The largest commercial cylindrical slide rule has a scale length of 24m
cacm.acm.org
cacm.acm.org
On a mildly related note, does anyone know if it's possible to construct a logarithmic scale from simple tools? A demonstration I've always wanted to try is building a slide rule "from scratch"
EDIT: by "simple tools" I mean no computers. Pen and paper, compass and straight edge, that sort of thing. I would assume in real life it was made via trial and error on a very large scale and shrunk down optically for a screen print, but I wonder if there's a "precise" way
Well, there were also 5 computers (one analog) onboard the spacecraft, multiple powerful IBM System/360 mainframes computing trajectories on the ground, a Honeywell 1800 assembling code, a whole pile of Univac computers (1230, 494, 495) processing data, and RCA 110A computers for mission control (including one inside the launch platform under the rocket).
Indeed the whole notion of logarithms was developed and introduced by Napier to simplify calculations!
To build a cardboard slide rule get a table of logarithms accurate to around 3 digits and layout a "ruler" with marks for the values from 1.0, 1.1, 1.2, ... 10.0. These marks however are placed on the "ruler" at the location corresponding to the log of the values: 1.0 is placed at the start of the ruler since log(1.0) == 0 and 10.0 is placed at the end of the ruler since log(10.0) == 1. In between the over values are placed where their log says they should go, so for example log(5.0) == 0.699 so the 5.0 should appear on the ruler 69.9 percent of the way from the 1.0 mark to the 10.0 mark.
Two of strips of cardboard labeled in this fashion will give you a very basic slide rule. Placing them next to each other it is very easy to position the slides so that you are "adding" the logs of two numbers. This is how multiplication is done using a slide rule.
- draw a line
- pick two points on the line
- label them 1 and 10
- bisect the segment to get √10
- bisect the halves to get 10^¼ and 10^¾
- etc.
If you pick some given resolution limit, it could all be done by hand, but would take quite a while.
Relevant articles:
https://sliderules.lovett.com/cookiedev/extendeddisplayartic...
https://sliderules.lovett.com/cookiedev/extendeddisplayartic...
Also, not actual a logarithm, but a wicked clever hack:
Wikipedia has an article: https://en.wikipedia.org/wiki/E6B
There are other softer benefits too, such as making the quantities in the computation somehow more... visceral.
Compass and straight edges compute what are called the constructible numbers [1], which have 0, 1, and anything obtainable via addition, subtraction, multiplication, multiplicative inverse, and square roots of positive numbers.
These will not allow you to get to logarithms. You can't avoid having to calculate them numerically; from there you may also create approximations to construct them but you might as well just use a ruler at that point.
You can compute logarithms by hand but they're notoriously tedious even by 19th century standards (and they had a great deal more tolerance for that sort of thing than we do today, for obvious reasons), which is why you could buy books full of them, and that's generally what people used.
[1]: https://en.wikipedia.org/wiki/Constructible_number#Algebraic...
Yeah, I don't know how practical a construction would be overall for someone who seriously went at it; I was mainly moved to answer because this objection that constructions can't express transcendental numbers just doesn't seem relevant -- digitally you don't keep infinite precision either.
Square roots and multiplying are two of the simplest geometric constructions (geometric mean and taking a proportion), compass and straightedge operations can be accurate, you can construct it enlarged and then scale it down, and finally the precision you need to aim for at the end is bounded. A potentially fun project idea. Think of it as a kind of retrocomputing: how might Euclid or Archimedes have designed a slide rule?
After all, the slide rule was invented hundreds of years before the computer.
| 10 | => divide by log10(1/2) : 1
| 5 | 5 | => divide by log10(1/5) : 1
|1| 4 |1| 4 | => divide by log10(1/2) : 1
|1| 2 | 2 |1| 2 | 2 | => divide by log10(1/2) : 1
|1|1|1|1|1|1|1|1|1|1|https://en.wikipedia.org/wiki/Pantograph
Log scale is a linear fractal, self-similar.
Say you constructed a pantograph where the ratio of the "inner" point to the "outer" point was ... um ... log(5)? for a decimal scale? ( I think you could make a binary scale but I can't think what the ratio would be log2(1)? )
Anyway, you'd start with the pantograph's base and outer point at the ends of your ruler, mark off the inner point, and then repeat on each sub interval, and then again recursively until you ran out of room.
Like I said, I could be wrong about this.
I bought my slide rule in 7th or 8th grade with money I made from my paper route around 1964; I still have it and it functions just as well as when it was new.
I mentioned that we all had them, this was because there was really no alternative. Slide rules could perform all sorts of calculations, multiplication, division, exponentials, trig functions, all to an accuracy of around 3 significant digits. Computers existed, but terminals (with few exceptions) did not. Any calculation with a real computer required getting to the comp center and punching cards (any mistake on their funny keyboards meant throwing the card away and starting over). After that one would have to submit the deck to an operator behind a glass window. In ten minutes to an hour you would get the first result of running your program produced on fan fold paper, usually with green and white tinted background on the paper. The printing was done with a line-printer, often in upper case only. Naturally, the first few attempts ended up with syntax errors and it was easy to waste a lot of time on simple calculations so the 3 significant digits of an ordinary slide rule started to look good enough.
Of course, we all also had (right next to our collegiate desktop Websters dictionary) a copy of the CRC Standard Mathematical Tables. This book, hundreds of pages long, had tables of logarithms and trig functions accurately to 5 digits which could solve these problems to 5 or 6 digits accuracy with careful interpolation techniques (which were taught in high school back then).
A year or two after I bought my slide rule I saw an early black and white episode of Lost in Space, a 60's TV show about a family lost on a remote planet. On the program the character Will Robinson was using a handheld calculator. It was pure science fiction device about the size of large 6cm thick hardback book. It contained a keyboard of perhaps 16 keys and a large, say 5cm, high display. I thought that it was so incredible, like the space suits and robots that appeared in the show. I wished that there was someway in the distant future that I would ever have such an amazing device!
https://www.sliderulemuseum.com/Manuals/KL-1_RussianCircular...
(I now need reading glasses to use it- so annoying).
I was disappointed
Coincidentally, there's one for sale on eBay right now.
I found it on the scrap pile when an old building on my university was being renovated. It didn't have a university inventory serial number on it, so they weren't allowed to surplus it and had to toss it. I was in utter shock that it was going to get tossed, so took it.
The building it was in was built in 1913, originally to hold the School of Mines for Oregon State University, so I imagine it used to belong to a professor or researcher there when the School was quite new.
I've never actually used it, but perhaps some day can find a the original manual to learn how.
If you 'Unwrap' a Thacher's it ends up being the equivalent of a regular slide rule that's 59 feet / 18 meters long.
Here's one in a collection with a picture and some background...
https://americanhistory.si.edu/collections/search/object/nma...
Most of them are pretty cheap on Ebay, <$200 not including shipping. The Addiators in particular are simple, cheap and small.