Mathematical Objects Relating to Charter Members of the MAA
In 1915, the Mathematical Association of America formed to encourage advanced mathematics teaching in the United States. Members received a journal called The American Mathematical Monthly and participated in regular meetings. To mark the centennial of the organization, we present a few objects associated with charter members of the MAA that survive in the collections of the National Museum of American History.
Born in Virginia, Elizabeth Brown (18631917) moved to Washington, D.C., began teaching, and enrolled at what is now George Washington University. Simon Newcomb hired her to do calculations for the Nautical Almanac Office, and encouraged her to work permanently as a computer there. Newcomb arranged for Elizabeth Brown Davis to enroll as a special student in mathematics at Johns Hopkins University (women were not then allowed as official graduate students). When the work of her husband, Arthur Davis, took him to Los Angeles in the early 1890s. Elizabeth went along, continuing computations for Nautical Almanac and seeking private mathematics students. The family soon returned to Washington, and Davis continued her work as a computer. In March and April of 1915, Davis published solutions to problems posed in the Mathematical Monthly. Later in the year, she became a charter member of the MAA. The Monthly well suited her mathematical tastes – she published a short article in early 1917 and submitted several other problem solutions before her death that year.
Derrick N. Lehmer (18631938) obtained his BS from the University of Nebraska in 1893, taught in that state for a few years, and then moved on to the University of Chicago where he studied with E.H. Moore. He taught mathematics at the University of California at Berkeley from 1900 until his retirement in 1937. Lehmer took an active interest in The American Mathematical Monthly, publishing short articles in the journal from 1905 onward. When the MAA was founded, Lehmer was appointed to the Executive Council. He would be elected a vicepresident of the organization and later served on the Board of Trustees. Fascinated by the properties of numbers, Lehmer published Factor table for the first ten millions containing the smallest factor of every number not divisible by 2, 3, 5, or 7 between the limits 0 and 10017000 in 1909. Assisted by the Carnegie Institution of Washington, he developed a set of paper sheets known as factor stencils to aid in factoring still large numbers.
Raymond C. Archibald 
Raymond Clare Archibald (18751955) once owned a German slide rule that is now in the Smithsonian collections. The object well suggests his international background. Archibald was born and raised in Nova Scotia, did further work at Harvard University, and earned his doctorate in Germany. He then returned to teach in Canada for a time, moving on to Brown University in 1908. Archibald submitted a steady stream of problems and problem solutions to the British journal Educational Times. He also began sending problems and solutions to the American Mathematical Monthly in 1910. He was appointed to the editorial board of the Monthly in 1916, served as editorinchief from 1919 to 1921, and was president of the MAA in 1922. In addition to his mathematical work, Archibald did much to promote the study of the history of mathematics and the improvement of mathematical tables.

Dactyle Calculating Machine
 Description
 This pinwheel, leverset, nonprinting calculating machine was made by the French firm of Chateau Frères, sold under the name Dactyle, and constructed on the design of the Swede W. T. Odhner. Odhnerstyle machines were first made in Russia (as Odhners), then in Germany (as Brunsvigas) and then in France (as the Dactyle, from about 1905).
 In 1910, about a year after this machine was made, R. H. Marchant of San Francisco, the American agent for the Dactyle, decided to go into business himself, building a very similar machine. The Marchant Calculating Machine Company officially was incorporated in 1913, and made a wide range of calculating machines into the 1950s.
 The machine, painted black, has nine levers toward the top for setting numbers. The operating crank is on the right side. In front is the carriage, with ten numeral wheels on the left for counting revolutions and 18 numeral wheels on the right for recording totals. The numeral wheels of the revolution counter are numbered from 0 to 9 in white and then from 8 down to 1 in red. The result wheels have the digits from 0 to 9 around the edge. The zeroing screws for the registers are at the two ends of the carriage.
 A mark on the left front at the top reads: No. 5641.
 This machine came to the Smithsonian from the United States Naval Observatory in Washington, D.C.
 Reference:
 E. Martin, The Calculating Machines (Die Rechenmaschinen), trans. P.A. Kidwell and M.R. Williams, Cambridge: MIT Press, 1992, p. 164.
 Location
 Currently not on view
 date made
 ca 1909
 maker
 Chateau Frères of Paris
 ID Number
 2005.0174.02
 accession number
 2005.0174
 catalog number
 2005.0174.02
 Data Source
 National Museum of American History

