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- From: danno@eleazar.dartmouth.edu (Danno McKinnon)
- Newsgroups: alt.religion.computers
- Subject: Learning to use a slide rule (OVERDUE SUMMARY)
- Keywords: slide rule
- Message-ID: <1991Aug24.192609.7977@dartvax.dartmouth.edu>
- Date: 24 Aug 91 19:26:09 GMT
- Sender: news@dartvax.dartmouth.edu (The News Manager)
- Organization: Dartmouth College, Hanover, NH
- Lines: 291
-
- About 2 months ago, I asked for some help in learning to use
- a slide rule. Yes, I've been delinquent with my summary! I'm
- actually taking classes this summer, so I've been quite busy.
-
- My main question was whether there were useful texts still
- around for learning this arcane art, perhaps published in a
- revivalist sense. Well, there don't seem to be any! A lot of
- people mentioned a piece that Asimov did, but no one knew the
- title. I can't find anything in our library by him that looks
- like a slide rule text, so I can't help anyone there. (Perhaps
- it was just an essay in a collection with an unhelpful title??)
- Guess I'll just have to mosey on down to our engineering library
- and dig out some old texts...
-
- Included below are a few of the very detailed responses. I've
- edited redundant information in most cases, to make this more
- streamlined. Thanks to everyone who responded, especially to
- those who took time for these detailed diagrams!
-
- Anyone should be able to get the basics of using a slide rule
- from these responses. I've read them and can follow them (nice
- to see that not all math knowledge has drained from my head
- yet), but haven't spent much time trying to work things out on
- the slide rule itself.
-
- I've included a copy of my original request at the very end. And
- for those of you who were looking for more discussion, I seem to
- have caught the tail end of a thread in alt.folklore.urban on
- slide rules---don't know how =that= one got started...
-
- Thanks again!
-
- Ciao,
- Danno
- ======------
- From: raymond@math.berkeley.edu (Raymond Chen)
-
- >er, ``window sliding piece,'' for lack of the actual name.
-
- Believe it or not, it's called a `cursor'. Yep.
-
- ======------
- From: Stephen C. Trier <trier@usenet.INS.CWRU.Edu>
-
- Slide rules aren't really that hard to use. My first suggestion is that
- you should try playing with it a bit. Measure out a number (say, 3) on
- one scale and try to see what it translates to on the other scales. If
- the number looks like 9, it's a squaring scale. If it's 1.73, it's a
- square root. If it's .477, it's log10. If it's 1.09, that scale is natural
- log. In other words, experiment.
-
- I just got out my mother's old slide rule. I'll describe what I see and
- how it's used. Hopefully, yours will be similar. (I also have a smaller
- slide rule that I carry in my backpack. It's a really handy backup for
- my calculator. I've even taken physics and chem tests using it for the
- calculations.)
-
- This slide rule has A and B scales marked logrithmically from 1 to 100,
- and C and D scales marked logarithmically from 1 to 10 (marked as 1).
- Both of these scales can be used for multiplication. For example, to
- multiply 2 and 3, slide the rule until the B scale 1 is at 2 on the A
- scale. Then move the cursor (the clear sliding piece) to 3 on the B
- scale and read the result off the A scale. This should make sense if
- you realize that you are measuring off logarithmic distances and adding
- those distances.
-
- You can use the C and D scales the same way. To multiply numbers that
- don't fit on the scale, convert them to scientific notation and multiply.
- You will have to add the exponents yourself.
-
- The Ci scale is the inverse of the C scale. Find 2 on the C scale and
- the Ci scale will read 0.5. Find 4 on the C scale and the Ci scale will
- read 0.25.
-
- The C and D scales are the squares of the B and A scales, respectively.
- Find 3 on the D scale with the cursor, and you'll see a 9 on the A scale.
- Find the pi marker on the C scale and you can read off pi squared on the
- B scale.
-
- The K scale is the D scale cubed. You can do cubes and cube roots with
- it.
-
- The S, T, and L scales stand for sine, tangent, and log. It's assumed
- that one can work out the cosine by using the cos(x) = sin(90 - x) identity.
- I'm not entirely sure how to read the S and T scales yet, but the L scale
- is read by moving the C scale origin (the 1 on the left) to point to a
- number on the D scale. Flip over the rule, and read out the answer on the
- L scale. Again, it's the user's responsibility to track the powers of 10
- to make the answer come out right.
