Editing Slide rule (section)

==History==
[[File:oughtred.jpg|thumb|upright|[[William Oughtred]] (1575–1660), inventor of the slide rule]]
[[File:EveradeSlidingRule.pdf|thumb|1763 engraving of a slide rule]]

The slide rule was invented around 1620–1630, shortly after [[John Napier]]'s publication of the concept of the [[logarithm]]. In 1620 [[Edmund Gunter]] of Oxford developed a calculating device with a single logarithmic scale; with additional measuring tools it could be used to multiply and divide.<ref>{{cite book|url=https://books.google.com/books?id=eq5kDQAAQBAJ&pg=PA205|title=History of Mathematics|last=Smith|first=David E.|date=1958|publisher=Courier Corporation|isbn=9780486204307|pages=205}}</ref> In c. 1622, [[William Oughtred]] of Cambridge combined two handheld [[Gunter's scale|Gunter rules]] to make a device that is recognizably the modern slide rule.<ref>{{cite book|chapter-url=https://books.google.com/books?id=k43Q9RHuGXgC&q=William+Oughtred+circular+rule&pg=PT831|title=Encyclopedia of the Scientific Revolution: From Copernicus to Newton|last=Applebaum|first=Wilbur|date=2003-12-16|publisher=Routledge|isbn=9781135582555|chapter=Slide Rule }}</ref> Oughtred became involved in a vitriolic controversy over [[Scientific priority|priority]], with his one-time student [[Richard Delamain]] and the prior claims of Wingate. Oughtred's ideas were only made public in publications of his student William Forster in 1632 and 1653.

In 1677, Henry Coggeshall created a two-foot folding rule for timber measure, called the [[Coggeshall slide rule]], expanding the slide rule's use beyond mathematical inquiry.

In 1722, Warner introduced the two- and three-decade scales, and in 1755 Everard included an inverted scale; a slide rule containing all of these scales is usually known as a "polyphase" rule.

In 1815, [[Peter Mark Roget]] invented the log log slide rule, which included a scale displaying the logarithm of the logarithm. This allowed the user to directly perform calculations involving roots and exponents. This was especially useful for fractional powers.

In 1821, [[Nathaniel Bowditch]], described in the ''[[American Practical Navigator]]'' a "sliding rule" that contained scaled trigonometric functions on the fixed part and a line of log-sines and log-tans on the slider used to solve navigation problems.

In 1845, Paul Cameron of Glasgow introduced a nautical slide rule capable of answering navigation questions, including [[right ascension]] and [[declination]] of the sun and principal stars.<ref>"Cameron's Nautical Slide Rule", ''The Practical Mechanic and Engineer's Magazine'', April 1845, p. 187 and Plate XX-B</ref>

===Modern form===
[[File:Slideruleinuse.wpafb.chap2-2.jpg|thumb|Engineer using a slide rule, with mechanical calculator in background, mid 20th century]]

A more modern form of slide rule was created in 1859 by French artillery lieutenant [[Amédée Mannheim]], who was fortunate both in having his rule made by a firm of national reputation, and its adoption by the French Artillery. Mannheim's rule had two major modifications that made it easier to use than previous general-purpose slide rules. Such rules had four basic scales, A, B, C, and D, and D was the only single-decade logarithmic scale; C had two decades, like A and B. Most operations were done on the A and B scales; D was only used for finding squares and square roots. 

Mannheim changed the C scale to a single-decade scale and performed most operations with C and D instead of A and B. Because the C and D scales were single-decade, they could be read more precisely, so the rule's results could be more accurate. The change also made it easier to include squares and square roots as part of a larger calculation. Mannheim's rule also had a cursor, unlike almost all preceding rules, so any of the scales could be easily and accurately compared across the rule width. The "Mannheim rule" became the standard slide rule arrangement for the later 19th century and remained a common standard throughout the slide-rule era.

The growth of the [[engineering]] profession during the later 19th century drove widespread slide-rule use, beginning in Europe and eventually taking hold in the United States as well. The duplex rule was invented by William Cox in 1891 and was produced by [[Keuffel and Esser Co.]] of New York.<ref name="fn_3">{{cite book |url=http://www.mccoys-kecatalogs.com/K&EManuals/4081-3_1943/4081-3_1943.htm |title=The Log-Log Duplex Decitrig Slide Rule No. 4081: A Manual |publisher=Keuffel & Esser |first1=Lyman M. |last1=Kells |first2=Willis F. |last2=Kern |first3=James R. |last3=Bland |year=1943 |page=92 |archive-url=https://web.archive.org/web/20090214020502/http://www.mccoys-kecatalogs.com/K%26EManuals/4081-3_1943/4081-3_1943.htm |archive-date=14 February 2009 |url-status=dead }}</ref><ref name="fn_4">''The Polyphase Duplex Slide Rule, A Self-Teaching Manual'', Breckenridge, 1922, p. 20.</ref>

In 1881, the American inventor Edwin Thacher introduced his cylindrical rule, which had a much longer scale than standard linear rules and thus could calculate to higher precision, about four to five significant digits. However, the Thacher rule was quite expensive, as well as being non-portable, so it was used in far more limited numbers than conventional slide rules.