Factor Stencils by Derrick N. Lehmer
 Description
 Derrick Norman Lehmer (1867–1938) was a distinguished American number theorist. Born in Somerset, Indiana, he obtained his BS from the University of Nebraska in 1893, taught there and at a Nebraska academy for a time, and then moved on to the University of Chicago where he studied with E. H. Moore. After obtaining his PhD in 1900, he was hired by the University of California at Berkeley, rising through the ranks until his retirement in 1937. Assisted by the Carnegie Institution of Washington, Lehmer developed this set of factor stencils to aid in factoring large numbers.
 Each sheet is for a different quadratic residue, R. At the very top of each sheet is printed: R=. Different values of the quadratic residue R have been typed in next to the equals sign. Values range from R= 238 to R= 1 and from R= +3 to R= +238, with one stencil for each value of R. Values of R for which there are stencils correspond to those for which there are sets of punched cards in object 1988.0316.02. (The set of cards includes some higher values of R.) There are a total of 295 sheets. The sheets have fifty columns and 100 rows, allowing a position for each of the first 5000 prime numbers. If a prime number had a given quadratic residue, a hole is punched in the corresponding position on the sheet. Superimposing the sheets assisted in finding numbers with a group of quadratic residues, and greatly reduced the time required for factoring.
 Working with his son, number theorist D. H. Lehmer, D. N. Lehmer went on to develop an electric version of the factor stencils, which was exhibited at the Chicago World’s Fair in in the 1930s.
 Reference:
 Derrick N. Lehmer, Factor Stencils, Washington, DC: Carnegie Institution of Washington, 1929.
 Location
 Currently not on view
 date made
 ca 1929
 maker
 Lehmer, Derrick Norman
 ID Number
 1988.0316.01
 accession number
 1988.0316
 catalog number
 1988.0316.01
 Data Source
 National Museum of American History

A. W. Faber Mannheim Simplex Slide Rule
 Description
 This onesided, teninch wooden rule has a layer of white celluloid on the front side. It has unlettered A and D scales on the base and B and C scales on one side of the slide. The other side of the slide has lettered S, L, and T scales. The bottom left corner is marked: QUOTIENT (/) +1. The bottom right corner is marked: PRODUCT (/) –1. The indicator is glass in a metal frame, with a circular scale and pointer on the right side of the frame for registering digits to be added or subtracted during the calculation. The top edge is beveled and has a 25centimeter scale, divided to millimeters. A second scale, 27 centimeters in length, is on the front edge. Underneath the slide is a third centimeter scale, numbered from 30 to 55.
 The bottom of the base is marked in gold: A. W. FABER. D.R.G.M. 98350 & 116832. A set of tables of equivalent measures printed in German on paper is glued to the back of the instrument. The rule is in a cardboard case covered with black leather. The case is marked: Rechenstab (/) von (/) A. W. Faber. Inside the case is written in pencil: Mit Anlistz (/) [illegible] 10 (/) R. C. Archibald. On the back of the inside is written in pencil: RCA.
 A. W. Faber was a German company that began manufacturing slide rules in 1882 and introduced this form of instrument around 1894. German patent 116832 was issued to A. W. Faber in June 1899. The digitregistering cursor was added in 1905. Although there is no model number on this rule, it was sold as model 367 from 1905 to 1913. The firm was renamed FaberCastell in 1905, although instruments continued to be marked "A. W. Faber" as late as 1913.
 This slide rule reflects the rich intermixture of cultures that characterizes the American mathematical community. It was owned by Raymond C. Archibald (1875–1955), a Canadian born in Nova Scotia. He began his college education in Canada and completed a bachelor's and a master's degree from Harvard University in Cambridge, Mass. Then, like several other late 19th and early 20thcentury North American mathematicians, Archibald traveled to Germany, spending the academic year 1898–1899 at the University of Berlin and 1899–1900 at the University of Strasbourg. He obtained his Ph.D. in Strasbourg in 1900 and may have purchased this slide rule near the end of this European sojourn. Archibald then returned to Canada, where he taught for several years before joining the faculty of Brown University in Providence, R.I., in 1908. He remained at Brown for the rest of his academic career. Archibald's wide ranging interests included the history of mathematics, the computation of mathematical tables and the development of computing tools. In 1943, he became the founding editor of the journal Mathematical Tables and Other Aids to Computation, a publication that included some of the first articles published about electronic computers.
 References: Peter M. Hopp, Slide Rules: Their History, Models, and Makers (Mendham, N.J.: Astragal Press, 1999), 25–26, 41; Dieter von Jezierski, Slide Rules: A Journey Through Three Centuries, trans. Rodger Shepherd (Mendham, N.J.: Astragal Press, 2000), 24; George Sarton, "Raymond Clare Archibald," Osiris 12 (1956): 4–34; Charles N. Pickworth, Instructions for the Use of A. W. Faber's Improved Calculating Rule (New York: A. W. Faber, [after 1900]), 36–40. This work is undated, but it refers to a prize awarded to Faber at the Exposition universelle held in Paris in 1900. The pages cited describe "a new form of A. W. Faber's calculating rule," the form of the slide rule catalogued here.
 date made
 19001908
 maker
 Faber, A. W.
 ID Number
 MA.304722.02
 accession number
 304722
 catalog number
 304722.02
 Data Source
 National Museum of American History
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