Module Trifold

An Addition Rule

You can use a pair of rulers to add. It's easiest to think about if you imagine that the ruler only goes up to 10 inches. If you want to add 2 and 4, you could line up the 0 on the lower ruler with the 2 on the upper ruler. Then look for the four on the lower ruler and find that it lines up with 6 on the upper ruler. 2 + 4 is 6.

THE SLIDE RULE:

THE POCKET CALCULATOR OF THREE CENTURIES

The C and D scales

These are logarithmic scales. The logarithms of the numbers on the scale are evenly spaced. Pairs of numbers which have the same ratio are the same distance apart.

8:2 = 4:1. You can check and see that 1.6 and 6.4 are also the same distance apart as 1 and 4.

A History of the Slide Rule

Backdrop: Turn of the century ca 1600

Elizabeth I is Queen of England.
Shakespeare is writing plays and poetry.
New World: Jamestown 1607. Plymouth, MA 1620.
Copernicus had proposed the sun-centered solar system. Tycho Brahe is charting the stars at his observatory.
Kepler is analyzing large quantities of astronomical data.
The problem:
Tedious 7-digit multiplications for astronomy & navigation!
The solution:

1614 "A Description of the Wonderful Canon of Logarithms" is published by John Napier, a Scottish baron. His lifelong work: to simplify multiplication. Logarithms substitute addition for multiplication.

What if you want to add to numbers which sum to more than 10 , such as 7 and 8? If you follow the exact same procedure and then look for the number on the upper ruler, you find that the upper ruler is not quite long enough!

Instead of lining up the 0 on the lower ruler with the 7 on the upper ruler, line up the 10 on the lower ruler with the 7 on the upper ruler. Now locate 8 on the lower ruler and read 5 above it on the upper ruler. You know that the number must be somewhere between 10 and 20, so your answer is 10 + 5 or 15.

What is a logarithm?

The common logarithm, or logarithm base 10, of a number is the power to which you need to raise 10 to produce that number.
10³ (10 raised to the 3rd power) is 1,000.
The common logarithm of 1,000 is 3.
10⁵ (10 raised to the 5th power) is 100,000.
The common logarithm of 100,000 is 5.

The power to which 10 is raised doesn't have to be a whole number.
100^.301 is 2.
The common logarithm of 2 is 0.301.

Addition property of logarithms

log xy = log x + log y
Why? It's connected with the addition property of exponents.
10³ is 10x10x10.
10⁵ is 10x10x10x10x10.
Multiply: 10x10x10 x 10x10x10x10x10 = 10⁸.

1,000 x 100,000 = 100,000,000
log1,000 + log100,000 = log(100,000,000)
3 + 5 = 8

Slide rule multiplication is based on this addition property of logarithms.

Mechanical improvements:

1620 Edmund Gunter invents the Gunter scale: a logarithmic scale engraved on wood. A pair of dividers is used to measure a length and transfer it along the scale.
1630 Invention of the slide rule by William Oughtred. A pair of Gunter scales slide along each other.
Obsolescence: the pocket calculator

1960's Up until now, the slide rule has changed very little and is still in use by engineers, scientists, architects, accountants, etc. for routine calculations. Middle school students learn to use slide rules in school.
1968 Hewlett-Packard produces its first pocket calculator.
1980's Calculators are now inexpensive, convenient to use.
2000+ Pocket calculators are more powerful than computers of the 50's and 60's. Use of the slide rule is a dying art.