Everyone seems to be able to come up with a slide rule, but let's face it: not many people know how to use them anymore. With practice, though, using a slide rule can be faster than punching the same arithmetic or trigonometry into a TI-89. Unless you try to punch straight algebra into a slide rule. That just doesn't work. Thus, a good math grounding is essential for efficient slide rulings.
Here's what a slide rule can do for you: (this list also shows you the contents)
Neat, huh? However, there's beginner stuff to be gone over first.
How to Hold a Slide Rule
Hold the slide rule horizontally, and with both hands. Hold it overhand, i.e. with your hands on top, palms facing the slide rule (but don't let the palms touch it). Your thumbs, which are on the bottom, are on the runner, which is that clear plastic piece. This setup allows for easy, quick, and precise adjustments.
How to Read a Number from the Slide Rule
Slide rules are generally accurate to three significant digits. (i.e. they can multiply 13 and 243, but if you attempt 3 and 7664, there will be some rounding.) A scale on the slide rule is divided into three parts: divisions, sections, and spaces. A division is the area between two numbers, of the first digit. A section is the area between two numbers of the second digit, and a space is the area between the numbers of the third digit. For those who need a picture:
| | |
| i | i | i | i | i | i | i | i | i | i |
Between 4 and 5 is a division, between the double pipes is a section, and between the 'i's is a space. Thus, with 4 significant digits, estimation is a problem.
There are many scales on a slide rule, some more functional than others. There's the C (and CI) and D scales, which are used for multiplying and dividing, as well as a starting point for all the other functions. Also, there's the A and K scales, which are used for squaring and rooting respectively, the L, LL1, LL2, LL3 scales for logarithms, and finally the trig scales S, T1, T2, DF, ST, and P. Note that on each scale, decimal points are irrelevant. Thus, 23, 2.3, .0023, and 23000 are on the same spot. When working with numbers not directly indicated on the scale, remember to keep track of the decimal point.
Beginner stuff over. On to neat stuff.
- Multiplication: Move the slide (the center piece with scales on it) so that the number 1 of the C scale is over the first number to be multiplied on the D scale. Then, move the runner to the second number to be multiplied on the C scale. Then, read the answer under the runner of the D scale. For example, to multiply 35 and 72, move the slide so that one end of the C scale is at 35 (or 3.5 on the scale), and the runner can be moved to 72(or 7.2). If 72 is off the slide rule, then you've picked the wrong end. Now, move the runner to 72 and read the number under the runner on the D scale. Adjust the decimal point, if necessary. This is your answer, which is 2520(or 2.52).
- Division: Division works exactly backwards from multiplication. To divide, simply place the runner over the dividend on the D scale, then slide the divisor on the C scale so it lines up with the dividend. Then, read the answer (adjusting for decimals if necessary) off of the D scale, directly under one end of the C scale.
- Squaring: Move the runner over the number to be squared on the D scale, then look under the runner on the A scale for the answer. Adjust decimals if necessary. To square root, do the opposite. Find the number on the A scale, answer is on the D scale.
- Cubing and Cube rooting: Same as squaring, except the K scale should be used instead. Same goes for rooting.
- Sines, Cosines, and their inverses: Using the runner, locate the angle in degrees on the S scale. The answer is under the runner on the D scale. Note: when using cosine, the angle values should be a different color and reverse of the sine values. To find the inverse, move the runner over the number on the D scale, and the sine or cosine is under the runner on the S scale.
- Tangents and Co-tangents: Use the runner to line up the angle (on the T1 or T2 scale) for the calculation. Make sure that the slide is even, by comparing the C and D scales. Where one says 1, the other should say 1. Then, read the C scale (or D scale, if that's your thing) and find your answer. Do the opposite (by locating with C and reading with Tx) to find tan-1.
- Logarithms: Use the runner to line up your number (C or D scale) to be logged. Look on the L scale to find the answer. Antilog in reverse.
Care for Your Slide Rule
Don't bend it. Don't break it. It won't work right if you do. </commonsense>
If you find that the slide has difficulty moving, detach it from the slide rule, and run a pencil over its edges. This provides lubricant as well as dirt removal. Also, make sure that the screws in the runner are tight. If they fall out, you'll have to put them back in before the slide rule will work again.
In time, you'll be faster than a calculator. Back up your slide ruling skills with some algebra and you'll be set for whatever comes your way!
ariels says re Slide rule : Maybe mention the fast way to compute fractions like (a*b*c)/(d*e*f)? Instead of computing (a*b*c) and then dividing by d, then e, then f, compute a, divide by d, multiply by b, divide by e, multiply by c, finally divide by f. This is much faster, because you already line up one scale for the next operation (try it and you'll see -- mine is a rotten explanation for a simple thing).
What ariels means is that it's faster to just do a/d*b/e*c/f, and just alternate between the multiplication terms and the division terms. And it is.