Astronomical work also required precise computations, and, in 19th-century Germany, a steel slide rule about two meters long was used at one observatory. It had a microscope attached, giving it accuracy to six decimal places.{{Citation needed|date=February 2011}}

===20th century===
[[File:Buzz and his pipe.jpg|thumb|[[Buzz Aldrin]] with slide rule during [[Gemini 12]] mission]]

In the 1920s, the novelist and engineer [[Nevil Shute|Nevil Shute Norway]] (he called his autobiography [[Slide Rule: Autobiography of an Engineer|''Slide Rule'']]) was ''Chief Calculator'' on the design of the British [[R100]] airship for [[Vickers#Aviation|Vickers Ltd.]] from 1924. The stress calculations for each transverse frame required computations by a pair of ''calculators'' (people) using [[Fuller's cylindrical slide rule]]s for two or three months. The simultaneous equation contained up to seven unknown quantities, took about a week to solve, and had to be repeated with a different selection of slack wires if the guess on which of the eight radial wires were slack was wrong and one of the wires guessed to be slack was not slack. After months of labour filling perhaps fifty [[Paper size#Traditional inch-based paper sizes|foolscap]] sheets with calculations "the truth stood revealed (and) produced a satisfaction almost amounting to a religious experience".<ref>{{cite book |last= Norway |first= Nevil Shute |title=[[Slide Rule: Autobiography of an Engineer|Slide Rule]] |year= 1954 |publisher= William Heinemann |location= London |pages= 76–78 }}</ref>

In 1937, physicist [[Lucy Julia Hayner|Lucy Hayner]] designed and constructed a circular slide rule in [[Braille]].<ref>{{Cite journal |last=Witcher |first=C. M. |date=1954-12-01 |title=Physics without sight  |journal=Physics Today |volume=7 |issue=12 |pages=8–10 |doi=10.1063/1.3061483 |bibcode=1954PhT.....7l...8W }}</ref>

Throughout the 1950s and 1960s, the slide rule was the symbol of the engineer's profession in the same way the [[stethoscope]] is that of the medical profession.<ref>{{Cite journal |last=Stoll |first=Cliff |date=2006 |title=When Slide Rules Ruled |url=https://www.jstor.org/stable/26061456 |journal=Scientific American |volume=294 |issue=5 |pages=80–87 |doi=10.1038/scientificamerican0506-80 |jstor=26061456 |pmid=16708492 |bibcode=2006SciAm.294e..80S }}</ref>

Aluminium Pickett-brand slide rules were carried on [[Project Apollo]] space missions. The model N600-ES owned by [[Buzz Aldrin]] that flew with him to the Moon on [[Apollo&nbsp;11]] was sold at auction in 2007.<ref>{{cite web |url=http://historical.ha.com/c/item.zx?saleNo=669&lotIdNo=41035 |title=Lot 25368 Buzz Aldrin's Apollo 11 Slide Rule – Flown to the Moon. ... 2007 September Grand Format Air & Space Auction #669 |publisher=Heritage Auctions |access-date=3 September 2013 |archive-date=3 September 2013 |archive-url=https://archive.today/20130903142931/http://historical.ha.com/c/item.zx?saleNo=669&lotIdNo=41035 |url-status=dead }}</ref> The model N600-ES taken along on [[Apollo&nbsp;13]] in 1970 is owned by the [[National Air and Space Museum]].<ref>{{cite web |url=http://airandspace.si.edu/collections/artifact.cfm?id=A19840160000 |title=Slide Rule, 5-inch, Pickett N600-ES, Apollo 13 |publisher=Smithsonian National Air and Space Museum |access-date=3 September 2013 |archive-date=9 October 2013 |archive-url=https://web.archive.org/web/20131009225758/http://airandspace.si.edu/collections/artifact.cfm?id=A19840160000 |url-status=dead }}</ref>

Some engineering students and engineers carried ten-inch slide rules in belt holsters, a common sight on campuses even into the mid-1970s. Until the advent of the pocket digital calculator, students also might keep a ten- or twenty-inch rule for precision work at home or the office<ref>Charles Overton Harris, ''Slide rule simplified'', American Technical Society, 1961, p. 5.</ref> while carrying a five-inch pocket slide rule around with them.

