Slide RulesLinear Slide Rules
Between 1614 and 1622, John Napier discovered logarithms, Edmund Gunter devised a scale on which numerals could be multiplied and divided by measuring the distance between two logarithmic numbers with a pair of dividers, and William Oughtred put two such scales alongside each other, moving one on a slide so that the distance between the numbers could be read off directly. The speed with which these developments unfolded suggests the power that logarithms provided for reducing the tedium of calculation. By the 1680s, the English used slide rules in carpentry and in gauging (estimating liquid volumes)—the instruments were quite helpful for determining excise taxes on barrels of liquor.
It was not until the late eighteenth century that slide rules were commonly utilized in the manufacture of machines and machine tools, most notably by James Boulton and James Watt. Several more decades passed before slide rule use became widespread throughout Europe. French artillery officer Amedée Mannheim fostered acceptance of the rectangular or linear form of the instrument in 1851 by standardizing the general types of scales and the order in which the scales were arranged. Mannheim also developed the cursor or indicator, which made it easier to read results from two scales that were not adjacent to each other. By the 1870s, German companies made slide rules one of the first consumer products to be fashioned out of plastic (specifically, sheets of celluloid laminated to a wooden frame), and they built dividing engines that permitted mass production of the scales engraved on slide rules. In the United States in the 1890s, Keuffel & Esser of New York City pioneered first the import and then the domestic manufacture of linear slide rules. Numerous other companies entered the market in the 20th century.
A quick tour of what you can expect to see on a slide rule starts with the C and D scales, which both represent the standard number line. To multiply two numbers, set the 1 on the C scale above the first number to be multiplied on the D scale. Look at the second number to be multiplied on the C scale; the number below it on the D scale is the answer. For example, to multiply 2 by 3, set 1 on C over 2 on D, and then look below 3 on C to see the answer 6 on D. Division is accomplished by reversing the process. To calculate 6 ÷ 3, set 3 on C over 6 on D, then look at 1 on C to see the answer 2 on D. To deal with numbers larger than 10 or smaller than 1, the user must mentally move the decimal point. Slide rule users also had to be able to estimate distances between marks on the scales, since there was no way to include all of the digits needed to solve a problem such as 3.14 X 2.7. (On linear and circular slide rules, the answer is "approximately 8.48." Web sites on the Resources page provide more detailed training in using slide rules.)
|Instructions for multiplying two numbers on a slide rule. Eugene Dietzgen Co., Self-teaching Instruction Manual [for] Maniphase Slide Rule (Chicago, [1950s]), 4. NMAH Mathematics Collection, cat. no. 1988.0367.02. AHB2013q009216|
The basic process for setting up and solving problems is the same for operations on other scales. If the numbers used in the calculation produce a result off the ends of the scales, a user employs the CI and DI scales, which put the number line in inverse, or reverse, order. If the numbers still extend past the end of the instrument, the user may try the "folded" CF and DF scales, which start numbering at π instead of at 1. The A and B scales are number lines of squares, so they are used with the C or D scales to square (or take the square root of) a number. The K scale provides cubes and cube roots. L scales represent common logarithms, S scales give sines and cosines, and T scales indicate tangents.
"Slide Rules - Linear Slide Rules" showing 1 items.
- This is an eight-inch, four-sided boxwood slide rule used for measuring and taxing barrels of liquid. On one end of the rule, the slides on each side have been labeled with the four Roman numerals, I, II, III, and IV. On side I, the base has logarithmic scales that run from 1 to 8 and from 8 to 100. It is labeled Seg St (Segments Standing) at the top left and SS at the bottom right. The slide has two identical C scales, logarithmically divided from 1 to 9. This side was used to estimate the volume of a barrel that was standing vertically and partially filled. The back of the slide lists calculating factors used in computing taxes on various liquors. For instance, the duty on one barrel of vinegar was equivalent to the duty on 7.56 barrels of small beer.
- On side II, the base has logarithmic scales that run from 0 to 4 and from 4 to 100. The bottom right corner is labeled SL (Segments Lying) for estimating the volume of a partially filled barrel lying on its side. The slide has two identical B scales, logarithmically divided from 1 to 10. The point 231 is marked W, showing the number of cubic inches in a wine gallon, and pi (314) is marked with a C. The back of the slide has a table of gauge points for converting between volumes in cubic inches and numbers of gallons for substances in square or circular containers.
- On side III, the base has an A scale, logarithmically divided from 1 to 10, and an MD (Malt Depth) scale that runs logarithmically in the opposite direction from somewhat less than 3 to 20. Point 2150 on the A scale is marked MB, for the number of cubic inches in a malt bushel, and point 282 is marked A, for the number of cubic inches in an ale gallon. The slide has two identical B scales, logarithmically divided from 1 to 9. The back of the slide has a scale of inches, a scale labeled Spheroid, and a scale labeled 2d Variety. These scales are for determining the diameters of two different shapes of barrels. Underneath the slide is marked: LEWIS & BRIGGS : Makers. No. 52. BOW. LANE. Cheapside. LONDON.
- On side IV, the base has a D scale, logarithmically divided from 1 to 3.2 and from 3.2 to 10. Point 17.15 is marked WG, for the diameter in inches of a cylinder that contains one gallon of wine when filled to a depth of one inch. Point 18.95 is marked AG for the diameter of a cylinder containing one gallon of ale. Point 46.3 is marked MS, for the side of a square vessel that contains a solid bushel per inch of depth, and point 52.32 is marked MR, for the side of a square vessel that contains a malt bushel per inch of depth.
- The slide has two identical C scales, logarithmically divided from 1 to 10. The back of the slide has a table of divisors for converting between volumes in cubic inches and numbers of gallons for substances in square or circular containers. The numbers in this table are squares of the gauge points in the table on the back of the slide on side II. Underneath the slide is marked: Willm. Wright : April. 30. 1795.
- According to Gloria Clifton, the firm of Lewis & Briggs operated in London from at least 1795 to 1799. The Smithsonian acquired this object in 1961.
- References: Colin Barnes, "The Customs and Excise Gauging Slide Rule," Journal of the Oughtred Society 4, no. 2 (1995): 53–57; Ron Manley, "Gauging," http://www.sliderules.info/a-to-z/gauging.htm; Gloria Clifton, Directory of British Scientific Instrument Makers (London: National Maritime Museum, 1995), 167.
- Currently not on view
- Currently not on view
- Currently not on view
- date made
- Lewis & Briggs
- ID Number
- catalog number
- accession number
- Data Source
- National Museum of American History, Kenneth E. Behring Center