Episode: 2166
Title: HPR2166: How to use a Slide Rule
Source: https://hub.hackerpublicradio.org/ccdn.php?filename=/eps/hpr2166/hpr2166.mp3
Transcribed: 2025-10-18 15:09:56

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This is HPR episode 2,166 entitled How to Use a Side Rule.
It is hosted by Dave Morris and is about 15 minutes long.
The summary is, I pop your request, a description of how a side rule works.
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Hello everyone this is Dave Morris.
Today I'm talking about slide rules.
The reason I'm doing this is because back two years ago now I mentioned the subject
on the show I did show 1,664 and I was asked if I could talk more about the subject.
So I was just saying it's taken two years to get to this for which I apologise.
It's probably, I don't know how interesting people be in it, so it's moderately dry subject perhaps.
So I'm not going to go into a vast amount of detail.
I did use a slide rule as a schoolboy.
In the 1960s I had one and it was the thing I mentioned and showed a picture of back in that episode.
So let's start by looking at what a slide rule is.
Slide rules is an analog computer.
You can use it to do multiplication and division and a bunch of other things.
It depends on the sophistication of your slide rule.
You can do quite a lot with it just a basic one.
But I'm just going to deal with multiplication and division.
I don't really feel I'm qualified to get into very much more to be honest.
I don't think we use them to do anything very sophisticated as a school children in the high school.
Anywhere a slide rule consists of a device with a movable central part, sort of a slider,
which runs through a central slot.
The top and bottom areas above and below the slider have got various different scales on them,
which I'll talk about later.
And the slider has its own scale as well.
And there's a transparent cursor, which you can slide up and down to make it easier to read off from one scale to another scale.
That's the basics of it.
They come in all sorts of shapes and sizes and there's a picture I've taken from Wikimedia on there in the notes.
I've got quite long notes about this.
Lots and lots and lots of links if you want to delve into it anymore.
So as I said, I've still got my slide rule from my school days.
And it's a Faber Castell model 1960s vintage.
There's a picture of it from my previous show.
I don't seem to be able to find it anymore somewhere in the house, but I don't know where it is.
It looks really battered.
It was always carried in my school bag and I used to cycle turn from school about a five mile journey.
So I guess all that shaking and rattling around really beat the hell out of it.
It's just a shame actually, because it's quite a nice looking device.
So I was thinking about doing this episode.
I had a conversation where I said something like I don't think slide rules are much available these days.
And I was challenged on this.
So I went to look on eBay to see if they were available much.
Of course I discovered they are, they're there in the bucket load.
And within an hour I'd found one that looked really interesting for not a lot of money.
£9.99 was the current bid on it.
And so I put my bid of £9.99 on it and won it.
There we are, it's as interested.
It's another Faber Castell, mainly made of wood and looking at the historical documents about these things.
It was probably box wood or mahogany.
It's got a material on the face with the where the scales are, which looks a bit like ivory, but of course it wasn't.
It was an early plastic celluloid, most likely I think.
It's quite a lot older than my 1960s model.
The model number is in the pictures.
And it's made in Bavaria, because it says so on the cursor.
And the vintage is somewhere around 1935, just judging by the model number.
There's loads of information about the history of these things, which I'll mention in a bit more detail later.
So there's three pictures of it showing the front face with the cursor.
It's got red and black scales on it.
And they're quite nice looking cursor with a metal rim around the outside.
The back, you can see the wood.
And it's got various numerical tabley things on the back, which I've not yet had to use.
There was no instructions with this.
I haven't managed to find anything that really would teach me how to use it fully.
And it's also got scales on the back for various purposes that I'm not entirely clear about.
When you take the slider out, which is the way you identify these things,
you can see the model number inside.
You can actually use it for measurement as a ruler.
And it's got millimeters and inches on it.
So it's a strange or wonderful device, I think.
Anyway, that's my Fabricastel acquisition.
So let's look at how a slider works.
Basically, it uses logarithmic scales to perform its various functions,
like multiplications and division.
And I thought, well, we better digress a bit and talk about what a logarithm actually is.
So logarithm is the exponent to which a base must be raised, a power, really,
to which a base should be raised in order to produce the number.
So if you take an example, if the base is 10, which is very often the case,
and a base 10 logarithm is called a common logarithm,
and you write it as the word log with a subscript 10.
Then if 100 is 10 to the power of 2, then the exponent there is 2.
So the log 10 of 100 is 2.
And similarly, the log, the base 10 of 1000, which is 10 to the power of 3, is 3.
There's a Wikipedia page on the logarithm, which I've referenced here.
And it does a better job than I can do on explaining it, I think.
So if you want to get deeper into this, then I would recommend that you have a look at that.
Now, at the time I was using a slider all back in the 1960s,
we were expected to know how to use logarithms,
and we were each allocated a book of log tables, which we used throughout our school life.
I think I still have edge, I think that was our...
Because I get pretty tady after six years of school, so I don't know where it is,
somewhere in this house, as are many other things.
Anyway, the log tables allowed you to look up the common logarithm of a number,
and also to convert logarithm back into a number.
A great advantage of logarithms is that multiplication can be achieved by a simple addition,
and division is simply a subtraction.