In 2004, education researchers David B. Sher and Dean C. Nataro conceived a new type of slide rule based on ''[[prosthaphaeresis]]'', an algorithm for rapidly computing products that predates logarithms. However, there has been little practical interest in constructing one beyond the initial prototype.<ref>{{cite web |url=http://www.findarticles.com/p/articles/mi_qa3950/is_200401/ai_n9372466 |archive-url=https://web.archive.org/web/20050510072825/http://www.findarticles.com/p/articles/mi_qa3950/is_200401/ai_n9372466 |url-status=dead |archive-date=2005-05-10 |last1=Sher |first1=David B. |last2=Nataro |first2=Dean C. |title=The Prosthaphaeretic Slide Rule: A Mechanical Multiplication Device Based On Trigonometric Identities |work=Mathematics And Computer Education, Vol. 38, Iss. 1 (Winter 2004): 37–43 |via=Findarticles.com |date=2009-06-02 |access-date=2010-02-20}}</ref>

===Specialized calculators===
Slide rules have often been specialized to varying degrees for their field of use, such as excise, proof calculation, engineering, navigation, etc., and some slide rules are extremely specialized for very narrow applications. For example, the John Rabone & Sons 1892 catalog lists a "Measuring Tape and Cattle Gauge", a device to estimate the weight of a cow from its measurements.

There were many specialized slide rules for photographic applications. For example, the [[actinograph]] of [[Hurter and Driffield]] was a two-slide boxwood, brass, and cardboard device for estimating [[Exposure (photography)|exposure]] from time of day, time of year, and latitude.

Specialized slide rules were invented for various forms of engineering, business and banking. These often had common calculations directly expressed as special scales, for example loan calculations, optimal purchase quantities, or particular engineering equations. For example, the [[Fisher Controls]] company distributed a customized slide rule adapted to solving the equations used for selecting the proper size of industrial flow control valves.<ref>{{cite web|url=http://www.natgasedu.com/vm004.html |archive-url=https://web.archive.org/web/20100106031649/http://www.natgasedu.com/vm004.html |archive-date=6 January 2010 |title=Fisher sizing rules |access-date=2009-10-06 |work=natgasedu.com |url-status=dead }}</ref>

Pilot balloon slide rules were used by meteorologists in weather services to determine the upper wind velocities from an ascending hydrogen or helium-filled pilot balloon.<ref>{{cite web|url=http://www.pilotballoon.com/slide.htm|title=Pilot Balloon Slide Rules|work=www.pilotballoon.com|access-date=28 September 2016|archive-url=https://web.archive.org/web/20160928041013/http://www.pilotballoon.com/slide.htm|archive-date=2016-09-28|url-status=dead}}</ref>

The [[E6B|E6-B]] is a circular slide rule used by pilots and navigators.

Circular slide rules to estimate ovulation dates and fertility are known as ''wheel calculators''.<ref>{{cite journal |doi=10.1080/14767050412331312200 |pmid=15061314 |title=Circle of time: errors in the use of the pregnancy wheel |journal=Journal of Maternal-Fetal and Neonatal Medicine |date=2003 |volume=14 |issue=6 |pages=370–372 |first=M. G. |last=Ross }}</ref>

A Department of Defense publication from 1962<ref>{{cite web|url=https://www.fourmilab.ch/etexts/www/effects/|title=The Effects of Nuclear Weapons|access-date=2021-05-02}}</ref> infamously included a special-purpose circular slide rule for calculating blast effects, overpressure, and radiation exposure from a given yield of an atomic bomb.<ref>{{cite web|url=https://www.fourmilab.ch/bombcalc/|title=Strangelove Slide Rule|access-date=2021-05-02}}</ref>

<gallery>
File:E6b-front.jpg|An E6-B aviation computer
File:John Rabone 1892 Cattle Gauge.png|John Rabone & Sons 1892 cattle gauge
File:HD Actinograph.jpg|[[Hurter and Driffield]]'s [[actinograph]]
File:Cryptographic sliding rule-IMG 0533.jpg|Cryptographic slide rule used by the Swiss Army between 1914 and 1940
Keuffel & Esser Model 4180, Fraction Adder - MIT Slide Rule Collection - DSC03616.JPG|Rare fractional adder
</gallery>

===Decline===
{{See also|History of computing hardware (1960s–present)}}
[[File:TI-30 LED.png|thumb|upright=.7|The TI-30 scientific calculator, introduced for under US$25 in 1976]]
The importance of the slide rule began to diminish as electronic computers, a new but rare resource in the 1950s, became more widely available to technical workers during the 1960s.

