two.  As an example, to multiply 2 times 3, find the tick mark
on the fixed scale marked "2".  Slide the slide until the "1" mark on
it is opposite the "2" on the fixed scale.  Find the mark "3" on the
sliding scale.  Opposite it on the fixed scale is a tick mark which is
labeled "6", which is the product.

               -------------------------------------------------
 Sliding Scale | 1                   3                       10|
               |_|___________________|_______________________|_|
 --|-------------|-------------------|---------|--
 | 1             2                   6         10|   Fixed Scale
 |_______________________________________________|

This works because of the law of exponents:  10^a * 10^b = 10^(a+b).
In the example, 2*3 = 10^(0.3010)*10^(0.4771) = 10^(0.3010 + 0.4771)
= 10^0.7781 = 6.

A similar method allows one to divide.

Of course not all the tick marks have labels, just as they don't on
most rulers, and you have to figure out what number is represented 
by what mark.  Furthermore, many numbers do not have tick marks to 
represent them, so you may have to imagine a virtual tick mark between 
real ones.

Many slide rules have more scales than just the two described above.
Often there is a scale to allow squaring, which goes from 1 to 100.
There is usually a reverse scale from 10 to 1 to compute reciprocals.
There may be an evenly marked scale, like a ruler, which allows
computing of logarithms. Some have more scales to deal with
exponentials and trigonometric functions like sine, cosine, and
tangent.

Another feature of a slide rule was a transparent slide bearing a
hairline mark perpendicular to the scales. This was to assist in
reading extra scales, and deciding which tick marks on one scale
correspond to which ones on another scale.

A real drawback to this device is that three digit accuracy was pretty
much the limit given the technology.  Another drawback was that adding
was not easy to do!  :-) 

See:

   Basic Slide Rule Instructions - MoHPC
   http://www.hpmuseum.org/srinst.htm

-Doctor Rob,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/