Linear 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.

Image of an advertisement for an Engineers Slide Rule
Keuffel & Esser was one of the first American firms to import linear slide rules from Europe. Catalogue and Price List of Keuffel and Esser, 13th ed. (New York, 1880), 71. NMAH Trade Literature Collection, Smithsonian Institution Libraries. AHB2013q009220

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 frpm the Eugene Dietzgen Co.,
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.

This ten-inch mahogany duplex linear slide rule is almost completely coated with white celluloid. The frameless glass indicator has plastic edges. On one side, the base has K and A scales at the top and D and DI scales at the bottom. The slide has B, T, SRT, and S scales.
Description
This ten-inch mahogany duplex linear slide rule is almost completely coated with white celluloid. The frameless glass indicator has plastic edges. On one side, the base has K and A scales at the top and D and DI scales at the bottom. The slide has B, T, SRT, and S scales. Divisions of angles are indicated in decimal fractions. The left side of the slide is marked with the serial number 330508, with the number 508 printed on the left side of both parts of the base.
The other side of the rule has a DF scale on the top of the base and D and L scales on the bottom of the base. The slide has CF, CIF, CI, and C scales. The top of the base is marked in red: KEUFFEL & ESSER CO.; PATS. 2,500,460 2,168,056 2,170,144 PAT PEND.; MADE IN U.S.A. The right side of the slide is marked with the K&E logo, a copyright sign, and the model number, 4071-3. The instrument fits in an orange leather case with the K&E logo on the flap. Inside the flap is written in ink: H. R. L. (/) JULY '62.
Keuffel & Esser Company of New York sold this model from 1939 to 1967. The combination of scales on this example was sold beginning in 1955, and the model was renumbered in 1962 to 68-1502. Thus, the rule was probably manufactured between 1955 and 1962. The serial number is consistent with this dating.
The donor, Alfred E. Brown, was a research chemist for Celanese Corporation, which partnered with K&E in the 1960s to produce a special version of the 68-1555 slide rule (see 1993.0357.01). However, it is not known how this rule came into Brown's possession.
References: Clark McCoy, "Collection of Pages from K&E Catalogs for the 4071-3 Family of Slide Rules," http://www.mccoys-kecatalogs.com/KEModels/ke4071family.htm; Carl M. Bernegau, "Slide Rule" (U.S. Patent 2,168,056 issued August 1, 1939); Lyman M. Kells, Willis F. Kern, and James R. Bland, "Slide Rule" (U.S. Patent 2,170,144 issued August 22, 1939); Herschel Hunt, "Slide Rule" (U.S. Patent 2,500,460 issued March 14, 1950); Walter Shawlee II, Ted Hume, and Paul Ross, "Keuffel & Esser Co. Slide Rules," Sphere Research Corporation, http://www.sphere.bc.ca/test/ke-sliderule.html; "Alfred E. Brown Chemist," The Washington Post, March 19, 2004, http://www.washingtonpost.com/wp-dyn/articles/A9676-2004Mar19_2.html.
Location
Currently not on view
date made
1955-1962
date received
1993
maker
Keuffel & Esser Co.
ID Number
1993.0482.01
accession number
1993.0482
catalog number
1993.0482.01
This aluminum slide rule is coated in "Eye Saver" yellow, as denoted by the model number. It is held together with aluminum braces; the indicator is nylon (also denoted by the model number) with three metal screws.
Description
This aluminum slide rule is coated in "Eye Saver" yellow, as denoted by the model number. It is held together with aluminum braces; the indicator is nylon (also denoted by the model number) with three metal screws. The front of the rule has A, D, and L scales, with B, CI, and C scales on the slide. The scales are about ten inches long. The slide and the top of the rule are both marked: MODEL N901-ES (/) SIMPLEX (/) MATH RULE. The other end of the slide bears the Pickett logo and the mark: MADE IN U.S.A.
The back of the rule has X and D* scales, with Y and C* scales on the slide. The top of the rule is marked: PICKETT, INC.; MODEL N901-ES; SIMPLEX MATH RULE. The bottom of the rule is marked: COPYRIGHT 1965; PICKETT, INC. SANTA BARBARA. CALIF.; MADE IN U.S.A.
The rule fits in a black leather sheath. The sheath was received in a green, white, and black cardboard box. One end of the box is marked: PickETT (/) 901-ES (/) ELEMENTARY MATH. It also is marked: about this rule: (/) 10 scales are keyed to (/) new math. Aids under- (/) standing of addition, (/) subtraction, multiplica- (/) tion, division and Base 10 (/) relationships. Grade 3 up. The inside of the box top flips up for display. The box slides into a green, white, and black cardboard cover. The top and sides of the box cover are each marked: PickETT; ALL METAL (/) SLIDE (/) RULE.
The box also contains a yellow paper slide rule guarantee and registration card. The object's serial number is A1216143. A 48-page instruction manual by Maurice L. Hartung is stored separately (1995.0126.02.01).
