Mad Slide Ruling Know your A, B, Cs and DsHelping Students Understand the Basic Principles2013 Ferric Grayhttp://theferrickfiles.comPickett

PPT2Introduction

The ordinary slide rule is used to multiply and divide numbers and can do many other more complicated calculations.

To understand how it works, lets see how a slide rule for addition can be made.

Scales for Addition

A slide rule can be constructed from two linear rules to perform addition.

The X and Y rules above have been set for addition of 3.

With the 0 on the top rule above the 3 on the bottom rule, we can easily see facts like 3+4=7 and so on.

By moving the top rule, we can find other sums. The two rules form a slide rule for simple addition.

The marks and numbers on the rule are an example of a scale.

This is an example of a linear scale where the graduations are equally spaced for the entire length of the rule.

Using longer rules will allow the addition of larger numbers, but this will be impractical.

On most rules, there are finer marks or graduations. These allow the reading of fractional or decimal values.

By adding more graduations at say tenths, hundredths and thousandths, more decimal places can be achieved, but reading such scales will need a magnifier as the graduations would be too close.

These problems arise because the slide rule must be short to be practical.

Scales for Multiplication

An non-linear scale can be easily constructed.

In particular, this is a logarithmic scale. On this short scale we are representing every number from 1 to 1,000,000.

There would be 8 marks between 1 and 10; 89 marks between 10 and 100, 899 marks between 100 and 1000 and so on.

As the scale is extended, the graduations would become greater in number and closer together.

The accuracy can be increased by lengthening the scales, but to be practical, the scales need to be short.

As a result many sub-divisions cannot be marked and one must estimate their relative position.

How Scales are Used

We can measure large distances with a shorter scale. (We do not need a measuring scale the same length as the object.)

When we use shorter scales, we need to keep track of how many times the scale was used.

To multiply numbers, we use shorter scales to show the numbers 1 to 10, but we need to keep track of the decimal point by some other method.

We can use the same section over and over.

The 1 can represent 1, 10, 100, 0.1, 0.01 etc..

The 2 can represent 2, 20, 200, 0.2, 0.02 etc..

In other words, we disregard the position of the decimal point when using the scale.

As an example consider the simple problem:

This time, the D scale represents numbers between 10 and 100.

The C scale represents number between 100 and 1000.

Our difficulty will lie in how to interpret our answer.

Here the 9 would represent 9000.

Several methods for placing the decimal point will be considered in later presentations.

CreditsSlide Rule ImagesDereks Virtual Slide Rule Gallery (Pickett N600-ES Log Log Speed Rule)

Slide Borders of ScalesScientific American Slide Rule Template