#
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 15 items.

Page 1 of 2

## 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

## Post Instruction Manual for Versalog Slide Rule

- Description
- This is a later printing of 1978.0800.02. Its citation information is: E. I. Fiesenheiser,
*Versalog Slide Rule Instruction Manual*, with R. A. Budenholzer and B. A. Fisher (Chicago: Frederick Post Company, 1963). The text appears not to have been revised since these three Illinois Institute of Technology engineering professors helped invent the Versalog slide rule and wrote instructions for using it in 1951. Marks inside the front cover indicate this copy was offered for sale in January 1969 for $1.00.

- Location
- Currently not on view

- date made
- 1963

- maker
- Frederick Post Co.

- ID Number
- 1980.0097.03

- accession number
- 1980.0097

- catalog number
- 1980.0097.03

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

## Numbers In Colour, A New Method of Teaching Arithmetic In Primary Schools

- Description
- During the 1950s, the Belgian teacher Emile-Georges Cuisenaire designed a set of rods to teach about numbers and basic arithmetic. Caleb Gattegno popularized his methods in Great Britain and the United States. This small paperbound book by Cuisenaire and Gattegno first appeared in 1954, was in its third edition by 1958, and was reprinted frequently in the next few years. This is a 1961 printing.

- For a set of Cuisenaire rods, see 1987.0542.01. For other related documentation see 1987.0542.03 through 1987.0542.07.

- Location
- Currently not on view

- date made
- 1961

- maker
- Cuisenaire, G.

- ID Number
- 1987.0542.02

- accession number
- 1987.0542

- catalog number
- 1987.0542.02

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

## Instructions for Otis King's Pocket Calculator

- Description
- This trifold pamphlet reprints the text found in 1987.0788.06, except for the section on [Pounds] Sterling Calculations, which is omitted. The columns of text are also laid out slightly differently, so that the page length is shortened from eight pages to six. These instructions accompanied 1989.3049.02. See also 1989.3049.04.

- Location
- Currently not on view

- date made
- ca 1965-1968

- maker
- Carbic Limited

- ID Number
- 1989.3049.03

- nonaccession number
- 1989.3054

- catalog number
- 1989.3054.01

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

## Book, Mathematical Puzzles and Pastimes

- Description
- The book
*Mathematical Puzzles and Pastimes*was obtained by Olive C. Hazlett (1890–1974) on May 27, 1965. Hazlett was one of America's leading mathematicians during the 1920s. She taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, New Hampshire. This volume, as well as other puzzle books and puzzles she owned, was collected from a community of Discalced Carmelite brothers who had lived in New Hampshire and who had befriended Hazlett there.

- The puzzles and pastimes of the book were gathered and edited by Philip Haber and illustrated by Stanley Wyatt. The book was published by The Peter Pauper Press of Mount Vernon, New York, in 1957. Haber collected problems that he wrote could “be solved primarily by clear thinking, arithmetic or algebra.” The book contains 113 problems with solutions given to some of them. Haber refers to the last four problems as “famous” and gives their names as: The Impossible Division Problem, The Unit Problem, The Apple Problem, and The Problem of Problems (Archimedes’ Cattle Problem).

- Hazlett wrote “$1. for 3” on the title page of this book. There is one other book in the museum collections,
*The Little Riddle Book*(2015.3004.02), that was also published by The Peter Pauper Press and also obtained by Hazlett on May 27, 1965. In that book she wrote “3 for $1.” Hazlett signed her name “O. C. Hazlett” on the dustcover of both books. She made other handwritten marks in*Mathematical Puzzles and Pastimes*, including several whose meanings are not clear.

- Location
- Currently not on view

- date made
- 1957

- ID Number
- 2015.0027.03

- accession number
- 2015.0027

- catalog number
- 2015.0027.03

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

## Handwritten Cipher Book of Jesse Harmon Alexander

- Description
- In the 18th and early 19th centuries, when paper was still expensive and textbooks not generally available, students who learned arithmetic sometimes wrote out their own texts by hand. This volume, covered with yellow, black, and red wallpaper, is such a “cipher book.”

- Jesse Harmon Alexander, who was born in 1810 and lived in Rockland, Delaware, prepared this manuscript exercise book in 1825. Each page contains one or two columns of problems and commentary. The first topic considered was the Single Rule of Three. Alexander went in the wrong direction on the very first problem, but he did reach the solution on subsequent problems. His style was typical of the 18th and early 19th centuries. For example, in division problems, he wrote the divisor, dividend, and quotient in a row from left to right. The remaining topics were also typical of the time: tare and tret (adjustments to the price of goods for the weight of the container and for imputities), the Double Rule of Three, direct and inverse proportion, interest, insurance commission and brokerage, compound interest, discount, equation of accounts, barter, loss and gain, foreign exchange, measurement of surfaces, vulgar fractions, reduction of decimals, alligation, single and double position, involution and evolution, extraction of square roots, cube roots, arithmetical and geometrical progression, annuities, and promiscuous questions.

