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Slide Rule

Slide Rule

Made of

Wood Aluminum Plastic

Brief description

A mechanical analog computer used primarily for multiplication and division, and also for functions such as exponents, roots, logarithms, and trigonometry. It consists of a set of graduated scales that can be moved relative to each other.

Use / Function

  • Calculation: Rapidly performing complex mathematical operations without electronic computers.
  • Engineering: Essential tool for engineers and scientists from the 17th century until the mid-20th century.
  • Navigation: Used for calculating positions and courses.
  • Scale: Handheld portable device.

Operating principle

The slide rule operates on the principle of Logarithms:

  1. Logarithmic Scales: The scales on a slide rule are not linear but logarithmic.
  2. Addition for Multiplication: Because $\log(A \times B) = \log(A) + \log(B)$, the physical addition of two lengths on logarithmic scales corresponds to the multiplication of the numbers they represent.
  3. Subtraction for Division: Similarly, subtracting lengths corresponds to division.
  4. Analog Nature: It provides a visual, analog representation of numerical relationships.

How to create it

1. The Body (Stock)

Create a stable frame with a central groove. Typically made of dimensionally stable Wood (like boxwood), Aluminum, or high-quality plastic.

2. The Slide

A matching piece that fits precisely into the groove of the stock and can slide smoothly back and forth.

3. The Scales

Mark precise logarithmic graduations on both the stock and the slide. Accuracy in the graduation is the most critical factor for the tool’s utility.

  • Scale C and D: Basic logarithmic scales for multiplication and division.
  • Scale A and B: Squares and square roots.

4. The Runner (Cursor)

A sliding window with a vertical hairline used to align marks on different scales that are not adjacent.

Materials needed

  • Wood: Specifically boxwood or mahogany for stability.
  • Aluminum: For more durable, modern versions.
  • Ivory or Bone: Historically used for the scales face.
  • Plastic: For low-cost mass production.
  • Glass: For the cursor window.

Variants and improvements

  • Linear Slide Rule: The most common form, resembling a ruler.
  • Circular Slide Rule: Compact version where scales are arranged in concentric circles.
  • Cylindrical Slide Rule: Allowed for very long scales (high precision) in a portable format.
  • Specialized Rules: Rules designed for specific fields like chemistry, aviation, or electrical engineering.

Limits and risks

  • Precision: Generally limited to 3 significant figures. Not suitable for tasks requiring absolute precision (like accounting).
  • Human Error: Misalignment or misreading the scales can lead to significant errors.
  • Addition/Subtraction: The slide rule cannot perform addition or subtraction; these must be done mentally or on paper.
  • The Decimal Point: The slide rule only provides the significant digits; the user must keep track of the decimal point’s position.