Keuffel & Esser 4051 Simplex Slide Rule

This 20-inch one-sided slide rule is made of wood with white celluloid scales and a frameless glass indicator with plastic supports. The base has A and D scales, and there are B and C scales on one side of the slide with S, L, and T scales on the other side. The A and B scales are divided logarithmically from 1 to 10 twice, the C and D scales from 1 to 10 once. The S scale gives angles in degrees and minutes, running from 0 to 90 degrees. The sine of an angle on the S scale is read off the A scale. The T scale gives angles running from 0 to 45 degrees. The tangent of these angles is read off the D scale, assuming that the endpoints of the scales are aligned. The L scale runs from 0 to 1, in such a way that if a number is read off the D scale, the mantissa of the logarithm to the base 10 of that number is indicated on the L scale, assuming that the endpoints of the scales are aligned.
A scale of 50 centimeters divided to millimeters is on the front edge, and a scale of 20 inches divided to 1/16-inch is on the other, beveled edge. A table of equivalents and slide rule settings is glued to the back of the rule. The table is marked: EQUIVALENTS AND ABBREVIATIONS FROM U. S. BUREAU OF STANDARDS CIRCULAR NO. 47; KEUFFEL & ESSER CO., NEW YORK. On the back of the rule is written in marker: E. + M. LAB (1). The back is also marked: A.C.P.L. 1132 (/) 23-4-B.
The top of the base is marked in red: PAT. JUNE 5, 1900; KEUFFEL & ESSER CO. N.Y.; MADE IN U.S.A. The slide is marked: AMHERST COLLEGE ACPL 1132. The right end of the slide is marked in red: < 4051 >. The back of the slide and the left end of the centimeter scale are marked with a serial number: 127849. The supports for the indicator are marked: PATENT 2,086,502 and KEUFFEL & ESSER CO. N.Y.
Keuffel & Esser first advertised the model 4051 Mannheim slide rule in 1900 and stopped selling it between 1936 and 1939. The serial number suggests a date around 1925, but the patent date on the indicator suggests that part was made in 1938. The indicator may thus be a replacement part. The rule was used in the electricity & magnetism laboratory of the Amherst College physics department.
References: Adolf W. Keuffel, "Runner for Slide Rules" (U.S. Patent 2,086,502 issued July 6, 1937); Catalogue of Keuffel & Esser Co., 30th ed. (New York, 1900–1901), 294; Catalogue of Keuffel & Esser Co., 38th ed. (New York, 1936), 311; Clark McCoy, "Collection of Pages from K&E Catalogs for the 4041 Family,"; Ed Chamberlain, "Estimating K&E Slide Rule Dates," 27 December 2000,
Currently not on view
Object Name
calculating rule
slide rule
date made
Keuffel & Esser Company
Physical Description
celluloid (laminate material)
glass (cursor material)
wood (overall material)
overall: 1.4 cm x 52 cm x 4 cm; 9/16 in x 20 15/32 in x 1 9/16 in
place made
United States: New York, New York
ID Number
catalog number
maker number
accession number
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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