Slide rules

[CatalinaWOW]

Here is a slide rule for everyone, right on screen.  And to cover the operations a slide rule can't do, an abacus is thrown in.

[bsfeechannel]

1.It was a Faber-Castell 52/82. Required by the school.

2.I can't remember. But we had classes on how to use it.

3. I never used a slide rule except for the time in school. I gave it away as soon as the classes ended. Everybody had calculators back then. To me it seemed to be an anachronistic tradition. Most manufacturers had already ceased the production of slide rules and I've never seen them used in any professional environment where I worked.

4. Several years ago I was struck by a bout of nostalgia and bought a 1973 Faber-Castell 52/82 off Ebay. It came in almost mint condition with minimal signs of wear. I relearned how to use it and now I occasionally show young players the evolution of mathematical mechanization with it.

[TimFox]

One important side-effect of slide rules was the concept of "slide-rule accuracy" in a computation.  It was important to understand when slide-rule accuracy was sufficient (e.g., calculating a 5% resistor value), and when it was not (e.g., balancing ones checkbook).

[notadave]

I inherited two kinds, one for EE and one for banking.

The slide rule has one big advantage: It shows many results at the same time. I marked the E12-series on two regular rulers and my slide.
As a human you can perform discrete math with it.
I use the concept whenever I have to find e.g. resistors. The E6 values should be 1.4678x apart so you can not have any other factor, but because of rounding you can.

10	12	18	39	33
15	18	27	56	47
1.5	1.5	1.5	1.44	1.42

Some are too high others too low.
By adjusting the slide rule to the factor you want you can look for the best match even though they should all be the same.

[chickenHeadKnob]

As I mentioned to edy in reply #  23   I have two plastic school slider rules which are11 inches (279 mm ) long and are marked 'Sterling Slide Rule' and 'made in U.S.A.'
These are for give-away with edy having first choice of one. You pay postage from Canada.  The all white one appears to be a model 684 5 bridge version which has a cracked end bridge on the left. the other one appears to be a model 689 green slider 5 bridge. No model numbers are embossed in the plastic so can't be sure.
https://www.sliderulemuseum.com/Sterling.htm

[edy]

As I mentioned to edy in reply #  23   I have two plastic school slider rules which are11 inches (279 mm ) long and are marked 'Sterling Slide Rule' and 'made in U.S.A.'
These are for give-away with edy having first choice of one. You pay postage from Canada.  The all white one appears to be a model 684 5 bridge version which has a cracked end bridge on the left. the other one appears to be a model 689 green slider 5 bridge. No model numbers are embossed in the plastic so can't be sure.
https://www.sliderulemuseum.com/Sterling.htm

Thanks, I PM'd you my info, please let me know through there how to arrange the rest, thanks again! By the way I also introduced my kids to the soroban to get their heads working because it also helps you keep track of things mentally and in some cases faster than a calculator. With a soroban and sliderule they will exercise their mental muscles and check their answers far better than blindly relying on a calculator.

[soldar]

I still have my pocket-size Faber Castell "167/87" with the leather slide-in case. I probably got it around 1968.

Just basic multiplication, square, cube, log in front and trig functions in back.

https://fabercastell.reglasdecalculo.com/167_87/167_87.html
https://www.sliderulemuseum.com/isrm/hmd/fc%20slide%20rule%20pages/fc%2088%20167-87/fc%2088%20167-87.htm

Now that I have a second look, those pictures show slide rules in black and white but mine has the sliding scales in green. Otherwise they are alike. I guess it depended on the model year.

[cliffyk]

Here's mine from when i was in school in the mid-late 60s--until needed it was in in my shirt pocket (with a pocket protector of course):



Perfect model # too:

[Johnboy]

Thanks to all for replies. Fairly diverse around here as far as the rules used and why, and I'm glad to see that diversity. Mainly general-purpose rules, although it seems the specialty rules tended to stick around longer, and I can grok the reasons for that.

