Editing Slide rule (section)

===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}}