## Object Groups

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## Suan-p'an, or Chinese Abacus

- Description
- This abacus fits in a black wooden box with a wooden cross piece. Eleven parallel bamboo rods carry seven beads each. Two beads are above the cross piece, five below. The beads are rounded, like those on Chinese abaci. One rod is broken and another cracked. The abacus was received as a gift from the Department of Mathematics of Brown University in 1973. There are no marks by a maker.

- Location
- Currently not on view

- ID Number
- MA*304722.01

- catalog number
- 304722.01

- accession number
- 304722

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

## A. W. Faber Mannheim Simplex Slide Rule

- Description
- This one-sided, ten-inch 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 25-centimeter 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 digit-registering 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 Faber-Castell 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 20th-century 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.

- Location
- Currently not on view

- date made
- 1900-1908

- maker
- Faber, A. W.

- ID Number
- MA*304722.02

- accession number
- 304722

- catalog number
- 304722.02

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

## Plain Dividers

- Description
- These metal dividers are noticeably corroded. They are called "plain" because, although there is a screw at the top for adjusting the width to which the dividers are set, there is no second screw or hairspring on one of the legs for refining the setting. The short needle points are not removable. The upper part of the legs is indented, so that an oval is seen when the dividers are closed. The Brown University mathematics department donated these dividers to the Smithsonian in 1973.

- Location
- Currently not on view

- date made
- ca 1900

- ID Number
- MA*304722.03

- accession number
- 1973.304722

- catalog number
- 304722.03

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

## Eagle Pencil Company Model 569 Compass and Divider

- Description
- This metal compass is noticeably corroded. The compass is held together by a screw at the top. A spring inside the mechanism below the screw allows the two legs to be squeezed together. The mechanism is marked on both sides: EAGLE PENCIL CO. (/) NEW YORK (/) PAT. DEC.11.1894 (/) PAT. GT.BRITAIN. The legs are embossed with a floral pattern. The two needle points slide into slots at the end of each leg. One point is made of the same metal as the compass. The other point is a metal that does not corrode, possibly German silver. The German silver point is reversible and holds a pencil lead in its other end.

- German immigrant Heinrich Berolzheimer opened Eagle Pencil Company as a pencil shop in New York City in 1856, with a factory in Yonkers. By 1880, the firm made mechanical pencils as well as pens and erasers. In 1969, the company changed its name to Berol Corporation, and the Empire Pencil Corporation purchased it in 1986. Harrison Cole of Columbus, Ohio, applied on April 16, 1894, for a patent on a braking screw bolt that would help compasses or dividers stay set in position and received it on December 11 that year. The Brown University mathematics department donated this instrument to the Smithsonian in 1973. Compare to 1981.0933.17.

- References: Harrison Cole, "Drawing Instrument" (U.S. Patent 530,680 issued December 11, 1894); "Eagle Divider and Compass,"
*School Journal*56 (1898): 389.

- Location
- Currently not on view

- date made
- ca 1900

- maker
- Eagle Pencil Company

- ID Number
- MA*304722.04

- accession number
- 1973.304722

- catalog number
- 304722.04

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

## James W. Queen & Co. Triangular Offset for Architect's Rule

- Description
- This three-inch triangular boxwood rule is grooved on each side. The top edge of one side is divided to 1/10" and numbered by ones from 0 to 3. The bottom edge is divided to 1/50" and numbered by twos from 0 to 14. This side is marked: QUEEN & CO. PHILAD'A.

- The second side is divided to 1/60" and numbered by twos from 0 to 18 along one edge and divided to 1/30" and numbered by twos from 0 to 8 on the other edge. The third side is divided to 1/40" and numbered by twos from 0 to 12 along one edge and divided to 1/20" and numbered by ones from 0 to 6.

- James W. Queen of Philadelphia sold a two-inch triangular boxwood scale for offsets as model 464-1/2 from at least 1874 to at least 1884 for 75¢. No three-inch scale is mentioned in catalogs from this time period. The Department of Mathematics at Brown University gave this object to the Museum in 1973.

- References: James W. Queen & Co.,
*Priced and Illustrated Catalogue and Descriptive Manual of Mathematical Instruments and Materials*(Philadelphia, 1874), 41; James W. Queen & Co.,*Priced and Illustrated Catalogue and Descriptive Manual of Mathematical Instruments and Materials*(Philadelphia, 1884), 44.

- Location
- Currently not on view

- date made
- late 19th century

- Maker
- Queen & Co.

