Slide rule tutorial?

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Slide rule tutorial?

Postby ks_physicist » Thu Aug 30, 2007 10:47 pm UTC

My curiosity has the best of me, and I am looking for a good tutorial to learn how to use a slide rule. I figured out some functions, but I am not proficient and I think I probably don't know the tricks and shortcuts.

I have three of them, a POST/Hemmi, a Pickett Microline 120 (found behind a drawer in my office desk while I was a grad student!), and a Pickett Trainer 120 that came free with the POST/Hemmi.
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Postby Nimz » Thu Aug 30, 2007 11:37 pm UTC

Are you looking for something online tutorial, or for someone to write up a tutorial here? If you're looking for the latter, I can probably give you a good start. I'll need (one of) my (three) slide rule(s) in front of me to make sure I don't mislabel the scales, and the like. I might even be able to find the manual that came with my grandfather's Ricoh slide rule. Most (if not all) of what's there should be applicable to Pickett slide rules, too.

[edit: adding mini-tutorial]
I'm basing this mini-tutorial on my Pickett Microline 140.

Multiplication is usually done with the C and D scales, though it can be done with the CF and DF scales and even the B and A scales. Slide the 1 on the C scale (or CF or B, respectively) next to the first factor on the D scale (or DF or A, respectively). Then put the hairline on the second factor on the C scale and read off the product on the D scale. So 2x3 should look something like:
Code: Select all
  -------------------------------------------
  -------------------------------------------
  |            ------------------------------|----------
C |            1------------2-----3-----4--5-|6--7--8-91
D 1------------2------3-----4--5--6--7--8-91-
  -------------------------------------------

The 1 on the C scale is lined up with the 2 on the D scale, and the 3 on the C scale is lined up with the answer to 2x3 on the D scale. I don't think I'm going to be doing any more ascii pictures.

With division, you do the opposite as multiplication. Dividend / Divisor = Quotient, so you line the dividend on the D scale up with the divisor on the C scale and read off the quotient (lined up with the 1 on the C scale) on the D scale. Using the same picture, 6/3 = 2. Cake and pie, right? Piece of cake and easy as pie.

So you want to extract square roots, do you? Well, that's what the A and B scales are for. To find the square root of 5, line up the hairline with the (first) 5 on the A scale and read off the answer on the D scale, or you can use the B and C scales, respectively. If you want to find the square root of 50, line up the hairline to the second 5 on the A scale and read off the answer on the D scale. Sqrt 10 = 3.16... and not 1 followed by zeros. That's why you need two copies of every number on the A and B scales. You have to be very careful of whether the power of ten is even or odd.

Squares are the reverse direction of square roots. Go from D to A instead of A to D.

Cube roots use the K scale with the D scale (K to D). The process is just like square roots. Likewise for cubes. 3/2 powers and 2/3 powers are simple extensions using the K and A scales.

What are the CI and DI scales for? They are the reciprocals of the C and D scales, respectively. You can use that as an alternate method for division, for instance.

The S, ST, and T scales are for trig functions. If you want to know what sin(35 degrees) is, find where the second number on the S scale is 35 (the first number is for cosine) and drop the hairline down to the C scale. I get about 0.573 or 0.574 on my slide rule. Windows calculator says 0.57357643635104609610803191282616, fwiw.

Arcsin and arccos are done in the opposite direction. You are limited in that you cannot get, say arcsin 0.05, but at that point, you may as well use small angle approximations, anyway and just multiply (by the R on the C and D scales - it's right at 180/pi).

The ST scale is for sec and csc, much like S is for cos and sin. Everything should work the same way. Likewise, T is for cot and tan.

LL1, LL2, and LL3 are for e^x and ln x. There are two of each of these scales: LL1 has one marked -0.01 and one marked +0.01 (if you look on the left side, that is. The right side has -0.1 and +0.1... there's a good reason for that, but whatever. I'm not going into that.). LL2 has one marked -0.1 and one marked +0.1. LL3 has one marked -1.0 and one marked +1.0. If you want to find e^0.125, find 1.25 on the D scale and read off the answer on the LL2(+0.1) scale. The +0.1 refers to the fact that you multiply 1.25 by +0.1 to get 0.125.

If you want to know ln 0.98, find 0.98 on one of the LL scales (LL1(-0.01)) and read your answer off on the D scale. Then mentally multiply by -0.01 to get approximately -0.02020.

The only scale left to talk about, then, is the L scale. That gives you the common log of the C scale (and that's why everything is evenly spaced on the L scale). If you want to know log 57.5, move the hairline to 5.75 on the C scale and read off the L scale (don't forget to add the characteristic, 1, to the answer, since L only gives you the mantissa). The reverse process gives you 10^x.
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Postby ks_physicist » Fri Aug 31, 2007 6:32 am UTC

That is awesome, and I appreciate the time it must have taken to write that up.

