Keuffel & Esser 4088-3 Polyphase Duplex Slide Rule

This ten-inch duplex linear mahogany slide rule is completely coated with white celluloid and held together with L-shaped metal end pieces. The indicator is frameless glass with metal edges and held together with metal screws. One edge is marked: PAT.APPL'FOR. On one side of the rule, the base has DF and D scales, with CF, CIF, and C scales on the slide. Near the left end, the top of the base is marked in red: PAT. JUNE 5, '00 DEC. 22, '08. The slide is marked: < 4088-3 >. The bottom of the base is marked: KEUFFEL & ESSER CO. N. Y. Both pieces of the base and the slide are stamped on one end: 85.
On the other side, the base has K, A, D, and L scales, with S, T, and CI scales on the slide. The K scale is divided logarithmically three times in the length of the scale, for use in finding cubes and cube roots. The A scale is divided logarithmically from 1 to 10 twice in the length of the scale and provides the square of numbers on the D scale. The S scale gives the sines of angles from less than 40 minutes to 90 degrees. The T scale gives tangents of angles from somewhat less than 6 degrees to 45 degrees. The CI scale is divided logarithmically from 1 to 10 once the length of the scale; it runs in the opposite (inverse) direction from the D scale below it. The L scale is a scale of equal parts running from 0 to 10 and provides the mantissa for the logarithm of D.
The Keuffel & Esser Company of New York sold model 4088-3, a polyphase duplex slide rule, from 1913 to 1939. The indicator used in 1913 had vertical metal bars on the sides, while the patent for the frameless indicator was issued in 1915 and mentioned on K&E slide rules almost immediately. Since the markings on this example indicate the patent had not yet been granted, this rule must have been manufactured around 1914. Model 4088-3 sold in 1913 and 1915 for $7.00. Compare to MA*318476 and 1981.0933.03.
References: Catalogue of Keuffel & Esser Co., 34th ed. (New York, 1913), 304a; Catalogue of Keuffel & Esser Co., 35th ed. (New York, 1915), 307b; Willie L. E. Keuffel, "Slide-Rule Runner" (U.S. Patent 1,150,771 issued August 17, 1915); Wayne E. Feely, "K & E Slide Rules," The Chronicle of the Early American Industries Association 49, no. 5 (June 1996): 50–52; Peter M. Hopp, Slide Rules: Their History, Models, and Makers (Mendham, N. J.: Astragal Press, 1999).
Currently not on view
date made
Keuffel & Esser Co.
place made
United States: New York, New York
Physical Description
mahogany (overall material)
celluloid (laminate material)
glass (cursor material)
metal (part material)
overall: 1 cm x 31 cm x 4.1 cm; 13/32 in x 12 7/32 in x 1 5/8 in
ID Number
accession number
catalog number
Credit Line
Transfer from Interstate Commerce Commission
Rule, Calculating
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Slide Rules
Data Source
National Museum of American History, Kenneth E. Behring Center


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