Today's acquisition was a USA-made-1965-or-thereabouts Dietzgen Microglide 1734. I swore I was done collecting these things, but an infamous auction site, via email, "helpfully" warned me to the fact that there was one available for actually less than it sold for in 1965, so I found myself being thanked for my order before I could come to my senses and remind myself that I need another slide rule like I need an aperture in my forehead.

The Dietzgen Microglide, by the way, was not a huge seller in the States, compared to the bestselling models by K&E, Post, and Pickett. It was one of the better-selling models of Dietzgen's own slide rule products, though, and I saw why as I ran the slide for the first time-- absolute butter. The slide moves almost of its own accord. I was reminded of the first time I played a Paul Reed Smith guitar back in the early 1990's and how low the string action was to the fretboard-- one barely had to touch them to fret them. This slide rule is the same thing-- mechanically efficient to the extreme. Turns out Dietzgen came up with a fairly masterful design concept: "Let's put Teflon inserts on either stator so there's less resistance for the slide." And boy, does it work. Let me tell you it works. Anyone here who's compared a mahogany rule by K&E to a bamboo rule made by Post or Hemmi knows the latter have an almost reptilian smoothness in comparison. Well, these Teflon inserts are so enabling of horizontal, seemingly-frictionless movement that it makes the bamboo rules feel downright clunky. (See the cross-sectional picture below; the teflon inserts are the U-shaped things between slide and stator, and they run the entire length of the latter on both edges of the slide.)

So why wasn't everyone using them back then? It works like a dream! Ah, there's the rub, no pun intended.

Most slide rules take quite a beating in the mail, and this one was no exception, so the alignment of the upper bout was out by an half-centimeter. I grabbed a screwdriver to put it back in alignment, and wouldn't you know it?

Darned near impossible.
This thing is so slippery when making tiny adjustments that it's like trying to hold an angry mamba recently kicked by a horse. Try as I might, and wrestle with it as I would, there was nothing I could do to get this thing exactly right. Even gradually tightening the stator screws was like kicking that snake again. The Teflon simply works too well; too much of a good thing.

So I'm off to find a second vise to finish the job. Might need to borrow a couple of extra hands while I'm at it, at this rate.

[bsfeechannel]

Well, these Teflon inserts are so enabling of horizontal, seemingly-frictionless movement that it makes the bamboo rules feel downright clunky.

Silicone grease works wonders on my all-plastic Faber-Castell rule.

[artag]

None of that back-and-forth crap.
Round and round we go.

There are some beautiful circular Russian slide rules widely and fairly cheaply available on ebay. Strongly recommended for slide-rule fans.

https://mostlymaths.net/2013/11/my-russian-kl-1-circular-slide-rule-and.html/

[Johnboy]

Well, these Teflon inserts are so enabling of horizontal, seemingly-frictionless movement that it makes the bamboo rules feel downright clunky.

Silicone grease works wonders on my all-plastic Faber-Castell rule.

Thank you. I have some around for heat sinks and I'll give it a shot. I have read that it's useful, but most of the info I've read about care and maintenance is decades old and I didn't want to damage them. I've gotten into the habit of carrying a slide rule at all times; I find them a great distraction while I'm being "processed". I'm also one of those people who look up from their slide rules and note that everyone around me in the doctor's office is playing with their cell phones. They never seem to notice anything odd, and if they do, they don't say, "pardon me, sir, but you seem to have a rather large grease stain creeping through your breast pocket." 

[edy]

Thanks to @chickenHeadKnob who graciously has allowed me to introduce my household to the slide rule. Now I have a few questions after reading the various manuals on calculating using a basic Sterling slide rule (having A, B, C1, C, D, K, S, T, L rules) and having to actually start using them in practice with my 10 year-old who was doing basic multiplication and division yesterday! By the way we also have a Soroban so I am trying to figure out how the Slide-Rule fits in with my strategy to work the brain muscles of my 3 kids.