Now I just need to practice!
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Postby scowdich » Fri Aug 31, 2007 7:29 pm UTC

That's...pretty comprehensive.

I just felt like the dude in my avatar needed to make an appearance in this thread.

As far as my slide rule skills go, I have a very nice 30-odd-years-old one that I got from my dad...I learned how to use it from the book that came with it.
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Postby Handsome » Fri Aug 31, 2007 7:54 pm UTC

I learned to use my slide rule from my dad. He still uses his, and I've been able to use mine on Calc exams. As far as using one goes, what Nimz said will probably be all you need.
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Postby scowdich » Fri Aug 31, 2007 10:39 pm UTC

Very few of the computer science-y and electrical engineering-y courses here don't allow calculators. The same goes for several physics courses.

That said, I have brought my slide rule to several final exams - and used it, with minimal complaint from the proctor.
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Postby Mathmagic » Sat Sep 01, 2007 1:09 am UTC

I suddenly have an insane compulsion to buy a slide rule now.

Very excellent tutorial Nimz!

EDIT: Any recommendations on where/what/how to buy? I'm looking on eBay right now, and there's just so many different kinds! :shock:
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Postby ks_physicist » Sat Sep 01, 2007 1:20 am UTC

When in doubt, go ebay for a good condition Sun Hemmi, Post Hemmi, or Pickett.

This is my semi-uneducated opinion, since I'm not a hard-core collector. My thesis advisor, though, was the person who sparked my interest, and he drools over the Sun Hemmi SRs.
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Postby Mathmagic » Sat Sep 01, 2007 1:31 am UTC

Thanks for the heads up.

Do the slide rules come in different sizes? What difference does the size make?

EDIT: Is there a difference between the different "Pickett Microline"s?
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Postby Nimz » Sat Sep 01, 2007 9:21 am UTC

* takes a few bows, then gets back down to business *

Size matters. The bigger the slide rule, the better you can read the divisions, the better the precision of your answer. That said, one extra digit precision means 10x the size. I have seen slide rules that take up an entire wall, but if you get something about a foot long, that should be good for up to 3 digits (4 digits if the leading digit is 1).

Material matters. Slide rules come in a variety of materials, from paper to plastic to wood to ivory... if you can mark lines on it and get it to slide, you can make a slide rule from it. When looking at the material, consider the durability, the colo(u)r (e.g. if yellow bothers you, don't get yellow plasic), and the stickiness of the material. If the stuff sticks together, making fine adjustments can be a challenge, as it will tend to jump instead of slide. If it is too slick, though, keeping it in place while adjusting the hairline can be a challenge. My Pickett Microline 140 is very similar to this. It is yellow plastic, about a foot long, and depending on the weather will sometimes jump and sometimes slide.

Make sure you have some kind of sleeve or cover for your slide rule. Putting your slide rule away properly should help prevent wear.

I don't know much about the quality of various slide rule brands. I have one cheap slide rule and two of decent quality. The quality ones I have are Ricoh brand and Pickett brand. The third one I have is more of a trainer that only has the A, B, C, CI, D, DI, and K scales on it, all on one side. Whatever you get, if you want to use all the scales, you will need a slide rule that is double-sided.

Just as I don't know squat about brands, I don't know about the different products within a brand, either. This link has a lot of Picketts (mine is slightly different than the listed variations, fwiw). In fact, http://www.sliderulemuseum.com has quite a bit on slide rules in general, and they've got a much prettier tutorial than mine, too.
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Postby Mathmagic » Fri Sep 14, 2007 2:40 am UTC

UPDATE!

My slide rule came in! :D

It's a Vintage Pickett All-Metal Slide Rule. Pictures are available here.

I'm very excited to learn to use it, thanks to this tutorial! :)

Thanks for all the advice that was given in looking for slide rules and how to use them. :)
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Postby platypus01 » Mon Sep 17, 2007 3:55 am UTC

if anyone else (still) wants a slide rule, you can also check out Sphere Research Corp's Slide Rule Universe. they seem pretty reputable, have a decent collection, and ive gotten one from them (a small pocket one to play around with. one of these days ill get myself a bigger one with real scales...)

sphere also has other cool stuff like oscilloscopes. which i also want. cept im too poor to get one. haha.......
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Postby Pesto » Mon Sep 17, 2007 5:35 pm UTC

mathmagic wrote:Thanks for the heads up.

Do the slide rules come in different sizes? What difference does the size make?

EDIT: Is there a difference between the different "Pickett Microline"s?

My geometry teacher in middle school had one that was six feet long.
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Postby bonder » Tue Sep 18, 2007 6:10 am UTC

mathmagic wrote:It's a Vintage Pickett All-Metal Slide Rule. Pictures are available here.


I believe I have the same slide rule. Mine has some simple instructions on the back. It's maybe not the best explanation, but it's good in the event that you need to refresh your memory.
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