# 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 form1929 – 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 ($395)

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

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

1976 – the last slide rule to be produced in the U.S. is manufactured by K&E, donated to the Smithsonian Institute in Washington, D.C., USA