- ID Number
- MA*304722.05

- accession number
- 304722

- catalog number
- 304722.05

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

## Hart Combination Protractor, Rule, and Square

- Description
- In the early 20th century, some authors of mathematics textbooks and their publishers began to include protractors in the endpapers of the books. They wanted middle and high school students to informally experience geometry through drawing and experiment before moving on to constructing formal geometrical proofs. Walter W. Hart, a professor of mathematics at the University of Wisconsin, went so far as to design a combination protractor and ruler for insertion in the textbooks he authored with professional mathematics textbook author Webster Wells.

- By 1921, Hart's protractor was described and illustrated in the text with a cardboard version included for student use. If students lost their protractors, teachers could order replacements from D. C. Heath & Co. for four to five cents each, depending on the quantity ordered. By 1926, Hart was boasting that his invention had anticipated the standards recommended in 1923 by the Mathematical Association of America's National Committee on Mathematical Requirements. This example probably dates from one of Hart's later textbooks.

- This paper semicircular protractor is divided by degrees and marked by tens from 10 to 170 degrees in both directions. The letter A is printed in the bottom left corner of the protractor, and B is printed in the bottom right corner of the protractor. Centered under the origin point of the protractor is printed the inventor's mark: COMBINATION PROTRACTOR, RULE, AND SQUARE (/) W. W. HART, UNIVERSITY OF WISCONSIN. A ruler along the top edge is divided to 1/8-inch, and marked by ones from 0 to 5. A ruler along the bottom edge is divided to millimeters and marked by ones from 0 to 12. This protractor was donated by the Brown University mathematics department in 1973. It is notably discolored and stained. See also MA*304722.07.

- References: Peggy Aldrich Kidwell, Amy Ackerberg-Hastings, and David Lindsay Roberts,
*Tools of American Mathematics Teaching, 1800–2000*(Baltimore: Johns Hopkins University Press, 2008), 176–179, 364–365; Walter Wilson Hart,*Junior High School Mathematics*, vol. 1 (Boston: D. C. Heath & Co., 1921), vii, 131; Webster Wells and Walter W. Hart,*Modern Plane Geometry*(Boston: D. C. Heath & Co., 1926), 3, 16; National Committee on Mathematical Requirements,*The Reorganization of Mathematics in Secondary Education*([Oberlin, OH]: Mathematical Association of America, 1923), 22. See also Walter Wilson Hart,*Progressive Plane and Solid Geometry*(Boston: D. C. Heath & Co., 1936), iii–vii, 16–17; Claude H. Ewing and Walter W. Hart,*Essential Vocational Mathematics*(Boston: D. C. Heath & Co., 1945), 99; and Walter Wilson Hart, Veryl Schult, and Henry Swain,*Plane Geometry and Supplements*(Boston: D. C. Heath & Co., 1959), 24.

- Location
- Currently not on view

- date made
- after 1930

- Date made
- post 1930

- designer
- Hart, Walter Wilson

- ID Number
- MA*304722.06

- accession number
- 1973304722

- catalog number
- 304722.06

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

## Hart Combination Protractor, Rule, and Square

- Description
- This paper semicircular protractor is divided by degrees and marked by tens from 10 to 170 degrees in both directions. The letter A is printed in the bottom left corner of the protractor, and B is printed in the bottom right corner of the protractor. Centered under the origin point of the protractor is printed the inventor's mark: Combination Protractor, Rule, and Square (/) W. W. Hart, University of Wisconsin.

- A ruler along the top edge is divided to 1/8-inch and marked by ones from 0 to 5. A ruler along the bottom edge is divided to millimeter and marked by ones from 0 to 12. The typeface of the inventor's mark is similar to that shown in Hart's textbooks published in the 1920s, such as Walter Wilson Hart,
*Junior High School Mathematics*, vol. 1 (Boston: D. C. Heath & Co., 1921), vii, 131. See also MA*304722.06.

- Location
- Currently not on view

- date made
- ca 1925

- designer
- Hart, Walter Wilson

- ID Number
- MA*304722.07

- accession number
- 1973.304722

- catalog number
- 304722.07

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

## Keuffel & Esser 1855 8" Drafting Triangle

- Description
- This 7-3/4" 30°-60°-90° yellowed plastic triangle was originally transparent and 8" tall. Like many plastic objects from the early 20th century, it is rapidly deteriorating. A small triangular hole in the interior has notches or bevels around its edges. The object is marked along the short edge: KEUFFEL & ESSER Co. (/) N. Y.; 8; TRADE MARK (below the K&E eagle logo). By 1909 K&E offered xylonite triangles for use in engineering drawing; the 8-inch size sold for 55¢. By 1936 the price was 50¢. The Department of Mathematics at Brown University gave this object to the Museum in 1973.