The X and Y scales were used for addition and subtraction and were unique to Pickett. Donor Lawrence J. Kamm conjectured that Hartung, a mathematics professor at the University of Chicago, recommended they be added to this product. According to Kamm, Hartung encouraged company cofounder Ross Pickett to market its slide rules only to schoolchildren. In order to provide scientists and engineers with access to rules such as the Decimal Keeper (1995.0126.01), Kamm opened a mail-order business that distributed Pickett's products.
References: Peter M. Hopp, Slide Rules: Their History, Models, and Makers (Mendham, N.J.: The Astragal Press, 1999), 209–210; Maurice L. Hartung, Complete, Semi-Programmed Teaching Instructions for the Use of Elementary Simplex Math Slide Rule (Santa Barbara, Calif.: Pickett, Inc., 1965); accession file; International Slide Rule Museum, "Pickett," http://sliderulemuseum.com/Pickett.htm.
Location
Currently not on view
date made
after 1965
date received
1995
maker
Pickett & Eckel, Incorporated
ID Number
1995.0126.02
accession number
1995.0126
catalog number
1995.0126.02
This rule consists of a clear plastic envelope, glued together along the back bottom edge, and a white plastic slide.
Description
This rule consists of a clear plastic envelope, glued together along the back bottom edge, and a white plastic slide. The front of the rule has six windows for reading off conversions between yards or feet and meters; centimeters and inches; square yards and square meters; square centimeters and square inches; cubic meters and cubic yards; and liters and imperial gallons or U.S. gallons. The front also has tables of equivalents and a scale for converting between Fahrenheit and Celsius temperatures. The top right corner is marked: GRINDSTED (/) PRODUCTS, INC. (/) Research for quality (/) 2701 ROCKCREEK PKY. (/) NORTH KANSAS CITY, (/) MISSOURI 64116. It is also marked: TEL: 816-842-6500 (/)TELEX: 4-2565 (/)GRINDSINC NKSC. A table for decimal equivalents between fractions, millimeters, and inches runs down the middle of the slide.
The back has six windows for reading off conversions between pounds and kilograms; ounces and grams; PSI and atmospheres or kilograms per square centimeters; inches or centimeters of mercury and PSI; BTU and kilocalories or watt hours; and meter-kilograms and foot-pounds or joules. The back also has more tables of equivalents.
Grindsted is a Danish brand for bulk food products, such as animal feed and emulsifiers for human foods. In 1989 it merged into the Danish conglomerate Danisco, which in turn was purchased by DuPont in 2011. The logo on this rule was in use from 1975 to 1991. Grindsted's factory in the Kansas City suburbs opened in 1975 and filed an annual report in 2012. Compare this rule to metric converters 1990.0689.01 and 1990.3231.01. For the style of manufacture, compare to 1988.0795.02.
References: "Articles of Incorporation of Grinsted Products, Inc.," Missouri Secretary of State Business Name History, https://www.sos.mo.gov/BusinessEntity/soskb/Corp.asp?165854; "History - DuPont Danisco," http://www.danisco.com/about-dupont/duponttm-daniscor/history/; U.S. Patent and Trademark Office, Trademark Electronic Search System.
Location
Currently not on view
date made
1975-1991
maker
Grindsted Products, Inc.
ID Number
1988.3078.05
catalog number
1988.3078.05
nonaccession number
1988.3078
This rectangular white cardboard rule has four slides and is held together with ten metal rivets. The top two slides are used to calculate the annual operating cost of a natural gas furnace, while the bottom two slides perform the same calculation for an electric heat pump.
Description
This rectangular white cardboard rule has four slides and is held together with ten metal rivets. The top two slides are used to calculate the annual operating cost of a natural gas furnace, while the bottom two slides perform the same calculation for an electric heat pump. Tables on the back of the instrument give values for building heat loss, typical heating system efficiencies, and heating load hours for the states covered by the Tennessee Valley Authority: Alabama, Georgia, Kentucky, Mississippi, North Carolina, and Tennessee. A sample calculation is also provided on the back.
The front and back are both marked: Electricity (/) THE POWER (/) OF CHOICE. Both sides are also marked: TVA. The rule thus advertised TVA's ability to supply inexpensive public electric power and promote energy conservation. The back bottom left corner is marked: © 1990 Datalizer Slide Charts, Inc., Addison, IL 60101. A former employee of the Perrygraf (or Perry Graf) Corporation (see 1979.3074.03) established Datalizer around 1960, and the company remained in business as of 2012.
References: "From the New Deal to a New Century," Tennessee Valley Authority, http://www.tva.com/abouttva/history.htm; "Slide Chart Specialists," Datalizer Slide Charts, http://www.datalizer.com/about-us/.
Location
Currently not on view
date made
1990
maker
Datalizer Slide Charts, Incorporated
ID Number
1996.3078.02
nonaccession number
1996.3078
catalog number
1996.3078.02

Our collection database is a work in progress. We may update this record based on further research and review. Learn more about our approach to sharing our collection online.

If you would like to know how you can use content on this page, see the Smithsonian's Terms of Use. If you need to request an image for publication or other use, please visit Rights and Reproductions.