Firstly, for doing multiplications of two 3-digit numbers, for example 761 x 423, I am using a Soroban to essentially add up the following:

          3   (1 x 423)
        20
      400
      180  (60 x 423)
    1200
  24000
    2100   (700 x 423)
  14000
280000
=====  SUM
321903

Of course all this is done in the Soroban "on the fly" so you move beads around as you pair-off multiply the various digits so it is fairly fast but most importantly, it comes up with the exact answer. So I was going over this with my 10 year-old daughter and trying to show her how to use the slide-rule and I was puzzled as to how to get precise exact answers, if there is some "trick" or not. If they were used for calculations that were critical to have exact answers, how was that done?

Right now, to do the above multiplication I would set the numbers to scientific notation as 7.61 x 10^2 * 4.23 x 10^2. Then I would slide my "C" rule index 1 (the right side one) to match up with the 7.61 on the D scale, then wander along on the C until I see 4.23 and then read off the D scale. So I tried it out on this virtual slide rule:

http://www.antiquark.com/sliderule/sim/n909es/virtual-n909-es.html

So I did that as precisely as I could and ended up with 3.21 - 3.22. Of course, keeping in mind the 10^2 * 10^2, the answer ends up being 3.21-3.22 x 10^4 or around 321000 - 322000. This is approximately close to our exact answer of 321903. However, I had to make sure I lined up the "C" index 1 with 7.61... not exactly easy, and any error there would also misalign the 4.23 as well which would throw off reading the answer. And even when I did get an answer it would be only to maybe 3 digit precision, +/- on the last digit:



How am I supposed to get exact answers? Is there a way of "dividing and conquering" with this thing? Is it purely a quick estimation device? How could they land people on the moon using non-exact answers, or am I missing the point? More importantly... I am trying to teach my kids how to use and integrate the slide-rule into their homework and the math they are being asked to do wants exact answers!

Same goes for division... My daughter is learning simple long-division such as 3157 divided by 7 where we do this:

           4 5 1
      ________
7   |  3 1 5 7
        2 8
        ----
           3 5
           3 5
          -------
              0 7
                 7
           - -----
                 0

So with the slide-rule, I would use the "C1" and "D" scales again as follows with 3.157 x 10^3 and 7... First I slide the 3.157 on "C1" to match up with "1" on the "D" scale so I am actually multiplying 1/3.157 with 7 on the "D" scale. I then slide cursor over to 7 on the "D" scale and I can see that my "C1" scale shows just barely over 4.5:



Again, keeping tabs on our powers we would have to divide out 10^3 (3.157) by 10^1 (of the 7) so we get 4.5 x 10^2 which is 450 or close to our answer but not exactly.

Can someone please let me know how (or if) I should be integrating a slide rule into these types of math problems the kids are getting at this point? If it is not possible to get the exact numbers they need for their test, is it just an easy way for them to check? Is there something else they can use it for? I am excited about using the Soroban and Slide-Rule with the kids and forgetting the calculator but I want to make sure I am using them in the appropriate ways.

[artag]

I'm no expert and I hope someone will correct me if I'm wrong, but I wouldn't want to use anything liable to cause a grease stain.

From experience with other tools, I'd suggest that if the slide rule has wooden slides, beeswax-based furniture polish (as used by woodworkers to protect cast iron surfaces without staining the woodwork job) would be good.

If it has plastic slides, I'd use silicone spray (mould release, also used on plastic curtain rails, a silicone oil in an alcohol carrier) or PTFE 'dry' cycle lubricant (which is PTFE flakes in an alcohol carrier).

I wouldn't use thermal grease. Although the silicone content would OK, i'd be less happy about the zinc oxide or whatever filler it is that gives it the white colour.

