#
Science & Mathematics

The Museum's collections hold thousands of objects related to chemistry, biology, physics, astronomy, and other sciences. Instruments range from early American telescopes to lasers. Rare glassware and other artifacts from the laboratory of Joseph Priestley, the discoverer of oxygen, are among the scientific treasures here. A Gilbert chemistry set of about 1937 and other objects testify to the pleasures of amateur science. Artifacts also help illuminate the social and political history of biology and the roles of women and minorities in science.

The mathematics collection holds artifacts from slide rules and flash cards to code-breaking equipment. More than 1,000 models demonstrate some of the problems and principles of mathematics, and 80 abstract paintings by illustrator and cartoonist Crockett Johnson show his visual interpretations of mathematical theorems.

"Science & Mathematics - Overview" showing 3 items.

## Book, The Ancient Quipu or Peruvian Knot Record

- Description
- From ancient times, bureaucrats have kept numerical records of people and property. Those working for the Inca emperor in 16th-century Peru recorded data on arrangements of knotted strings known as quipus. The devices may also have been used as aids to memory in recounting histories of Inca exploits—the Incas had no written language.

- Particularly from the 1880s, collections in South America, Europe, and the United States began to include quipus, usually recovered from the graves of makers or users. The devices were of great interest to historian of mathematics Leslie Leland Locke, a charter member of the Mathematical Association of America. Locke (1875–1943), a native of Grove City, Pennsylvania, received his A.B. from Grove City College in 1896 and his M.A. in 1900. He studied further at Pennsylvania State University, Cornell University, and Columbia. He came to Brooklyn to teach at Adelphi College and then worked from 1908 to 1933 at Maxwell Training School for Teachers, later moving to Brooklyn Technical High School. He also taught in the evening session at Brooklyn College.

- Around 1909, while studying under historian of mathematics David Eugene Smith at Teacher’s College of Columbia, Locke became interested in the quipu. He examined several examples at the American Museum of Natural History in detail. In a 1912 paper, Locke argued that the knots on the strings of a quipu represented the decimal digits of numbers, arranged vertically by place value. He extended this research in this volume, published by the American Museum of Natural History in 1923. It includes excerpts of numerous early Spanish and other European texts relating to the quipu, and lists forty-five surviving examples. Locke deemed five of these modern or spurious. He obtained and published illustrations of over thirty of the objects, laying the foundation for further studies.

- Locke also took great interest in more modern innovations in computing, particularly the calculating machine. He inscribed and presented this copy of his book to Dorr E. Felt, the head of Felt & Tarrant Manufacturing Company. Felt had invented, and Felt & Tarrant manufactured, the Comptometer, a leading adding machine of its day. The book, along with the rest of Felt’s library relating to the history of mathematical instruments, was given to the Smithsonian Institution by Victor Comptometer Corporation, the successor to Felt & Tarrant.

- In addition to joining the MAA when it was established, Locke was a charter member of the History of Science Society and active in the National Council of Teachers of Mathematics.

- References:

- Marcia Ascher and Robert Ascher,
*Mathematics of the Incas: Code of the Quipu*, Mineola, New York: Dover, 1997. This is a corrected republication of the book*Code of the Quipu: A Study in Media, Mathematics, and Culture*, published in 1981 by the University of Michigan Press.

- Stefanie Gaenger.
*Relics of the Past: The Collecting and Study of pre-Columbian Antiquities in Peru and Chile,1837–1911*, Oxford: Oxford University Press, 2014, esp. 101–159.

- L. L. Locke, “The Ancient Quipu, A Peruvian Knot Record,”
*American Anthropologist*, n.s. vol. 14, #2 (1912), pp. 325–332.

- “Teacher 45 Years: Educator in Mathematics and an Expert on Calculating Machines Dies. . .,”
*New York Times*, August 30, 1943, p. 15 (this is an obituary of Locke).

- For a recent database of quipus, see the Khipu Database Project at http://khipukamayuq.fas.harvard.edu.

