Slide Rule

1. Old School
Slide rule for fun and profit.
Or
An elegant computer from a more civilized age.

2. Slide rules are based on logarithms:
Two logarithmic scales next to each other will align at the product.
Therefore, align the value of the first operand with the “one” value, the
position on the second scale of the second operand aligns with the
product of the two numbers.
In 1614, John Napier discovered the logarithm which made it possible
to perform multiplications and divisions by addition and subtraction.
Ie:
a*b = 10^(log(a)+log(b))
and
a/b = 10^(log(a)-log(b))
First Principles

3. Aligning Scales
Two rulers aligned will perform addition:
Line up the 0 position with the first value and then find the value across
from the second.
Two logarithmic scales will perform multiplication.
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4. My Slide Rule
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2 x 2 = 4

5. You can also use non-actual values with simple magnitudes of 10 to
estimate values out of the immediate range to the rule.
Here, we have removed the 10 from the 16.6 and treated the 4 mark as
10, that means the product must take back the power of 10 we cut from
the C scale. Actual slide rule starts at 0, so you could point to actual
16.6
Advanced

6. Pickett == Company that made slide rules
Pickett Scales == Most common labels on
the various scales.
The C and D lines are as above, but the Pickett 120 has three other
inner scales and three other outer scales.
Pickett

7. A 1960 Pickett manual said:
"When people have difficulty in learning to use a slide rule, usually it is
not because the instrument is difficult to use. The reason is likely to be
that they don't understand the mathematics on which the instrument is
based, or the formulas they are trying to evaluate. Some slide rule
manuals contain relatively exhaustive explanations of the theory
underlying the operations. In this manual it is assumed that the theory
of exponents, of logarithms, of trigonometry, and of the slide rule is
known to the reader, or will be recalled or studied by reference to formal
textbooks on these subjects."
From the Pickett Manual

8. C + D = Multiplication
CI + D = Reciprocals
CI = 2, D = 5 == .5 since
.2 is the reciprocal of .5
A + B = Square Roots Align the base on
A, and look across to D to find
The square root.
S + D = Sine and Cosine. This scale runs in reverse and aligns
angles on D.
T + D = Tangent (See above)
L + Any= Log base 10 of value – this is simple a linear scale like
a ruler!

Pickett Scales

9. C + D = Multiplication
CI + D = Reciprocals
CI = 2, D = 5 == .5 since
.2 is the reciprocal of .5
A + B = Square Roots Align the base on
A, and look across to D to find
The square root.
S + D = Sine and Cosine. This scale runs in reverse and aligns
angles on D.
T + D = Tangent (See above)
L + Any= Log base 10 of value – this is simple a linear scale like
a ruler!

Pickett Scales