[rstofer]

You don't get exact answers with a slide rule but you probably don't have exact input either if the numbers come from measurements.  That's the whole point of slide rules:  Fast and close enough!  If you want precision, you drag out pencil and paper and get with it,

I wouldn't introduce the slide rule until logarithms come up and that's usually at some time late in high school.  Even then, I would introduce it as a novelty.  The slide rule was king when I was in college right up until HP introduced the HP35 calculator.  That was the death of an era, may it RIP.

The HP35 was magnificent for its time but it pales in comparison to the advanced calculators available today.  Not only do we have great calculators, we also have computers and software like wxMaxima, MATLAB, Octave, Mathematica and a host of others.

Things have changed, the slide rule is an artifact.  A glorious one, we mostly got to the moon with slide rules, but nobody wants to go back to using one as an only tool.

[soldar]

How am I supposed to get exact answers?

My 16 cm pocket slide rule will give me about 3 digits. A bigger one will give you more but forget multiplying two five digit numbers and getting a ten digit answer.

You are not dealing with exactly precise numbers.  In engineering you rarely need to. One thing I notice about beginners in engineering is that they will carry absurdly precise numbers. A resistor of 56.367 ohms and a transistor with a current gain of 156.78. Those things are meaningless. Just the physical variations among units will make those numbers meaningless.

If you need more precision then you need other tools.

[artag]

When I was at high school, my father was selling early calculators to business users. They were common, but too expensive to be found in high street shops or given away as gimmicks. I made pocket money doing repairs to Canon desktop calculators (nixie tubes, RTL and silver delay-line memories), and Bowmar pocket models that needed Nicads replacing.

A few of us science geeks bought our own calculators in the 6th form (I don't know what that is in US grades, but it's the last 2 years of school before going to college for a degree course). My technical drawing course required me to buy a slide rule but I wasn't required to have one for maths (though we were taught to use them).

Nobody was expected to buy a fancy expensive calculator and our teachers cautioned us against using excess and inappropriate precision, both because it wasn't needed and because it wouldn't go down well with the exam board. Exams were based around slide rules - so calculations didn't need to be precise, just as in real life. The situation is different now : the exams are set using the assumption of either manual methods or calculators so exact answers are expected purely for convenience in marking. Inexact answers would be because of errors, not approximations (though they might expect proper rounding strategies).

Students should understand this, IMO. But should also appreciate that many problems can be adequately solved using 2 or 3 digits of precision, and for non-exam purposes a slide rule or an approximation (like 3 for pi) for calculations in your head is good enough to get you a ballpark answer.

I suspect the reason slide rules for good enough to 'go to the moon' is not that they were used to get precise results for long calculations planning a flight in detail. Instead, they would be used for a succession of rapid calculations that effectively iterated to a result : eg calculating the burn rate for the next few seconds and then repeating the calculation seconds or minutes later.

[bsfeechannel]

So I was going over this with my 10 year-old daughter and trying to show her how to use the slide-rule and I was puzzled as to how to get precise exact answers, if there is some "trick" or not. If they were used for calculations that were critical to have exact answers, how was that done?

The slide rule is an analog calculator, so precision is, in theory, arbitrary, only limited by the resolution of the scale. However, you will see its use, when compared to the soroban, when you have to calculate things like f = 1/(2π · √(LC)), the resonance frequency of an LC tank.

Let's suppose that C = 470pF and L = 3.3µH. First, you figure out the powers of ten: 470p = 470 · 10⁻¹⁰ and 3.3µ = 10⁻⁶.

10⁻¹⁰ · 10⁻⁶ = 10⁻¹⁶. Therefore, √( 10⁻¹⁶) = 10⁻⁸.

So f = 10⁸/(2π ·  √(4.7 · 3.3)). Now let's get the slipstick.

Find 3.3 on scale A with the help of the cursor line. Now place B 1 under the cursor line. Move the cursor line to 4.7 on scale B. You will find 15 something on scale A. If you don't move the cursor,  you'll find its square root on scale D below under the same cursor line to be about 3.95. If I flip the rule, I have the CIF scale, which is the C scale inverted and divided by π. This will give me 1/(π ·  3.95). So maintaing the cursor where it is, I align C with D and read something that is a tad grater than .0805, let's say .0806. Dividing by two, it gives me .0403.

