Slide rule
Wojciech Sawicki
A few words on how to use the slide rule How to adjust the decimal point location Slide rule photos www.sawicki.cc Instructions on how to make calculations using the slide rule are available on many websites, such as International Slide Rule Museum (www.sliderulemuseum.com), so there is no need to repeat them here. Among them we discovered the following description: “Calculate 2.3 x 4.5. ... Extrapolate the answer 1.035. Do a rough approximation by rounding 2.3 to 2 and 4.5 to 5. We mentally calculate 2 x 5 = 10, so we adjust the decimal place to get 10.35 or 10.4” What you can see above is really horrible. It is true, but it is rather amusing or even childish. This is not how the slide rule should be used. Someone who wrote it did not have the faintest idea of how to perform slide rule calculations and surely had never used it professionally. Let us show them how to compute (320 x 0.0063) / 0.045. In his well-known article entitled When Slide Rules Ruled (Scientific American Magazine, May 2006), Professor Cliff Stoll wrote only about “difficulty of keeping track of the decimal point”, passing over in silence the problem of decimal place adjustment. (???!!!) To estimate the order of magnitude, i.e. to determine how many digits precede or how many zeros follow the decimal point (which is represented by a comma in Poland), making up a fraction, one must add (multiply) or subtract (divide) the magnitude of the components while taking into account their signs and adjustments as shown below. We assume that: 320000 has +6 digits so its magnitude is +6 3200 means +4 32 means +2 3.2 means +1 0.32 means 0 0.032 means –1 0.00032 means –3
The calculation result in the original example is as follows: (320 x 0.0063) / 0.045 equals (+3) plus (–2) minus (–1)
That is not all, however. We know that 2 x 4 returns a one-digit while 2 x 6 a two-digit value, which should be taken into account when performing a calculation (the same applies for dividing). There are many methods that instead of mental estimation recommend using the slide rule in a sort of “automatic” way. This generally involves identifying which number (the left 1 or the right 10) of the scale is used for each calculation (the left or the right index) or which side of the slide goes off the slide rule. The most convenient method, however, is to examine which side the cursor (sliding “window” with hairline) has been moved to along the basic scale from the original number to the calculation result, which also gives the freedom of using the inverse scale (!). Hence: - in multiplying we move the cursor to the right and subtract 1 from the number representing the order of magnitude (see example above: 2 x 4). - in dividing we move the cursor to the left and add 1 to the balance representing the order of magnitude (example: 6 : 3). - no adjustments are needed for other calculations such as multiplication, when the cursor is moved to the left (example: 2 x 6), or dividing, when the cursor is moved to the right (12 : 3). It is handy to have a slide rule that in addition to the hairline indicator has the following markings placed on the cursor: < : + 1 | x – 1 > In our example, (320 x 0.0063) / 0.045 = 4-4-8 (or 4.48), the order of magnitude is as follows: +3 + (–2) – (–1) = +2. This produces a two-digit outcome, and since no correction was needed for the above, we adjust the decimal point so as to arrive at 44.80 (or 44.8). So there you are – all the mystery of slide rule calculation. Wojciech Sawicki
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