- date made
- 1923

- maker
- Locke, L. Leland

- ID Number
- 1991.3107.08.15

- nonaccession number
- 1991.3107

- catalog number
- 1991.3107.08.15

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Keuffel & Esser Instruction Manual for Polyphase Duplex Slide Rule

- Description
- This 92-page salmon-colored paperback book was received with 1981.0933.03. Its citation information is: William E. Breckenridge,
*The Polyphase Duplex Slide Rule: A Self Teaching Manual*(New York: Keuffel & Esser Co., 1924). Breckenridge earned an A.M. in mathematics from Columbia University in New York City, was chair of the mathematics department at Stuyvesant High School around 1909–1910, served as an associate editor of*The Mathematics Teacher*from 1913 to 1928, and apparently also taught at Columbia.

- Breckenridge explains the basic features and operations of the slide rule, discusses the history and theory of slide rules, provides methods for solving "advanced problems," treats plane trigonometry, solves triangle problems, and provides "typical examples relating to various occupations," such as secretarial work, excavation, and retail. Finally, he shows how to set the slide rule to solve various mechanical formulas and lists tables of equivalents for the basic C and D scales. In chapter one, a previous reader, presumably the donor, William J. Ellenberger, has checked off the examples and filled in the answers to the problems. An advertisement for K&E's other specialty and general slide rules appears at the back of the book. This manual sold for 50 cents.

- A digitized copy of
*The Polyphase Duplex Slide Rule*is available at http://sliderulemuseum.com/Manuals/M205_KE_PolyphaseDuplexSlideRule_4088-3_1924.pdf.

- Reference: Keuffel & Esser Co.,
*Price List, Applying to General Catalogue*, 36th ed. (New York, 1925), 44, 90.

- Location
- Currently not on view

- date made
- 1924

- author
- Breckenridge, William E.

- ID Number
- 1981.0933.04

- accession number
- 1981.0933

- catalog number
- 1981.0933.04

- Data Source
- National Museum of American History, Kenneth E. Behring Center

## Keuffel & Esser Instruction Manual for Mannheim and Polyphase Duplex Slide Rules

- Description
- This 72-page salmon-colored paperback book was received with 1981.0933.03 and 1981.0933.05. Its citation information is: William Cox,
*The Mannheim (Polyphase) and the Duplex (Polyphase-Duplex) Slide Rules Complete Manual*(New York: Keuffel & Esser Co., 1920). It sold for 50 cents. William Cox helped introduce the Mannheim slide rule to the United States, invented the duplex slide rule, and served as a mathematical consultant to Keuffel & Esser Company of New York, thus launching that firm into pioneering the American manufacture of slide rules. He first wrote this manual in 1891 and revised it in 1917, adding instructions for K&E's Polyphase Duplex slide rule (model 4088-3).

- A notice inside the front cover explained how K&E had updated the Mannheim line (models 4031–4056) since Cox first wrote the manual. Cox thoroughly described the characteristics, operations, and scales of Mannheim and Polyphase (which was especially useful for problems involving powers or roots) slide rules. He provided a lengthy table of equivalents for the base scales, C and D, as well as methods for working out mechanical and other formulas. He then went through a similar discussion for the eight-inch Duplex rule (model 4065) and for the ten-inch Polyphase-Duplex rule (model 4088). A supplement by J. M. Willard of the State College of Pennsylvania addressed the solution of problems in plane trigonometry. Finally, there are advertisements for K&E's general and specialty slide rules, the frameless indicator patented in 1915, a magnifier, and surveying equipment.

- References: William Cox, "Engineer's Slide-Rule" (U.S. Patent 460,930 issued October 6, 1891); Florian Cajori,
*A History of the Logarithmic Slide Rule and Allied Instruments*(New York: Engineering News Publishing Company, 1909); Dieter von Jezierski,*Slide Rules: A Journey Through Three Centuries*, trans. Rodger Shepherd (Mendham, N.J.: Astragal Press, 2000), 14, 35; Clark McCoy, ed., "K&E Slide Rule Manuals," http://www.mccoys-kecatalogs.com/KEManuals/manuals.htm.

- Location
- Currently not on view

- date made
- 1920

- author
- Cox, William

- ID Number
- 1981.0933.06

- accession number
- 1981.0933

- catalog number
- 1981.0933.06

- Data Source
- National Museum of American History, Kenneth E. Behring Center