#
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 33 items.

Page 1 of 4

## Flash Cards - Maxson's Self-Keyed Fundamental Number Work Self Keyed Set. No. 10

- Description
- In the early twentieth century, progressive educators sought more efficient ways to teach arithmetic. Some used flash cards. This is set of flash cards for arithmetic drill. Each of the sixty numbered cards has eight multiplication problems written on it. The first six problems on each card concern multiplying two 3-digit numbers; the last two show the product of a three-digit and a four-digit number. This is the tenth in a group of 13 drill sets intended for students in grades three through eight. It was designed for fifth graders.

- The cards fit in a cardboard box along with two leaflets. The first lists the drill sets for each grade, and describes checking procedures for students and teachers. The second describes which cards were to be used which day of the week for how long in various grades.

- According to the box, the cards were “A systematic, economical and thorough arrangement of numbers for acquiring accuracy and rapidity in the fundamental operations.” This set sold for sixty cents and was distributed by J. L. Hammett Company of Newark, N. J. and Cambridge, Ma. One leaflet has copyright date 1915, the other 1934. William Silas Maxson (1867-1937) worked as principal of schools in Somerset, Ky.; Chicago, Ill.; and the following towns in New York: Alfred, Yonkers, Sackets Harbor and White Plains. He retired in 1926 from a White Plains elementary school. A 1917 textbook mentions the cards.

- Referencs:

- Louis W, Rapeer, ed.,
*Teaching Elementary School Subjects*, New York: Scribners, 1917, pp. 26, 31.

*]New York Times*, August 19, 1937, p. 20.

- Location
- Currently not on view

- date made
- 1934

- maker
- Hammett Company, J. L.

- ID Number
- 2009.0017.91

- accession number
- 2009.0017

- catalog number
- 2009.0017.91

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

## Geometric Model by A. Harry Wheeler, Snub Dodecahedron

- Description
- The Archimedean solids are polyhedra with regular polygons for sides and edges of equal length. For example, the faces of this surface are twelve regular pentagons and eighty equilateral triangles. It is called a snub dodecahedron. The model is cut and folded from paper. A mark on two faces reads: XII (/) 17. A. Harry Wheeler (/) Nov.1.1931 (/) Pat. 1292188. A paper sticker glued to another side reads: 17. Wheeler assigned the model the number 17, and referred to it as Archimedean solid XII.

- References:

- Magnus J. Wenninger,
*Polyhedron Models*, Cambridge: The University Press, 1971, p. 32.

- A. H. Wheeler,
*Catalog of Models*, A. H. Wheeler Papers, Mathematics Collections, National Museum of American History.

- Location
- Currently not on view

- date made
- 1931

- patentee
- Wheeler, Albert Harry

- maker
- Wheeler, Albert Harry

- ID Number
- MA*304723.062

- accession number
- 304723

- catalog number
- 304723.062

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

## Geometric Model by R. Anderson, a Student of A. Harry Wheeler, Great Rhombicuboctahedron

- Description
- The Archimedean solids are polyhedra with regular polygons for sides and edges of equal length. For example, this 26-faced model has twelve square sides, eight hexagonal sides, and six octagonal sides. The surface is called a truncated cuboctahedron, a rhombitruncated cuboctahedron, or a great rhombicuboctahedron.

- Archimedean solids were known to the Hellenistic Greek mathematician Archimedes and studied by the 17th-century mathematician and astronomer Johannes Kepler. This particular example was made from balsa wood by A. Harry Wheeler’s student R. Anderson, and is dated April 15, ’38. It is number 18 in Wheeler’s listing of models.

- For other examples of models of this surface, see MA*304723.063 (plastic) and MA*304723.064 (paper).

- References:

- Magnus J. Wenninger,
*Polyhedron Models*, Cambridge: The University Press, 1971, p. 29.

- A. H. Wheeler,
*Catalog of Models*, A. H. Wheeler Papers, Mathematics Collections, National Museum of American History.

- Location
- Currently not on view

- date made
- 1938

- teacher of maker
- Wheeler, Albert Harry

- maker
- Anderson, R.

- ID Number
- MA*304723.065

- accession number
- 304723

- catalog number
- 304723.065

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

## Geometric Model by Robert Chaffe, a Student of A. Harry Wheeler, Hyperbolic Paraboloid

- Description
- Suppose two opposite sides of a rectangle are joined by straight lines parallel to the other two sides. Lifting two opposite corners of the rectangle—and keeping the lines taut—one obtains a saddle-shaped figure known as a hyperbolic paraboloid.

- This model of a hyperbolic paraboloid was made from balsa wood by Robert Chaffe, a high school student of A. Harry Wheeler in the class of 1937. It is likely that this person is Robert C. Chaffe (1918–1991) who was born in Connecticut, attended high school in Worcester, Massachusetts, graduated from the Worcester Polytechnic Institute in 1942, and seems to have spent his career as a salesman and sales engineer in Worcester and nearby Auburn.

- References:

- Gerd Fischer,
*Mathematical Models*, vol. 2, Braunschweig/Wiesbaden: Friedr. Vieweg & Sohn, 1986, pp. 3–4.

- U.S. Census records.

- Massachusetts city directories.

- Location
- Currently not on view

- date made
- 1937

- teacher of maker
- Wheeler, Albert Harry

- maker
- Chaffe, Robert

- ID Number
- MA*304723.180

- accession number
- 304723

- catalog number
- 304723.180

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

## Geometric Model by Dick Holl, a Student of A.Harry Wheeler, Dodecadodecahedron

- Description
- In this model, the twelve faces of a dodecahedron are replaced by twelve stars. Below and parallel to each of the stars is a regular pentagon. Only five rhombuses from the corners of a pentagon show beneath each star. The pentagons intersect one another.

