What is a slide rule?Date: 07/27/97 at 14:59:59 From: Cherie Subject: What is a slide rule? Hi, My parents once showed me this funny slidey thing called a "slide rule." It looked really confusing to me. What does a slide rule do and how does it work? Cherie Date: 07/29/97 at 13:09:42 From: Doctor Rob Subject: Re: What is a slide rule? The slide rule was what engineers and scientists used to do calculations before the invention of the electronic pocket calculator. The main feature of the slide rule is two scales, one on the fixed part of the object, the other on the sliding part, each marked with little tick marks and numbers from 1 to 10. The marks are not evenly placed, as they would be on a ruler. Instead, they are placed in such a way that their distance from the 1 mark is the common logarithm of the number they represent. In other words, the mark for 3 is located about 0.4771 units from the mark for 1, because 3 = 10^(0.4771), approximately. The unit here is the distance from the 1 mark to the 10 mark, which is the length of the entire scale. Similarly the mark for 2 is located about 0.3010 units from the mark for 1, because 2 = 10^(0.3010), approximately. To use the slide rule to multiply numbers, find the tick mark on the fixed scale representing one of the numbers. Slide the slide so that the "1" mark on the slide lines up exactly with that mark. Then find the tick mark on the sliding scale which represents the other number. Directly opposite it on the fixed scale is a new tick mark, which represents a third number. That third number is the product of the first two. As an example, to multiply 2 times 3, find the tick mark on the fixed scale marked "2". Slide the slide until the "1" mark on it is opposite the "2" on the fixed scale. Find the mark "3" on the sliding scale. Opposite it on the fixed scale is a tick mark which is labeled "6", which is the product. ------------------------------------------------- Sliding Scale | 1 3 10| |_|___________________|_______________________|_| --|-------------|-------------------|---------|-- | 1 2 6 10| Fixed Scale |_______________________________________________| This works because of the law of exponents: 10^a * 10^b = 10^(a+b). In the example, 2*3 = 10^(0.3010)*10^(0.4771) = 10^(0.3010 + 0.4771) = 10^0.7781 = 6. A similar method allows one to divide. Of course not all the tick marks have labels, just as they don't on most rulers, and you have to figure out what number is represented by what mark. Furthermore, many numbers do not have tick marks to represent them, so you may have to imagine a virtual tick mark between real ones. Many slide rules have more scales than just the two described above. Often there is a scale to allow squaring, which goes from 1 to 100. There is usually a reverse scale from 10 to 1 to compute reciprocals. There may be an evenly marked scale, like a ruler, which allows computing of logarithms. Some have more scales to deal with exponentials and trigonometric functions like sine, cosine, and tangent. Another feature of a slide rule was a transparent slide bearing a hairline mark perpendicular to the scales. This was to assist in reading extra scales, and deciding which tick marks on one scale correspond to which ones on another scale. A real drawback to this device is that three digit accuracy was pretty much the limit given the technology. Another drawback was that adding was not easy to do! :-) See: Basic Slide Rule Instructions - MoHPC http://www.hpmuseum.org/srinst.htm -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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