- Alexander's teacher was likely guided by one of the many old-fashioned arithmetic textbooks still in wide use in the 1820s. He (in 1825 most teachers teaching boys in the mid-Atlantic states were men) would have expected Alexander to memorize rules and examples and thus learn how to carry out the mathematical operations Alexander would use in business. The "vulgar fractions" section is one example of this teaching method, as Alexander copied down case after case rather than any general principles governing all fractions. The teacher probably also hoped Alexander would copy the material neatly. This not only offered practice his penmanship but prepared a reference book the boy could use as an adult.

- Alexander clearly returned to this exercise book later in his life, for dates from the 1830s dates are scattered throughout the book. New computations are written on the fourth page of the "interest" section. It is not clear, though, that Alexander's cramped handwriting and failure to clearly mark many of the solutions were any easier to read in the 19th century than now, when bleeding ink and worn page corners have also damaged the textual content.

- Several pages that are not from the original exercise book have been placed inside the front cover. These contain newspaper clippings (mainly poems and obituaries) pasted over accounts from 1831 and 1832.

- Reference:

- For an appreciation of the importance of cipher books in arithmetic education, see: Nerida Ellerton and M.A. (Ken) Clements,
*Rewriting the History of School Mathematics in North America 1607-1861: The Central Role of Cypher Books*, Dordrecht: Springer, 2012.

- Location
- Currently not on view

- date made
- 1825

- maker
- Alexander, Jesse Harmon

- ID Number
- MA*322685.01

- accession number
- 322685

- catalog number
- 322685.01

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

## Pickett Manual for Dual Base Log Log Slide Rules

- Description
- Pickett, Inc., was a slide rule manufacturer that started in Chicago in 1943, shifted most of its operations to Alhambra, Calif., in 1946, and moved to Santa Barbara, Calif., in 1964. Maurice L. Hartung, a mathematics professor at the University of Chicago, wrote several instruction manuals for the company, including
*How to Use Dual Base Log Log Slide Rules*. This 93-page booklet was intended for use with Pickett models 2, 3, and 4. It contains sections on the general operation of a slide rule, the use of scales for trigonometry and roots, elementary vector methods, the use of logarithmic scales, practice problems, hyperbolic functions, and circular functions. Hartung also showed how the double T scales could solve side-angle-side triangle problems in one step. Model 600 was advertised at the back of the manual, and instructions for caring for Pickett slide rules were provided inside the back cover.

- Although Hartung wrote the manual in 1947, this printing was made after the company moved to Santa Barbara in 1964. See the associated items, 1980.0097.01 and 1980.0097.06.

- Location
- Currently not on view

- date copyrighted
- 1947

- date printed
- ca 1965

- author
- Hartung, Maurice L.

- printer
- Pickett Industries

- ID Number
- 1980.0097.05

- accession number
- 1980.0097

- catalog number
- 1980.0097.05

- 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

## Keuffel & Esser Log Log Duplex Trig Slide Rule Documentation

- Description
- This green softcover instruction manual, advertising pamphlet for various pocket-sized Keuffel & Esser slide rules, and leaflet on "How to Take Care of Your Slide Rule" were received with 2007.0181.01. The citation information for the manual is: Lyman M. Kells, Willis F. Kern, and James R. Bland,
*Slide Rule Manual: Log Log Duplex Decitrig*, 4th ed. (New York: Keuffel & Esser Co., 1955). Kells, Kern, and Bland were all mathematics professors at the U.S. Naval Academy. The cover indicates that the manual is model "No. 68 2047 (/) OLD NO. 4187S," suggesting it was printed after 1962, when K&E changed all of its model numbers. The 125-page manual is designed for self-study and covers multiplication and division; proportion; squares, cubes, and roots; trigonometry; the log log scales; and logarithms and the slide rule. Answers to the exercises are in the back of the manual. See also 1987.0085.02.

- The pamphlet is marked with the motto: calculate wherever you circulate. It measures 2-1/4 X 8-1/4 inches and was copyrighted in 1960, 1962, and 1964. Information is provided for five-inch versions of K&E's Deci-Lon, Jet-log Jr., Polyphase Duplex Decitrig, Modern Polyphase, Polyphase, and Merchants slide rules. The leaflet is small (4 X 3 inches) and was copyrighted in 1944, 1949, 1958, and 1962. Users are to clean the slide rule only with a moistened cloth. Instructions are provided for adjusting and aligning the slide rule.

- Location
- Currently not on view

- date made
- 1964

- maker
- Keuffel & Esser Co.

- ID Number
- 2007.0181.01.01

- accession number
- 2007.0181

- catalog number
- 2007.0181.01.01

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