Short Slide Rule History

Within a few decades following the invention of the logarithm in the early 1600s, logarithmic scales were developed where adding lengths measured along the scale – at first by using “dividers” or “calipers” – could result in the product of two numbers, allowing for quick multiplication and division operations. Instruments improved in both accuracy and function over many years and by 1900 had gained widespread use in mathematics, science, engineering and finance. The story of the slide rule developed over the course of 350 years until the mid-1970’s at which time – essentially overnight – the introduction of the electronic calculator and the personal digital computer replaced the slide rule for everyday computational use.

Below is a condensed time line of the history of the slide rule, produced primarily from an appendix in the book Deci-Lon: An Instruction Manual, published by Keuffel & Esser Co. (K&e Slide Rules: Deci-Lon, an Instruction Manual 1962), and from the book Slide Rules: Their History, Models and Makers, by Peter M. Hopp (Hopp 1999).

A Short History

  • c.1590 – Galileo Galilei, Italy, uses a sector to calculate squares, reciprocals and tangents of numbers. From the Oughtred Society publication, All About Slide Rules: “Galileo’s design of the sector as a mathematical tool can be seen as the moment when calculation aids cease to be based upon counting and instead exploit the deeper relationships among numbers.”

  • 1614 – John Napier, Scotland, publishes Canon of Logarithms

  • 1617 – John Napier, Scotland, and Henry Briggs, England, publish Logarithmorum Chilias Prima (“The First Thousand Logarithms”), which gave a brief account of logarithms and a table for the first 1000 integers calculated to the 14th decimal place.

  • 1620 – Edmund Gunter, England, invents the straight logarithmic scale, used through the aid of “dividers” (compasses) to add logarithms to perform calculations

  • 1624 – Edmund Wingate, Paris, publishes description of Gunter’s logarithmic scale; English translation (1628) contains sector engraved with logarithmic Gunter’s scale

  • 1624 – William Oughtred, England, arranges two Gunter scales to slide along each other, kept together by hand – the first “sliding” rule

  • 1632 – William Oughtred, England, produces “Circles of Proportion,” a single circular sliding rule with logarithmic scales

  • 1675 – Sir Isaac Newton, England, solves the cubic equation using three parallel log scales; also first suggested using an indicator (or, “cursor”) about this time

  • 1677 – Henry Coggeshall, England, puts logarithmic scaled slide in two-foot folding ruler, adapted for timber measure; first “standard” rule of its kind, a type that lasted for about 200 years

  • 1722 – John Warner, England, first uses square and cube scales

  • 1775 – Thomas Everard, England, created inverted log scale, and “gauging”

  • 1775 – Matthew Boulton, England, and James Watt, Scotland, design an engineering slide rule, the Soho slide rule, for the design of their steam engine

  • 1779 – Boulton and Watt improve the accuracy of their rule; becomes a standard for the engineering profession

  • 1800-1810 – Joshua Routledge, England, invents the Engineer’s Rule, combining a 12-inch brass slide containing the logarithmic scales with an ordinary 2-foot folded ruler to which was added a table of commonly used gauge points; extending the brass slide can create a standard “yard” stick.

  • 1815 – Peter Roget, England, (yes, of Thesaurus fame!) invents the Log-Log scale

  • 1850 – Lieutenant Amédée Mannheim, France, presents his form of the slide rule, with the modern arrangement of scales (A, B, C, D); added cursor to his rule in 1851

  • 1859 – Amédée Mannheim, France, credited with the invention of first modern slide rule

  • 1878 – George Fuller, Ireland, invents the Fuller cylindrical long-scale calculator

  • 1881 – Edwin Thacher, USA, invents the Thacher long-scale calculator

  • 1890 – a survey showed that England, France and Germany were the only manufacturers of slide rules at this time

  • 1891 – William Cox, England, patents concept for the duplex (double-sided) slide rule, assigns patent to K&E in USA; K&E becomes first slide rule manufacturer in USA (see appendix in (Fiesenheiser 1951))

  • 1894 – slide rule production begins in Japan with formation of Sun/Hemmi

  • 1900 – folded scales (e.g., CF, DF) introduced about this time

  • 1902 – Max Rietz, Germany, proposes his new arrangement of scales which becomes a new standard; this arrangement includes the K and L scales for cubes and logs

  • 1909 – segmented (3 sections) Log-Log scales put on K&E rules

  • 1923 – Olin Parsons, USA, patents (applied for in 1919) special scales for finding hypotenuse of right triangle; similar scales later introduced on certain Sun-Hemmi rules (P, Q, Q’ scales) in Japan

  • 1925 – Max Rietz, Germany, adds reciprocal scales and small-angle scales to the Rietz arrangement

  • 1924-1928 – Albert Puchstein, USA, and Mendell Weinbach, USA, independently invent Log-Log Vector scale sets for evaluating hyperbolic functions with complex arguments in Cartesian and/or polar form

  • 1929 – Sadatoshi Betsumiya and Jisuke Miyazaki, Japan, invent the P and Q scales used on Hemmi rules for adding and subtracting numbers in quadruature

  • 1934 – Alwin Walther, Germany, at the Technische Hochschule Darmstadt, modified the Rietz system for the needs of engineers, establishing the System Darmstadt

  • 1937 – Patent issued for \(G_\theta\) scale on Hemmi rules, invented by Hisashi Okura, Japan, for finding values of hyperbolic functions

  • 1947 – James Bland, USA, patents set of scales, relating the LL0 scale (and all other scales on the rule) with the C/D scales, and grouping LLx and LL0x scales together for more easily calculating hyperbolic functions.

  • 1972 – Hewlett-Packard introduces the first “pocketable” scientific calculator, HP-3 (USD 395)

  • 1972-75 – development of Hewlett-Packard HP-35 and Texas Instruments SR-50 calculators drives down the cost of these devices (USD 100-300)

  • 1974 – first programmable scientific pocket calculator HP 65, with register and program memory on magnetic strips (USD 795)

  • 1976 – final slide rule produced by K&E donated to the Smithsonian Institute in Washington, D.C., USA