So I've used some formulae here, which are also available in the Wikipedia page,
but I thought I'd add them here just in case you didn't want to dig into the Wikipedia stuff.
And I also wanted to experiment with using Latech-Latech formulae,
to see if I could make them look reasonably nice.
What it's saying is the logarithm to an arbitrary base B of x times y
is equal to the log of that base of x plus log to the base of y.
In other words, x times y can be achieved by adding the logs of x and y,
and similarly x divided by y, the log of that is equal to the log to that base of x
minus to log of the same base of y.
The only proviso is that the base and x and y have to be positive,
and B must be greater than one.
The base, that is, got to be greater than one.
So when we were at school, we didn't really get to use slide rules until we were a bit further into mathematics.
And we used log tables. We got the given them very early on,
in our first year or something like that.
When multiplying two numbers, you take one of the numbers and look it up.
Look up its log to the base 10, write it down, do the same for the second number,
and add the two logs together, and the result could then be looked up in an anti-log table
to get the product.
And I decided not to go into the whole anti-log look up stuff,
but if you want to dig into that, you can, there's a reference here to what an anti-log table is
and how to use it.
Wish I could find mine actually, because it would have been easy.
I could have taken some pictures of it and maybe explained it better.
Here's also a wiki how article about how to use log tables, which I've referenced here.
I thought it would be worth just mentioning that logarithms were invented by a guy called John Napier,
and he was an Edinburgh man, I live in Edinburgh.
He was born in 1550 to parents who owned a sort of castle like tower like structure,
called Merkistan Tower or Merkistan Castle, and it still exists,
though the grounds of the original tower are now part of a university,
which not surprisingly is called Edinburgh Napier University.
It used to be Napier University, but they added the Edinburgh presumably to avoid confusion
with all the other Napier universities, I don't know.
The tower is part of the campus, it's got various corridors and bits of the buildings
sort of attached to it, but it looks very nice, it's been refurbished and looks good.
I included a picture of it from Wikipedia.
So after the digression into logarithms, it's easy to say that.
A slide rule was a sort of wipe using logarithms, without having to go through the tables,
and as a short circuit, a shortcut to the process of adding together logs of numbers.
Now there's an excellent Wikipedia article about how to use a slide rule, which I've referenced here,
but I thought I would go into a little bit of detail using my new old Faber Castell.
So we know that multiplication is done by adding logs, and the example I've got a picture
is showing the multiplication of three by two.
So I'm using my slide rule and I'm using the upper scale, and I've positioned it so that the one on
the slider is positioned under the two on the upper scale. So that's one of the multiplications.
Then you look at the three on the slider, and the answer is above it, which is six, obviously.
I've lined it up so that the cursor is being used to show the number we're interested in.
You can slide it along to look at what 3.5 is, two times 3.5 would be seven,
it's slide it but further along to two times four would be eight, et cetera, et cetera.
I use the upper scale in this case because it's just a little bit easier to read, I think anyway.
I also use the slide rule to demonstrate that you can multiply three and two together
in the other order so that you can place the one on the sliding scale against the three on
the upper scale, and then you can look along the sliding scale for the two, and you can see the
answer six a bit further along. You can see the three is not very clear, and you can see a nine
above it. So this is achieved by the fact that the scales are logarithmic. If you do division,
division is slightly different process. Again, using the Wikipedia example of 5.5 divided by two,
and on my slide rule I've aligned the 5.5 mark on the slider with the two on the upper scale,
and then you look underneath the one on the upper scale to get the answer. So I've aligned the
cursor with it, and you can see it's actually 2.75. Hopefully that's clear. I think it is. That's
what the cursor is for, basically. So it's easier to stop your eyes sliding about and missing the
actual thing that you're looking for. So I'm really going to leave my little tutorial on how to use
a slide rule there, and just mention that there are sources of further study if you'd like to dig
into this any more. The International Slide Rule Museum is a brilliant resource, which I've
referenced here obviously, and it's got many, many things that a slide rule enthusiast can delve
into. Certainly I found quite a lot of historical information about the slide rule I bought in there.
It's also a self-guided course, which goes into a lot of depth about how to use a slide rule,
and they even cater for the case people who don't have access to a slide rule by offering a
virtual slide rule, which I think is pretty, pretty smart. The other thing I've mentioned is that
judging by my experiences with this particular slide rule, you should be able to find one for yourself
if you really want to get into this, and I would have definitely have a look on eBay to see what
what you could find. Having bought this one, I wondered if I should see if I could find a couple more,
two or three more. I bought two more, actually. Around about £10 each on average, so the two more
cost me less than £20. One was in better condition than the other, but two more favour castell models,
more recent ones, not quite as nice as this old one, 1935 one. But you can see how, I can see
anyway, because I enjoy collecting stuff. You can see how people could get quite infatuated
with the process of collecting these things, and I've referred to a bunch of people who
do seem to have quite large slide rule collections, obviously a thing. Maybe it'll become an antique
and be worth lots of money. These sorts of things, I don't know, but they're not massively expensive now.
Okay, well, I'll leave it there. I hope you enjoyed that. Bye now.
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