So, f = 0.0403 · 10⁸ = 4.03 MHz.

My vintage Casio fx-21 gave me 4.0412361 MHz. Not bad for a beginner. There must be other ways, who knows, faster and more precise than what I did. But setting the cursor and the slide just two times each, without counting flipping the rule as an operation, you get your result very fast.

[edy]

Were there Venier scales used on slide rules to allow better precision? For example, like found on calipers as follows:



So far I have been eye-balling it and getting close. I'm using a practice app for iPhone called RuleCoach. It's free and tiny, shows you complex problems and tells you how close you are and tallies up your average error. It contains no virtual slide rule... you use a physical slide rule, it just gives you random calculations to do. I find it hard to keep track of order of magnitude... but getting better. Very good for learning!

For example if I do a few numbers together I have to keep track of the final value being larger. For example if I multiply 2x2x2=8. Or 20x20x20=8000. Because each is 2x10^1 so answer is x10^3. But if I use a larger number like 3x3x3=27... 30x30x30=27000, on slide rule I get 2.7 but actually need to remember it is 27x10^3. If I use say 5x5x5=125 it is now 10^2 greater just due to the digits never mind the original scientific notation. So that's a bit tricky at first.

[edy]

Seems like this Vernier question has been brought up before. There is even a Google patent for it from 1947 (https://patents.google.com/patent/US2424713A/en). Check out the patent PDF, it is fascinating:

https://patentimages.storage.googleapis.com/d2/ab/ad/c6d43a2420897c/US2424713.pdf

But could be it wasn't practical to implement or worthwhile? Or could be with proper technique you can use the slide rule itself as a Vernier... look at the method described in this article from 1948:

"Utilizing the Vernier Principle for Precise Readings of Slide Rule Settings"

https://aapt.scitation.org/doi/abs/10.1119/1.1991139?journalCode=ajp

Here is the text (it starts below at bottom):

[bsfeechannel]

Were there Venier scales used on slide rules to allow better precision?

Not sure. However, loupes were used.

[edy]

I noticed a mark on one Sterling slide-rule (graciously provided by @chickenHeadKnob) which first appeared like a pen mark at 785, but then after seeing it on both A and B scales and a 2nd slide-rule, I realised it was actually a gauge mark printed from the factory! The 785 is presumably Pi/4 which is 0.7854. It is visible on the pictures in the Sterling instruction manual but not mentioned explicitly.

I am trying to figure out what this can be used for and how you would do calculations with it. Why is Pi/4 so important, but not Pi/2? Or 2 Pi? Or Pi squared? Any ideas?

[jklasdf]

It's apparently for quickly finding the area of a circle given the diameter: http://www.tbullock.com/sliderule.html

[cliffyk]

jklasdf beat me to it...

Area of a circle is:  r² * pi(), or d² * pi() / 4...  A shortcut to getting circular area from diameter, volume of a cylinder from diameter and height, and other geometric formulae involving circular functions...

[Tom45]

Now that you know that they are called gauge marks, a search can find many references listing various gauge marks. For example:

  http://steves-sliderules.info/rule%20code/Gaugepoints.html

The K&E slide rules I used back in the day didn't have gauge marks and I was unaware of them until I started collecting slide rules many years later. Gauge marks seem to be much more common on European slide rules. They are also more common on specialty slide rules such as for electrical engineers. In the link above you will see gauge marks for copper and for converting between horsepower (HP) or Pferdestärke (PS) and kilowatts.

The K&E Decilon that I got when it was introduced while I was in college had only one gauge mark: pi on the C and D scales. A later variant of the Decilon dropped those pi gauge marks. With the folded scales (CF, DF, CIF) pi was always available by going between the regular scales and folded scales at the appropriate step.