About Slide Rules

Note: These pages best viewed with screen sizes of 1024 x 768, or more,
with browser window maximized. A maximized browser window on an 800 x 600
screen is the minimum usable (barely, IMO) window size.

Your browser should also support, and have enabled; html frames, Javascript, and cascading style sheets version 2 (CSS2) for all the features to work correctly.

If this page fills the whole window, and you don't see the slide rule above, then click here for correct view.

Your browser should also support, and have enabled; html frames, Javascript, and cascading style sheets version 2 (CSS2) for all the features to work correctly.

If this page fills the whole window, and you don't see the slide rule above, then click here for correct view.

What Is A Slide Rule?

It is a mechanical aid for multiplying, dividing and related mathmatical
operations by adding or subtracting distances. The major parts of a slide
rule are the fixed rules (show it),
the sliding rule (show it), and the sliding hair-line
cursor (show it).

If linear scales were used (1 = 1 inch, 2 = 2 inches; or 1 = 2.54cm, 2 = 5.08cm; etcetera), only the sum or difference can be calculated. For example:

To add 2 plus 3, a distance of 2 (green bar) has a distance of 3 (blue bar) added
to it by moving a set of numbers (a SCALE) so the blue bar starts where the green
bar ends. The sum, 5, is on the first scale where the blue bar ends.

On a slide rule with two linear scales addition and subtraction are possible. But, it becomes unmanagable with numbers greater than 100, or if one of the numbers is 10 or more times larger than the other. I will not discuss addition or subtraction on a slide rule any further.

For multiplication or division on linear scales the problem is ...
uh ... multiplied. Luckily there is a mathmatical function called
logarithm. In particular base 10 logarithms (Log_{10}), because the most
common human number system is also based on 10. (You don't actually need to
know this just to use a slide rule; though it can help to follow what's
happening.) The Log_{10} of number "X" is what power "Y" of 10 equals
"X" (log X = 10^{Y}). A feature of logarithms is if the Log_{10}
of a number is added to the log_{10}, then use the sum as the exponent of
10, the result is the same as multiplying the original numbers.

2 x 3 = 6

log 2 = 0.30102999566398119521373889472449

log 3 = 0.47712125471966243729502790325512

10^{0.77815125038364363250876679797961} = 6

log 2 = 0.30102999566398119521373889472449

log 3 = 0.47712125471966243729502790325512

0.30102999566398119521373889472449 | |

+ | 0.47712125471966243729502790325512 |

0.77815125038364363250876679797961 |

10

log_{10}2 + log_{10}3 = 0.47712125471966243729502790325512, 10^{0.47712125471966243729502790325512} = 6

Slides multiply by adding logarithmic spaced distances; and division by subtracting.

For the first few of the following pages I'll use example numbers between zero and ten. This will keep the answers greater than 1/100, and less than 100, so you can follow the pattern of what is happening. To really use a slide rule, you need to be comfortable with floatng point numbers; specifically scientific notation. If you need to "brush up" on scientific notation check some of the additional reading links below. You may wait till later to do that if you wish, because the first few pages are simple.

Additional reading:

I highly recommend Ask Dr. Math for explanations on arithmetic and mathmatic
topics. I did a search at Ask Dr. Math, and found these pages relavant to
scientific notation:

Explaining Scientific Notation,

Operations in Scientific Notation,

Rules
for Significant Figures and Decimal Places, and a link to

www.hpmuseum.org/srinst.htm "Basic Slide Rule Instructions".
Your own searches on "slide rule", "logarithm", "floating point" and
"scientific notation" may produce explanations you understand better. Checking
Ask Dr. Math's FAQ is sometimes a faster way to find an answer than
searching. (Or a smarter way to burn excess time if you're curious about math.)

The Additional Reading links will open in a new window so you can
keep your place here. But, clicking another of these links will reuse that same window
so your screen doesn't become too clutered.

This slide rule.

On a real slide rule the number tick marks can be made exactly at the position
corresponding to the number. For my digital image slide rule, in the top frame,
I chose 1000 pixels for the length from the left index to the right index. So for
marks that came close to a whole pixel I used a black line one pixel wide. The
others are two pixels wide of different grays to make it look to be in the correct
place.

In example calculations, on later pages, references to numbers on the slide rule are in brown. The format is the scale name, a vertical bar, and the number on that scale. Like: D|2.2 means 2.2 on the D scale.

An arrow image, , after a number reference pops up a larger green arrow pointing to that position when the mouse is over the small one. The pop up arrow disappears when the mouse is moved off the small one. These pointers will only be used on the "Simple" pages to help people who've never seen a slide rule before.

Number references that cause the sliding rule or cursor to move are a
lighter brown, and are "highlighted" by a lighter background color,
D|2.2. When you
click on them, the sliding rule or cursor will move to the scale|number
referenced. **Note -** After moving something, green arrows on previous numbers
will point to the **same position in the window**, possibly **NOT** where that
number currently is.

The slide rule's frame window automatically scrolls to make the last moved
to number visable. You may use your mouse to scroll the window, no
problem. The amount of scroll is based on an 800 pixel width
window. Wider windows **may** not need as much scroll, but it is
okay. The number appears closer to the center of the window.

Example calculations will be in a box. Here are examples for this section:

D|2.2
(Number ref. with pointer.)

C|1 to D|2.2 (A move ref. After clicking the move, notice that the C|1 arrow points to empty space.)

C|1 to D|9.8, find C|8.9 (Shows two auto scrolls.)

C|1 to D|2.2 (A move ref. After clicking the move, notice that the C|1 arrow points to empty space.)

C|1 to D|9.8, find C|8.9 (Shows two auto scrolls.)

Copyright © 2004, Dale Yarker