- References:
*Catalogue and Price List of Keuffel & Esser Co.*, 33rd ed. (New York, 1909), 208;*Catalogue of Keuffel & Esser Co.*, 38th ed. (New York, 1936), 229.

- Location
- Currently not on view

- date made
- early 20th century

- Maker
- Keuffel & Esser Co.

- ID Number
- MA*304722.08

- catalog number
- 304722.08

- accession number
- 304722

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

## Drafting Triangle

- Description
- This 5-1/2" 20°-70°-90° wooden triangle has a 3/8" round hole at the center for positioning and holding the instrument. Compare to MA*304826.137, MA*335331, and 1979.0876.02. A previous user has written the numbers 20, 70, and 90 at the appropriate corners. For other drawing triangles with unusual angle measurements, see MA*334622 and 1990.0690.01. The Department of Mathematics at Brown University gave this object to the Museum in 1973.

- Location
- Currently not on view

- date made
- ca 1900

- ID Number
- MA*304722.09

- catalog number
- 304722.09

- accession number
- 304722

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

## Peaucellier Inversor, Kinematic Model by Martin Schilling, series 24, model 10, number 349

- Description
- Around 1900, American mathematicians introduced ideas to their students using physical models like this one. This model is the tenth in a series of kinematic models sold by the German firm of Schilling to show a mechanical method for generating mathematical curves.

- Linkages are joined rods that move freely about pivot points. A pair of fireplace pincers is an example of a very simple linkage. Producing straight line motion was an important component of many machines. But producing true linear motion is very difficult. One area of research during the 19th century was to use linkages to produce linear motion from circular motion. In this context “inverse” is a geometric term that refers to the process of using algebra and trigonometry to convert or invert one geometric shape into another. In this case, the inverse of the circle will be a straight line. So an “inversor" is a device that finds the inverse of a geometrical object: the conversion of a circle to a straight line in the case of this model.

- In 1864 French engineer Charles Nicolas Peaucellier (1832-1913) created a seven-bar linkage which succeeded in producing pure linear motion. Since then, such seven-bar linkages are often referred to as “Peaucellier cells” or a “Peaucellier’s inversor.” His discovery was the first solution of what was referred to as the problem of parallel motion: converting rotational to linear motion using only “rods, joints and pins.”

- This linkage is constructed of seven metal armatures (two longer arms of 15 cm, four shorter arms of 5 cm) hinged so as to create a kite shape with a rhombus (diamond) shape at the top of the kite. This horizontal assembly is then attached to a central vertical axis that is rotated by turning a crank below the baseplate. Fingerholds are attached to the two primary hinge points to allow the linkage to be articulated from above. Below these fingerholds are metal points used to trace the motion of the linkage on the paper.

- The bottom (tail end) of the kite is fixed on a circle. As the dial is turned or the fingerholds are moved, the point internal to the linkage traces the circle, resulting in the point at the top of the kite tracing a straight line. The seven-bar linkage works by keeping one end of the linkage (the tail end of the kite) fixed on a circle. As the center point traces around the circle, the point at the opposite end of the linkage (the top of the kite) traces a straight line. The German title for this model is: Inversor von Peaucellier 1864.

- This model is marked Halle a.S., but this is lined through and has a Leipzig stamp. In or after 1903 Schilling moved the business from Halle to Leipzig. On top of the mounting plate is an aged paper sheet showing the name and maker of the linkage. Printed on the paper are a black circle and a red circle to show the circular path; a red curve; and, what was most likely a black linear path, but which is now worn through the paper with use.

- References:

- Johnson, Wm. Woolsey, “The Peauceller Machine and Other Linkages,”
*The Analyst*, Vol 2, No. 2, Mar 1875, pp. 41-45.

- Roberts, David Lindsay, “Linkages, A Peculiar Fascination” in
*Tools of American Mathematics Teaching, 1800-2000*, Kidwell, P. A. et.al., Johns Hopkins University Press, 2008, pp. 233-242.

- Schilling, Martin,
*Catalog Mathematischer Modelle für den höheren mathatischen Unterricht*, Halle a.S., Germany, 1911, pp. 56-57. Series 24, group IV, model 10.

- Mathematics and interactive Java applet can be found at http://www.cut-the-knot.org/pythagoras/invert.html\

- Location
- Currently not on view

- date made
- ca 1900

- maker
- Schilling, Martin

- ID Number
- MA*304722.21

- catalog number
- 304722.21

- accession number
- 304722

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