Hello, everyone!
Today, I want to show you this.
It's called a slide rule,
and I'm going to show you how to use this
to perform calculations--
so: multiplication,
division, squaring a number,
and so on.
It's what they used to use
before pocket calculators.
So people like mathematicians,
engineers,
physicists--
you know--
cool people!
I'm going to show you how to use this,
and then, finally,
I will show you why this worked.
They were big in the fifties!
But, then again,
so were rickets!
So when you first see one of these,
they look a bit baffling.
They look a little bit like a ruler,
except this bit here, in the middle, slides across.
So, hey! It's not just a clever name.
If you look closer, you'll notice that the scales
aren't uniform.
So here,
there's a large gap
between the numbers 1 and 2,
but there's only a small gap
between the numbers 8 and 9.
But how do I use this to multiply?
So, luckily,
we can ignore
most of the scales here on the slide rule.
The only ones we need to use
are the scale here on the sliding part,
and the scale underneath it.
So let's say I want to
double a number.
So what I'm going to do
is I'm going to move the scale across
so that the number 1
on the left-hand side
lines up
with the number 2
underneath it.
So I'll just slide that across
so now 1 becomes 2,
and I've doubled it.
But if I do that, the whole scale gets doubled--
2 becomes a 4,
3.2 becomes 6.4.
So that's how I would multiply by 2.
You slide it across,
so that it lines up with the number 2,
and then the whole thing gets doubled.
But the scales only go up to 10, so
how do you do something bigger?
What if I wanted to calculate
250 times 3?
How would I use the slide rule
to do that?
You have to make
all the numbers
less than 10.
And then you estimate
the magnitude of the final answer
at the end.
So if I want to calculate
250 times 3,
I can use the slide rule
to work out
2.5 times 3.
I can do that.
I just slide the scale along
so that the number 1
lines up with the 3,
this triples the whole scale,
and 2.5 times 3
is 7.5.
If I want to know 250 times 3,
well, that's just 100 times bigger.
So the answer is 750.
But what if I wanted to know
7 times 3?
If you can see
the 7--it falls off the end of the scale.
So how do I calculate 7 times 3?
You use the right-hand side
of the sliding scale
instead of the left-hand side.
So you move the right-hand side across,
so that it lines up with the 3,
and now 7
becomes 2.1.
But the answer, obviously,
isn't 2.1.
The answer is 21.
So you have to use your common sense.
What if I wanted to do something
a bit more complicated?
What if I wanted to calculate
455 times 615?
Well, I can use the slide rule
to calculate
4.55
times 6.15,
and I get the answer
2.8.
But that's not the final answer.
I need to calculate
the final magnitude of that.
Which is...
[calculator beeping]
Now division is just the reverse
of multiplication.
So if I line up
1 above 2,
then 2 times 4 becomes 8.
And if I want to know 8 divided by 4,
that's 2.
It's just
the reverse.
Let's have a look at some of the other scales.
Right here in the center,
this is the reciprocal.
So the reciprocal of 4 is 2.5--
you just read that straight off.
This scale here, near the top,
is the square of the number.
So 4 squared is 16.
And then right here at the top,
is the cube of the number.
So 4 cubed
is 64.
You can just read those straight off.
Here at the bottom
is the log of the number.
So what is a log?
The log is the power of 10
that you need
to make that number.
So the log of 100 is 2,
because you need 2 powers of 10.
10 times 10 is 100.
The log of 1,000 is 3--
you need three powers of 10.
10 times 10 times 10 is 1,000.
But you can do numbers in-between, as well.
The log of 525
is 2.72.
In fact,
we're going to use logs
to explain the secret
of the slide rule.
So how does the slide rule work?
Well, logs have a special property.
The log of x
plus the log of y
is equal to the log of x times y.
So if I wanted to work out
x times y
one way I can do it
is I can add the logs together,
log(x) plus log(y).
I get a result.
I then reverse the log process
and I get x times y.
So you add the logs together,
and then reverse the log process.
So, for example,
let's say I want to do
21 times 25.
Well, I can add the logs together
and I get 2.72.
I then reverse the log process,
and the reverse of the log process
that's 10 to the power 2.72,
and I get the answer,
525.
So, imagine we've got
two log scales.
And notice--
the log scales are not uniform.
There's a large gap
between log(1) and log(2),
but only a small gap
between log(8) and log(9).
Now, let's say I want to do something simple.
Let's say
I want to do 4 times 2.
So I'm going to add the logs together.
Log(4) plus log(2).
If I want to add log(2),
what I can do is just slide the top scale
across to the right--
log(2)--
log(2) across--
and that will add log(2)
to everything.
So log(4)
plus log(2)
is log(8).
I then reverse the log process
to get the final answer, 8.
Now, the scales on the slide rule
are designed
to do that last step
for you.
So you don't have to do
this reversing part of the process.
You can just read the answer
straight off.
And that's how
and why
a slide rule works.
So, well,
if you have been,
thanks for watching.