-
- If you figure out how to read the S and T scales, or if you figure out
- what the "C" indicator I have on my C slide at about 1.13, please let me
- know. I'm self-taught on these things, having been brought up on
- calculators and computers. :-)
-
- Anyway, if you know the relationships between the scales on the slide rule,
- you can do some pretty complicated arithmetic without much loss of accuracy.
- It's awfully hard to get more than two or three significant figures out of
- one, though.
-
- Hope this helps a bit. Let me know if you figure out the other scales.
-
- --
- Stephen Trier "48 61 70 70 69 6e 65 73 73 20 69 73 20 61
- Small Systems Guy 20 77 61 72 6d 20 68 65 78 20 64 75 6d 70
- Information Network Services 21 20 20 3b 2d 29" - Me
- Case Western Reserve University Mail: trier@ins.cwru.edu
-
- ======------
- From: arensb@kong.gsfc.nasa.gov (Andrew Arensburger - RMS)
-
- >DESCRIPTION:
-
- >This appears to be a pretty serious slide rule, and comes to me
- >complete with leather case. Made by Keuffel & Esser Co. of N.Y.,
- >the model number might be either `<N4059-3>' or `673145' (they
- >didn't put serial numbers on these things, did they?). The case
- >says K&E POLYPHASE, but I don't know if that is the name of the
- >case or rule. The scales are: A, B, CI (numbers in red), C, D,
- >and K.
-
- Hmmm... I never was too clear on what the 'extra' scales meant,
- and the teacher never discussed them (yes, I was lucky enough to have
- slide rules taught to me in school).
-
- +------------------------...------------------------+
- | ... |
- --> +------------------------...------------------------+ <--
- |||||||||||||||||||||||||...|||||||||||||||||||||||||
- +------------------------...------------------------+
- | ... |
- +------------------------...------------------------+
-
- Figure 1: a slide rule.
-
- Anyway, you should have two identical scales at the place marked
- by the arrows on Fig. 1 (these are probably the ones labelled A and B).
- These are the ones you'll be using for multiplication and division.
- A slide rule makes the fundamental assumptions that you know
- arithmetic, and that you have a brain. It works on the principle that
-
- log(a * b) = log(a) + log(b) (1)
-
- To see how this works, take two ordinary rulers and line them up:
-
- | 1 2 3 4 5 6 7
- | | | | | | | |
- +------------------------------------------------
- | | | | | | | |
- | 1 2 3 4 5 6 7
-
- Figure 2: two rulers
-
- Now suppose you want to figure out 2 + 3. Slide the bottom ruler along
- the top one (or vice-versa) so that the 2 on the bottom ruler lines up with
- the 0 on the top one (this says that you want to add 2 to something). Your
- rulers should now look like this:
-
- | 1 2 3 4 5 6
- | | | | | | |
- +-----------+------------------------------------
- | | | | | | | |
- | 1 2 3 4 5 6 7
-
- Figure 3: two ordinary rulers demonstrating 2+3
-
- Since you want to add 3, find the 3 on the upper ruler, then find out what
- number lines up with it on the bottom ruler. That number is 5. Presto!
- your rulers have just shown you that 2+3 = 5.
-
- 2 + 3 = 5 (2)
-
- The slide rule works exactly the same way, except that it adds
- logarithms, and therefore multiplies. Try the above exercise. It should
- give you 6 (if not, there's something seriously wrong!). The little slider
- is there to help you align the second term in the multiplication and the
- final result (3 and 5 in the above example). The only difference is that
- you need to line the first factor up with 1 instead of 0 (this makes sense:
- it's because x + 0 = x, whereas x * 1 = x).
-
- Division works exactly the opposite way: line up the numerator
- (on the bottom scale) with the denominator (on the top scale), and see what's
- opposite 1 (on the top scale).
-
- By now, you're probably thinking, "yeah, but the scales only go
- from 1 to 10. What if I want to multiply larger numbers? This is the part
- where you need to have a brain. What you need to do is to convert all the
- numbers to scientific notation. For example, to multiply 10.198 and
- 173.86, convert them to 1.0198 * 10^1 and 1.7386 * 10^2, respectively.
- Perform the multiplication as described above. The slide rule will give
- you the answer 1.7730, which you must interpret as 1.7730 * 10^N, where
- you have to figure out N by yourself: you multiplied something in the tens
- by something in the hundreds, so the answer has to be in the thousands.
