Using a slide rule

Close up of sliderule

Slide rules use the concept of logarithms to allow complex calculations to be done by simply adding linear quantities on adjacent but independently moved logarithmic scales.

To multiply two numbers, get the values in scientific notation, i.e. a * 10^''b''. Take the abcissa a from the first number. Slide the center part so that the number "1" (referred to as the index) on the C scale to the number a on the D scale. Then find the the abcissa of the second number on the C scale. See what's right below it on the D scale — this should be your answer.

You still need to handle the exponent part, but that's simple: 10³ * 10² = 10³⁺² = 10⁵. Used correctly, you can get about three significant figures out of your use of the slide rule.

The basic theory here is you use the properties of logarithms to change multiplication into addition. log x + log y = log x*y. You move the slide to the logarithm of the first number, and then add the length of log of the second number. You then read off their combined length in logarithm space, which effectively multiplies the numbers.

Slide rules came in linear, cylindrical and circular versions, the latter allow one to become completely dizzy in doing long multiplications! Cylindrical sliderules were amazingly expensive and precise. The late Dr. Issac Asimov, famed for his science and science fiction writings, owned a five foot cylindrical sliderule which he kept in the corner of his office.

You will note in the pictures that there are more scales than just the two adjacent log scales needed to perform multiplication. Most slide rules had scales for trig functions, scales for taking square roots, reverse scales for taking reciprocals, etc. The wiki article discusses some of the other scales which might commonly appear on a slide rule: http://en.wikipedia.org/wiki/Slide_rule#Other_operations

Overall view of a sliderule

Other references

• list other references about this skill here

Comments:

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2008-03-09 21:06:55   Concerning "knowledge assumed" - logarithmic scales are what make the thing work, but you don't really have to know anything about logarithms to use the device. Adding the logarithms together is done physically by lining up the scales and crosshair on the two numbers you want to multiply. You don't have to be aware of why it works when you're using it. —209.204.181.86

• So fix the entry!
  

2008-03-10 07:58:21   I would think sliding and lining up etc with no knowledge of logs is playing rather than using: a trap with using slide rules was to remember that you needed to add the exponents from each of the numbers being multiplied in order to find the answer (or subtract them when dividing) —221.133.214.214

2008-03-10 19:12:25   Well, my point would be that even many people who are fully aware of what logs are didn't necessarily think about them when using the slipstick to obtain an answer, particularly if they used them all the time. They just wanted to know what, say, 67.4 * 3.62 was for whatever reason. Knowing the general magnitude of the answer so that when they read "244" off the scale it meant 244, not 24.4 or 2440 was required of course, but there are many mental approaches to that, rather than actually thinking about adding exponents together. Personally, I'd mentally round the 67.4 to 70 and the 3.62 to 4, and know my answer was something in the rough vicinity of 280 - a bit less, since I rounded both up. I suspect there was a class of people that used slide rules on a daily basis who had forgotten what they had ever learned about logarithms. In many cases, their mental process of placing the decimal point in the answer was probably based on visualization of the physical problem they were solving.

Ability to estimate answers is something sadly lacking these days, of course. —209.204.181.86

• My wife informs me that among her undergraduate students, recognizing a mathematical answer is blatantly off is nearly never caught; there is very little common sense reckoning done to double check an answer.