The first step away from slide rules was the introduction of relatively inexpensive electronic desktop [[scientific calculator]]s. These included the [[Wang Laboratories]] LOCI-2,<ref>{{cite web|url=https://www.oldcalculatormuseum.com/wangloci.html|title=The Wang LOCI-2|work=oldcalculatormuseum.com}}</ref><ref name="Wang Ad 1966">{{cite journal |last=Wang Laboratories |title=Now you can determine Copolymer Composition in a few minutes at your desk |journal=Analytical Chemistry |volume=38 |issue=13 |pages=62A–63A |date=December 1966 |doi=10.1021/ac50155a005}}</ref> introduced in 1965, which used logarithms for multiplication and division; and the [[Hewlett-Packard]] [[HP 9100A]], introduced in 1968.<ref name="Leibson_2010">{{cite web |title=The HP 9100 Project: An Exothermic Reaction |date=2010 |first=Steven<!-- Steve --> |last=Leibson |url=http://www.hp9825.com/html/the_9100_part_2.html |access-date=2024-06-16}}</ref> Both of these were programmable and provided exponential and logarithmic functions; the HP had [[trigonometric function]]s (sine, cosine, and tangent) and hyperbolic trigonometric functions as well. The HP used the [[CORDIC]] (coordinate rotation digital computer) algorithm,<ref name="Volder_2000">{{cite journal |first=Jack E. |last=Volder |title=The Birth of CORDIC |journal=Journal of VLSI Signal Processing |issn=0922-5773 |volume=25 |issue=2 |pages=101–105 |date=June 2000 |url=http://late-dpedago.urv.cat/site_media/papers/fulltext_2.pdf |archive-url=https://web.archive.org/web/20160304064804/http://late-dpedago.urv.cat/site_media/papers/fulltext_2.pdf |url-status=dead |archive-date=2016-03-04 |access-date=2016-01-02 |doi=10.1023/a:1008110704586 |bibcode=2000JSPSy..25..101V }}</ref> which allows for calculation of trigonometric functions using only shift and add operations. This method facilitated the development of ever smaller scientific calculators.

As with mainframe computing, the availability of these desktop machines did not significantly affect the ubiquitous use of the slide rule, until cheap hand-held scientific electronic calculators became available in the mid-1970s, at which point it rapidly declined. The pocket-sized Hewlett-Packard [[HP-35]] scientific calculator was the first handheld device of its type, but it cost US$395 in 1972. This was justifiable for some engineering professionals, but too expensive for most students.

Around 1974, lower-cost handheld electronic scientific calculators started to make slide rules largely obsolete.<ref>{{cite book |title=Writing and reading across the curriculum |last1=Behrens |first1=Lawrence|last2=Rosen|first2=Leonard J.|year=1982|publisher=[[Little, Brown]]|page=273|quote=Then, just a decade ago, the invention of the pocket calculator made the slide rule obsolete almost overnight...}}</ref><ref>{{cite book |title=e: The Story of a Number |page=16 |last1=Maor |first1=Eli |publisher=Princeton University Press |year=2009 |isbn=978-0-691-14134-3 |quote=Then in the early 1970s the first electronic hand-held calculators appeared on the market, and within ten years the slide rule was obsolete.}}</ref><ref>{{cite book |title=Inventions that Changed the World |last1=Castleden |first1=Rodney |year=2007 |page=157 |publisher=Futura |isbn=978-0-7088-0786-6 |quote=With the invention of the calculator the slide rule became instantly obsolete.}}</ref><ref>{{cite book |title=Beyond calculation: the next fifty years of computing |page=xiv |last1=Denning |first1=Peter J. |author-link1=Peter J. Denning |last2=Metcalfe |first2=Robert M. |author-link2=Bob Metcalfe |isbn=978-0-387-98588-6 |publisher=[[Springer Verlag|Springer]] |year=1998 |quote=The first hand calculator appeared in 1972 and made the slide rule obsolete overnight. |url=https://archive.org/details/beyondcalculatio00pete}}</ref> By 1975, basic four-function electronic calculators could be purchased for less than $50, and by 1976 the [[TI-30]] scientific calculator was sold for less than $25 (${{Formatprice|{{Inflation|US|25|1976|r=2}}|0}} adjusted for inflation).

1980 was the final year of the [[University Interscholastic League]] (UIL) competition in [[Texas]] to use slide rules. The UIL had been originally been organized in 1910 to administer literary events, but had become the governing body of school sports events as well.<ref>{{cite journal |last1=Gabbert |first1=Mike |title=Slide Rule Competition in Texas High Schools |journal=Journal of the Oughtred Society |date=Fall 1999 |volume=8 |issue=2 |pages=56–58 |url=https://osgalleries.org/journal/pdf_files/8.2/V8.2P56.pdf |access-date=5 March 2025}}</ref>