- The correct result is therefore 1773.0 .
-
- That's about all I know how to do with a slide rule, although with
- a bit of experimentation, you can probably figure out what the other scales
- mean. Probable ones include square/square root (2 lines up with 4), cube/
- cube root (2 lines up with 8), sin/arcsin (1 lines up with pi), log base
- N, e^N.
-
- >In addition, the sliding piece has S, L, and T scales on the
- >back; I don't know if the slider is supposed to be flipped over,
- >or just read from the back---one of the short edges has a small
- >glass window with hairline on the back, alongside a listing of
- >english-metric conversion factors (and a few common formulas).
-
- Yes, I think the middle part is supposed to be slid out and
- flipped over, for some of the funkier scales, although I'm not sure. Too
- bad my slide rule didn't come with an instruction manual. I guess my grandpa,
- a hardcore engineer, thought it was too trivial to be kept :-)
-
- -------------------------------------------------------------------\\\\^
- Andrew Arensburger | K&R C! | I hate Lisp functions o\\\\\-
- arensb@kong.gsfc.nasa.gov | ANSI no! | that start with /
- ....!uunet!dftsrv!kong!arensb | | "(catch (mapcon (throw" \_/
-
- ======------
- From: aj009@cleveland.freenet.edu (Michael Somos)
- Subject: K&E Polyphase
-
- I just read your 16Jun91 article in alt.religion.computers about your
- grandfather's slide rule. That particular one is a beauty. That model
- has almost every scale imaginable. Genuine wood and leather. There are
- many books on the slide rule. Asimov even wrote one. Take good care of
- it and one day it might be a museum piece. Any calculator nowadays can
- run circles around it, but they can't match the style and feel of using
- a 'slipstick'. Don't worry too much about using to solve arithmetic type
- problems. Just holding it in your hands and manipulating it is enough.
-
- Shalom, Michael Somos <somos@ces.cwru.edu> or <aj009@cleveland.freenet.edu>
-
- ======------
- Below is my original article, included for reference purposes.
- ======------
- From: danno
- Newsgroups: alt.religion.computers
- Subject: Learning to use a slide rule
- Keywords: slide rule
- Reply-To: danno@dartmouth.edu
-
- While looking through some old stuff, I discovered my
- grandfather's slide rule (description below). I remember that
- there was a discussion of them a little while ago (either here
- or in alt.folklore.computers), so I thought I'd ask for some
- help.
-
- I'd like to learn how to use it, but the only references I can
- find in our library's online catalog are for old,
- boring-sounding engineering-type texts. I'm hoping that there is
- some sort of revivalist text, perhaps in a light-hearted vein;
- someone suggested that MIT Press might have published such a
- book. Can anyone help here? I'll dig those c.1950 texts out of
- the library if I have to, but there must be a better way...
-
- I hope someone can help me, as I have a love of things analog in
- this digital world (which is why pinball is still way cooler
- than video games =).
-
- DESCRIPTION:
-
- This appears to be a pretty serious slide rule, and comes to me
- complete with leather case. Made by Keuffel & Esser Co. of N.Y.,
- the model number might be either `<N4059-3>' or `673145' (they
- didn't put serial numbers on these things, did they?). The case
- says K&E POLYPHASE, but I don't know if that is the name of the
- case or rule. The scales are: A, B, CI (numbers in red), C, D,
- and K.
-
- In addition, the sliding piece has S, L, and T scales on the
- back; I don't know if the slider is supposed to be flipped over,
- or just read from the back---one of the short edges has a small
- glass window with hairline on the back, alongside a listing of
- english-metric conversion factors (and a few common formulas).
-
- The top edge has a 10 inch ruler on a slant, and the bottom edge
- has a 25 centimeter ruler. The rule is all wood, with a glass...
- er, ``window sliding piece,'' for lack of the actual name. From
- the back I see that there are 3 screws drilled into the rule,
- which seem to serve no function; perhaps they are just there for
- support.
-
- Finally, the slide rule claims patent number 1,934,232, and the
- ``window sliding piece'' claims patent number 2,086,502.
-
-
-
- --
- Danno McKinnon Distribute your
- =========================-------------------------- tension-cow to stores
- tragedy@dartmouth.edu throughout the state.
-