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See how calculations used to be done before the days of electronic calculators. Find out about an important piece of engineering history. All pieces of the slide rule are draggable.

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### The Slide Rule

Before electronic hand held calculators, the slide rule was widely used in Engineering, Science and Commerce for rapidly performing calculations involving multiplication and division which have to be accurate to not more than three or four decimal places. It can also be used for such operations as involution (raising to a power) and evolution (extraction of a root) and for calculations with trigonometric functions (sine, cosine, tangent, cotangent).

In addition to those for general use there where many different types of special purpose slide rules. What they all have in common is logarithmic scales.

A standard slide rule consists of the actual rule, the slide and the transparent cursor with a hair line. Various logarithmic scales are engraved on the rule and the slide. When the rule is "closed", the pairs of scales A & B and C&D respectively, coincide.

#### Example of a simple MULTIPLICATION

Use scales C & D

The index line on scale C is always put over the number to be multiplied on scale D. The answer is then read off scale D, below the multiplying, number on scale C, using the cursor line for ease and accuracy

e.g. set the 1 on scale C over the 2 on scale D (**note:** this is not the first 2 you can see as this is actually representing 1.2, it's the larger 2). You can now read off 4, 6, 8, 10 etc. on scale D under the figures 2, 3, 4, 5 etc. on scale C (Use the cursor line to find the answer).

Then if you slide the 10 on scale C over 2 on scale D you can read multiplication answers of 2 x 5, 6, 7, 8 & 9 beneath each number, so completing the scale (Use the left or right hand index,depending on the numbers to be multiplied)

**Exercise** : multiply 13.2 by 2, by 6, by16, by 9, by 72

(answers: 26.4, 79.2, 211.2, 118.8, 950.4)

#### N.B. the decimal point

When starting a calculation it is as well to make a mental note of where you expect the decimal point to appear in the answer, or if necessary, do a rough longhand reckoning to find out. For instance the Slide Rule's answer to 3.75 x 8.95 is 336. If we "round up" to 4 x 9, we know that the answer is 36. Clearly the answer then is 33.6.

#### Example of a simple DIVISION

Use scales C & D

This is very simply achieved by sliding the divisor on scale C over the number to be divided on scale D and reading the answer off on scale D under the left or right hand index

e.g. 8 divided by 2 = 4

Slide 2 on scale C over 8 on scale D using the cursor to help. Read off 4 on scale D under the L.H.I.

**Exercise** : divide 48 by 8, 392 by 14, 110 by 5, 2468 by 3.7

(answers : 6, 28, 22, 667 )

### Interesting facts

- The slide rule was invented around 1620 - 1630.
- Many people still use slide rules to this day, with a little practice you can perform calculations to a reasonable estimate very quickly.
- The military in many countries still teach slide rules as a backup in case of calculator malfunction
- Slide rules have even been used by astronauts. They have been used on 5 of the Apollo space missions.
- Some people belive the advent of electronic forms of calculation to have tainted the art of engineering. eg. When computers were first introduced new engineers went to them to solve problems that experienced engineers could solve quickly with a few quick uses of a slide rule. In fact several computer centers at the time had a framed slide rule hanging on the wall with the message "In case of emergency, break glass".
- Many people like to use a slide rule as a check to make sure they have calculated correctly on a calculator or computer. The slide rule will only be an estimate (though normally quite a close one) and will have to be done slightly differently, minimising the chances of duplicating mistakes.