Slide rules

In 1622, William Oughtred of Cambridge combined two logarithmically graduated rulers, which, by sliding, allowed the logarithms of the two numbers to be added. \(\log(a)+\log(b)=\log(a \times b)\); thus performing a product via an addition.

This instrument was perfected and enriched until the 1970s. The appearance of calculators at increasingly attractive prices led to the decline of "slide rules". High school and university students of my generation experienced this shift.

The Graphoplex 612 slide rule is part of the RIETZ range. It is the pocket version (15 cm) of the 620d (29 cm). To illustrate its operation, you will find here, greatly enlarged, the 3 parts of it:

• the immobile base (the stator),
• the sliding ruler (the slider),
• the sliding magnifier (the cursor).

To play with this virtual slide rule (Graphoplex 612), click on the rule below then,

• Click/Drag the cursor or the central slider.
• Use the left and right arrow keys on the keyboard to reach the parts of the rule that go off-screen.
• Trigonometric graduations are on the back of the sliding ruler. To display the trigonometric scales: click on the "Flip the sliding ruler" button

The scales engraved on the front are:

• B and b: the base numbers from 1 to 10 (actually from 0.9 to 11.1)
• a: the reciprocal scale. a=1/b
• b², B²: the squares scales of b and B.
• B³: the cubes scale of B.
• L: the Log₁₀ scale of B.

The trigonometric scales, engraved on the back of the movable central cursor, are:

• S: Arcsin(B) with 5.7° < S < 90°
• T: Arctan(B) with 5.7° < T < 45°
• S & T: Arcsin(B) ~ Arctan(B) with 0° < S & T < 5.7°

We therefore have a sine table for angles S ∈ [0, 90°] and a tangent table for angles T ∈ [0, 45°]. Then, for other angles, the rules (relations) of trigonometry do the rest.

My first 2 slide rules date back to my high school years. They were Graphoplex, more precisely from 1970.

• Graphoplex - 640 - electric log
• Graphoplex - 612 - reitz

Then, later, out of taste and nostalgia, I found some more or less old models.

• Dietzgen - N1733L - Polymath Decimal Trig Log Log
• Graphoplex - 620d - reitz
• Aristo - 0908 - TriLog
• Graphoplex - 690a - electric log log
• Graphoplex 692 (pocket)
• Netsler - N°21 - Darmstadt
• Netsler - Polymath- duplex - pocket
• Faber - 55/91 - reitz
• Faber - 360 - reitz
• Faber Castel - 375 - reitz
• Unique - Log Log - Pocket

• 1614 - Invention of logarithms by John Napier, Baron of Merchiston, Scotland.
• 1617 - Development of base 10 logarithms by Henry Briggs, Professor at Oxford.
• 1620 - Interpretation of logarithmic scales by Edmund Gunter, Professor of Astronomy in London.
• 1630 - Invention of the slide rule by the Reverend William Oughtred, London.
• 1657 - Development of the sliding part by Seth Partridge.
• 1775 - Development of the sliding cursor by Robertson of the Royal Academy.
• 1815 - Invention of the log log (LL) scale principle by P.M. Roget of France.
• 1850 - Amédée Mannheim, France, designed the modern arrangement of scales.
• 1886 - Dennert & Pape, Germany, used white celluloid as a new material for graduations.
• 1900 - More precise graduations on the slide rule.
• 1976 - The last slide rule left the K&E factories and was given to the Smithsonian Institute, Washington, DC, USA.