Introduction to the Slide Rule
William Oughtred and others developed the slide rule in the 17th century
based on the emerging work on logarithms by John Napier. Before the
advent of the pocket calculator, it was the most commonly used calculation
tool in science and engineering. The use of slide rules continued to grow
through the 1950s and 1960s even as digital computing devices were being
gradually introduced; but around 1974 the electronic scientific calculator
made it largely obsolete
Addition Using a Ruler
What addition sum does this show?
0
1
2+3=5
2+4=6
2+5=7
…
0
1
2
3
4
5
6
2
3
4
5
6
7
8
7
Alternatively this could be seen as a subtraction:
5–2=3
6–2=4
7–2=5
…
Addition Using a Ruler
What addition sum does this show?
2
3
4+3=7
4+4=8
4+5=9
…
0
1
2
3
4
4
5
6
7
8
5
6
7
Alternatively this could be seen as a subtraction:
5–4=1
6–4=2
7–4=3
…
Logarithmic Scales
We are going to replace the numbers 0, 1, ,2, 3 … with Powers of 2
1
20
0
2
21
1
4
22
2
8
23
3
16
24
4
32
25
5
64
26
6
128
27
7
256
28
8
Logarithmic Scales
This leaves us with the logarithmic scale shown below.
When we move one unit along instead of adding 1 we are doubling
1
20
1
2
21
2
4
22
4
8
23
8
16
24
16
32
25
32
64
26
64
128
27
128
256
28
256
This has the effect of extending the scale from the original 0 to 8 to 1 to 256
If we had picked Powers of 3 it would have been an even larger range …
Logarithmic Scales on a Slide Rule
0
20
1
1
21
2
2
22
4
3
23
8
4
24
16
5
25
32
6
26
64
7
27
128
8
28
256
We are now going to put the two logarithmic scale together and
see why this is useful
1
20
2
21
4
22
8
23
16
24
32
25
64
26
128
27
256
28
0
1
2
3
4
5
6
7
8
Logarithmic Scales on a Slide Rule
0
20
1
1
21
2
2
22
4
3
23
8
4
24
16
5
25
32
6
26
64
1
2
4
8
16
32
64
128
256
20
21
22
23
24
25
26
27
28
0
1
2
3
4
5
6
7
8
Previously we used this to show that 2 + 3 = 5
Or
5–2=3
7
27
128
8
2
25
Logarithmic Scales on a Slide Rule
0
20
1
1
21
2
2
22
4
3
23
8
4
24
16
5
25
32
6
26
64
1
2
4
8
16
32
64
128
256
20
21
22
23
24
25
26
27
28
0
1
2
3
4
5
6
7
8
7
27
128
Looking at the logarithmic scale we see that 4 x 8 = 32
Or
32 / 4 = 8
8
2
25
Logarithmic Scales on a Slide Rule
1
20
2
21
20
1
21
2
22
4
23
8
24
16
25
32
26
64
4
22
8
23
16
24
32
25
64
26
128
27
256
28
If we look at the powers we can see that 2 + 3 = 5
It becomes a multiplication because 22 x 23 = 25
We are adding the powers and therefore we are
multiplying the numbers
27
128
2
25
Logarithmic Scales on a Slide Rule
2
21
4
22
20
1
21
2
22
4
23
8
24
16
25
32
8
23
16
24
32
25
64
26
128
27
256
28
26
64
If we look at the powers we can see that 3 + 4 = 7
It becomes a multiplication because 23 x 24 = 27
Or a division because 27 ÷ 23 = 24
27
128
2
25
This is a simplified slide rule with just the two scales: Click here
This is complete slide rule (Use the A&B scales which go up to
100 or C&D scales which go up to 10): Click here
If you Flip the middle scale (see top right of the Slide Rule) you
can see some convenient conversion scales.
D to A is squaring
D to K is cubing