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Years ago, before everyone (or anyone) had electronic calculators, I had a pocket slide rule which I used in secondary school until the first TI-30 cane out.

Recently I dug it out. Here's a photo of one end of it.

Slide rule showing mysterious constant on the C and D scales

As you can see, there's a number $C$ marked at about $1.128$ (times some power of $10$; with a slide rule you supply that yourself) on the C and D scales. Reading across to the A scale, its square is about $1.27$. By the C1 scale (which reads reciprocals of the C scale) its reciprocal is about $0.886$ (times some power of $10$).

The only two special numbers marked are $C$ and $\pi$.

I'm not sure whether it's some frequently used constant that's used (eg) in some branch of engineering, or a number which is useful for some trick for using the slide rule.

Unlike $\pi$, which is marked on most of the scales, this mysterious $C$ only appears on the C and D scales, which are the main ones used for multiplication and division.

If you need me to, I can give more explanation of the various scales on the rule and how calculations are done. That might give some clues as to what $C$ is for.

I'm sure the instructions explained what $C$ was, but I last saw those in the 1970s.

Has anyone any idea what $C$ is and why it would be useful on a slide rule?

muru
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timtfj
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  • Please tag as appropriate—I'm not sure if the right tags and can't yet create a new "slide-rules" tag. – timtfj Nov 30 '18 at 02:59
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    Funnest question in forever. – Randall Nov 30 '18 at 03:03
  • Did anyone else here buy their kid a slide rule when he/she went off to engineering school. My daughter ended up with two (we are a family with many engineers). She dutifully sat through my instructions on slide rule use (twice), but I don't think she paid any attention. – Flydog57 Nov 30 '18 at 17:34
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    Shouldn't this go in retrocomputing.SE? ;-) – shoover Nov 30 '18 at 18:34
  • @shoover - good one! – davidbak Nov 30 '18 at 19:29
  • @Flydog57 - who is this "kid" you're speaking of? I bought my own damn slide rule (a K&E log log decitrig) with its orangy leather case with belt loop! And then the first 4-banger calculators came out - bought one for $120! (A large sum for the time when a college textbook cost $20-$25 - eat your heart out, current students!) – davidbak Nov 30 '18 at 19:34
  • This must be some new-fangled addition to slide rules. My dad's K&E 4080-3 (probably pre-1940) has no such markings. (Yes, I still have the orangy leather case, though the flap has broken.) – Llaves Nov 30 '18 at 22:47
  • @Llaves All I'm really sure of fanglementwise is that the fangle was in place by about Christmas 1975. – timtfj Dec 01 '18 at 03:27
  • One of my slides has $C$ but it is exactly at $1.2$. It has a whole bunch of other letters e.g. $F$ at $1.9$ and some two letter markings e.g. $Cl$ at $3.35ish$. – badjohn Dec 01 '18 at 09:31
  • Amazingly, Googling for "C 1.128" has the first result being page 130 of this book that has a totally unrelated "C" but has the exact ratio "$1 : 1.128$" given as the final answer to some question, and the line just above that says "$\sqrt{2} : \sqrt{8/3.142}$", from which we can work out what $1.128$ is! – user21820 Dec 01 '18 at 11:12
  • ries tells me $1.128$ is exactly $\frac{(\frac{4}{5})^2}{5}+1$. It's probably not how $C$ has been defined, though. – Eric Duminil Dec 01 '18 at 11:32
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    Thanks for the question ! I took my slide rule (I did buy it in 1958) and, thanks to you, I nticed that this $C$ was present ! I never noticed. Shame on me ! – Claude Leibovici Dec 05 '18 at 04:31

2 Answers2

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I found the answer by googling "slide rule markings"! It took me straight to the Glossary of the International Slide Rule Museum, which gives C its own entry:

C - Gauge mark found on the C and D scales denoting $\sqrt{4/\pi} = 1.128$ for calculating the area of a circle and the volume of a cylinder. Place the C mark on the C scale over the diameter of a circle on the D scale. The area of the circle is found above the index on the A scale. If this is the base of a cylinder, without moving the slide, move the cursor to the height of the cylinder on the B scale. The volume is read on the A scale. This gauge mark was rendered obsolete with the advent of multi-lined cursors.

And there is, of course, so much more at that site.

TonyK
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    Amazing. Like a moron I googled 1.128 and didn't get anywhere. – Randall Nov 30 '18 at 03:11
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    I've just tried calculating $\sqrt{4/\pi}$ on the slide rule and the result does line up nicely with the $C$ mark, so this is definitely it!. Thanks! – timtfj Nov 30 '18 at 03:23
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    The museum is amazing! I feel much younger now (maybe that such a musem can make me feel younger should make me feel old...) – Francesco Nov 30 '18 at 05:32
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    @Francesco "It makes me feel like a kid again, and that just reminds me how long it's been." –  Nov 30 '18 at 22:01
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    I wish I had that mark on my slide rule. I am always calculating the volume of a cylinder at the beer joint. But calculation of the volume of a Starbucks cup is best done with Simpson's rule. – richard1941 Dec 05 '18 at 04:10
  • I seems more suited to finding the diameter of a circle of known area which could be useful in some engineering contexts, especially pipe flow. – kjl Jun 29 '23 at 13:44
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TonyK's answer shows how to get area of one specific circle of known diameter. Another way to use the "C" gauge creates a table of values for lots of different circle diameters all at once:

Place the "C" mark over the index on the D scale. Then any value for diameter you read along the C scale (on the slide) will be associated with area of that circle on the A scale (on the stock).

Source: https://www.sliderulemuseum.com/Manuals/Hemmi_Mannheim_Instructions.pdf (1958 edition, pages 17, 18)

wij
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  • +1 As a general rule please don't touch old questions wtih good answers since that moves them to the active queue. But this is a real addition, even though no one uses slide rules any more. – Ethan Bolker Jul 12 '24 at 00:00