John Napier dramatically advances the understanding of number relationships in 1614 with his invention of logarithms. Since logarithms are the foundation on which the slide rule is built, its history rightly begins with him. His early concept of simplifying mathematical calculations through logarithms makes possible the slide rule as we know it today.
The ability of logarithms to decompose any number into two parts a base and an exponent allows the products and dividends of large numbers to be determined by addition and subtraction. Also, using base e (rather than the common base 10) opens the way for tremendous advances in engineering and science, induding the differential calculus.
Napier himself contributes Napiers Bones in 1617, calculating sticks based on the geologia (lattice) multiplication method. In 1620 Edmund Gunter of London makes a straight logarithmic scale and performs multiplication and division on it with the use of a set of dividers, or calipers.
In about 1622 William Oughtred, an Anglican minister ... today recognized as the inventor of the slide rule ... places two such scales side by side and slides them to read the distance relationships, thus multiplying and dividing directly. He also develops a circular slide rule.
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In 1675 Sir Isaac Newton solves cubic equations using three parallel logarithmic scales and makes the first suggestion toward the use of the cursor.
Early slide rules are carefully incised by hand on boxwood or pearwood, of no uniform length, with each bearing the scale divisions of a unique maker. Expensive handcrafted instruments find use among the scientific elite, but this is hardly a sufficient market to sustain slide rule production. Advances in rule design without practical business application are ignored and then forgotten.
In 1677, two years after Newton invents the cursor, Henry Coggeshall perfects the timber and carpenters rule. Newtons cursor fails to catch on at the time. The Coggeshall rule remains in common use 200 years later. His design and its standardization move the slide rule from a tool of mathematical inquiry to specialized applications.
Beginning in 1683, Thomas Everard popularizes the gauging rule, used to determine the content of ale, wine and spirits barrels and to calculate the excise tax thereon. This design, first created by William Oughtred in 1633, sees widespread use well into the 19th Century.
Throughout the 18th Century, slide rule production and use is mostly English, with limited penetration into other capitalist economies, including France and the Netherlands. Interesting to note is the lack of slide rules and makers in Germany, Switzerland, and Italy ... countries which at this time are producing cutting edge mathematics.
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The slide rule delivers the mathematical framework for advances in the industrial arts and for ways of thinking about numbers and their applications in engineering. These discoveries are in turn applied to improvements in the slide rules accuracy, precision, and mass production.
In 1722 John Warner, a London instrument dealer, uses square and cube scales. By 1790 James Boulton and James Watt are modifying slide rules to improve their accuracy and usefulness. By 1799 their Soho slide rule helps to usher in the lndustrial Revolution. It facilitates the design and manufacture of their seminal machine, the steam engine.
In the l9th Century the engineer learns that precision to the third decimal place suffices to create superb structures. The slide rule allows such calculation, while its portability encourages design verification and standardization on the job.
Modern engineering is invented through the use of the slide rule, itself a design that could only create this impact through modern engineering. In 1815 Peter Roget, an English physician (and the author of Rogets Thesaurus), invents a log log scale, which he uses to calculate roots and powers to any number or fraction thereof. It is regarded at the time as a mathematical curiosity.
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Fifty years later, advances in electrical engineering, thermodynamics, dynamics and statics, and industrial chemistry make these scales so necessary they are rediscovered. In the next fifty years they increase from three, to six, to eight scales on the slide rule, as engineering extends its grip on modern computation.
During the first half of the 19th Century slide rule use broadens with the extension of education, democracy and free trade. Britain sees tremendous expansion of slide rule types and manufacturers. Frances revolution of 1795 ushers in a period of extreme mathematical rationality. Results include invention of the metric system, advanced knowledge of the movements of the heavens and earth, and the first requirement that all civil servants demonstrate slide rule proficiency as a part of qualifying exams.
In 1851 a French artillery officer named Amedeé Mannheim standardizes a set of four scales for the most common calculation problems. The four scales include two double length, named A & B, for squares and square roots...and two single length, C & D, for multiplication and division. This scale set becomes the basis of slide rule design for the next 100 years and bears his name today. His design and use of a cursor hastens the eventual widespread acceptance of this feature.
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Tavernier & Gravet of Paris quickly develops an international reputation for accuracy in production of the Mannheim design. An inverted C scale (CI) and a K scale (for cubes and cube roots) were added later to the face of the rule by others, along with two trigonometry scales (S & T) and a logarithm scale (L) on the back of the slide. These additions comprise what is often called the Enhanced Mannheim scale set.
Belcher Brothers, New York (1821-1876), E.A. Stearns & Co., Vermont (1838-1863) and Stanley Rule & Level Co., Connecticut (1857-1920), add versions of English slide rule designs to their product lines. Palmers Calculator, a circular slide rule, is produced in the United States about 1845. Richardson follows soon after with a steel linear slide rule in 1851.
By 1870, Germany produces two giants of the slide rule world, Dennert and Pape (makers of Aristo), and Faber (later Faber-Castell). The Dennert and Pape contributions of engine divided (engraved) scales and the stable deposit of celluloid on wood are revolutionary. Slide rules can now be manufactured with any scale sets desired, to a high degree of precision, with highly visible, reproducible colored faces, allowing accurate calculations to three or four decimal places. The tool exactly corresponds to the revolution in engineering occurring at the same time.
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The slide rules importance to the Industrial Revolution, and the impact of the Industrial Revolution upon the slide rule, are demonstrated by the proliferation of designs. From 1625 to 1800, the first 175 years after its invention, a total of 40 slide rule types, including circular and spiral designs, are recorded. The next 100 years, from 1800 to 1899, sees the creation of 250 slide rule types and manufacturers. Over 90 designs are recorded in the first 10 years of the 20th Century.
Cylindrical calculators with extra long logarithmic scales are invented by George Fuller of Ireland in 1878 and Edwin Thacher of New York in 1881. The plates for printing the paper scales of both the Fuller and Thacher calculators are produced by Stanley of London, who probably makes the first Thachers. Production is soon taken over by a Hoboken, New Jersey instruments company, Keuffel and Esser, that had previously imported slide rules for sale.
A revolutionary linear slide rule construction with scales on both front and back and with a cursor referring to all scales simultaneously is patented in 1891 by William Cox...an invention he calls the duplex slide rule.
Folded scales CF, DF and CIF are put on slide rules about 1900 to reduce the amount of movement and resetting of the slide. Log log scales in three sections appear about 1901, enabling very accurate calculation of powers and roots to any number or fraction.
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Numerous improvements by several manufacturers follow, contributing to the widespread popularity of the slide rule and its many uses in the mathematics of science and engineering, as well as for calculations of all kinds in business and industry.
The evidence of the slide rules portable, immediate power stands everywhere around us as the 20th Centurys greatest engineering examples, from the Empire State Building to the Apollo lunar landings.
Our last century could not have been built without it, yet its direct evidence is almost totally missing to the uninformed eye.
Slide rule researchers have estimated that possibly 40 million slide rules were produced in the world in the 20th Century alone. Among these are many types of specialty slide rules developed and made for specific applications such as chemistry, surveying, electricity and electronics, artillery ranging, hydraulics, steam and internal combustion engines, concrete and steel structures, radio and other special fields.
The slide rule has a long and distinguished ancestry, from William Oughtred in 1622 to the Apollo missions to the moon ... a span of three and a half centuries ... it was used to perform design calculations for virtually all major structures built on this earth during that long period of our history ... an amazing legacy for something so mechanically simple.