- This model is cut and folded from tan paper. One star face and one three-sided dimple are shaded with pencil. A paper sticker gives Wheeler’s number for the model, 340. Another mark reads: Holl (/) Mar 23, 1934. A third mark reads: Dick (/) Holl (/) 34.

- Richard B. Holl of Worcester, Massachusetts, is listed in U.S. Census records for 1920 and 1930, with a birth date of about 1917. Richard Bernhardt Holl (1916–1985) is listed in Masonic records as born in Worcester, Massachusetts, and dying in Waltham, Massachusetts. Richard Bernhardt Holl also is listed in the 1934 yearbook of North High School in Worcester. Later city directories indicate that he became an engineer.

- References:

- Magnus J. Wenninger,
*Polyhedron Models*, Cambridge: The University Press, 1971, p.112.

- A. H. Wheeler,
*Catalog of Models*, A. H. Wheeler Papers, Mathematics Collections, National Museum of American History.

- Ancestry Library Edition, accessed January 23, 2015.

- Location
- Currently not on view

- date made
- 1934

- associated dates
- 1934-03-23

- teacher of maker
- Wheeler, Albert Harry

- maker
- Holl, Dick

- ID Number
- MA*304723.186

- accession number
- 304723

- catalog number
- 304723.186

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

## Mathematical Table, The Macmillan Table Slide Rule

- Description
- John Perry Ballantine (1896–1970), a mathematician on the faculty of the University of Washington, published this set of tables in 1931 as an inexpensive alternative to the slide rule. The paper instrument includes two 8-1/2” x 11” (22.3 cm. x 28 cm) cards which have printed tables on both sides. These are for multiplication, finding powers of numbers, sines, and tangents. Four narrower tables are placed next to these. Two of these are for multiplication, one for division and one for square root. Each of the wider tables has 20 columns of numbers in 100 rows. The narrower ones have ten columns of numbers in ten rows. Tables are based on antilogarithms to base 10. A leaflet of instructions and a paper dust cover are included.

- This example was the property of Oscar W. Richards of the Osborn Zoological Laboratory of Yale University. It is marked with his stamp. A mark on the corner reads: THE MACMILLAN (/) TABLE SLIDE RULE. Another mark there reads: New York (/) THE MACMILLAN COMPANY (/) 1931.

- Ballantine was born in Rahuri, India, the son of a medical missionary and a teacher. He graduated from Harvard in 1918 and then taught briefly at the University of Maine, Pennsylvania State College, and the University of Michigan. He attended graduate school at the University of Chicago, where he met and married fellow graduate student and mathematician Constance Rummons. They both received doctorates from Chicago in 1923. J. P. Ballantine then spent three years teaching at Columbia University before joining the faculty of the University of Washington in 1926. He stayed there, except for a stint in American military schools, until his retirement in 1966.

- Ballantine’s slide rule was reviewed in the
*Journal of the American Statistical Association*, the*American Mathematical Monthly*, and the British educational journal*Mathematical Gazette*. It cost only fifty cents, but, as reviewers pointed out, was less portable and less durable than a conventional slide rule. No second edition was required.

- Ballantine did not limit his interest in technical improvement to classroom devices. In 1932, he applied for a patent relating to electric power meters, receiving it in 1935. In 1938, he published the textbook
*Essentials of Engineering Mathematics*. Neither of these projects was particularly influential.

- References:

- Advertisement,
*The American Mathematical Monthly*, 38 (May 1931), unnumbered page.

- E. J. Atkinson, “The Macmillan Table Slide Rule,” reviewed in
*The Mathematical Gazette*, 16 (May 1932), pp. 140–141.

- Dorothy C. Bacon, “The Macmillan Table Slide Rule,” reviewed in
*Journal of the American Statistical Association*, 26 (Sept 1931), p 373–374.

- J. P. Ballantine, “Multiple-rate Power Metering,” U.S. Patent #2000736, May 7, 1935.

- R. E. Gilman, “The Macmillan Table Slide rule,” reviewed in
*The American Mathematical Monthly*, 39 (May 1932), pp. 295–296.

- J. Green and J. LaDuke,
*Pioneering Women in American Mathematics: the Pre-1940 PhD’s*, Providence: American Mathematical Society, 2009, pp. 131–132.

- Location
- Currently not on view

- date made
- 1931

- maker
- MacMillan

- ID Number
- 1979.3074.08

- nonaccession number
- 1979.3074

- catalog number
- 1979.3074.08

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

## Burroughs Model 9 Adding Machine

- Description
- This full-keyboard manually operated printing adding machine has seven columns of color-coded number keys, with nine keys in each column. To the left of these are three rows of black keys with a key for each month and additional red number keys for days. To the right of the central number keys is a column of five keys for subtotal, total, non-add, repeat, and error. There is a lever below these marked “-” at the top and “+” at the bottom. The crank on the right has a wooden handle.

- At the top is a wide adjustable carriage with a ribbon and printing mechanism in front of it. The rightmost type bar is for symbols. The next seven type bars are for totals, subtotals, etc. The three leftmost type bars are for days of the week and months. The machine has a serrated edge above the platen for tearing the end of the paper tape, an adjustable paper guide behind the platen, and a dowel mounted at the back to hold a roll of paper. The ribbon and its spools are covered, with screws holding the spool containers in place. The serial number, stamped on the keyboard below the keys, is: 9A67626.

- The machine was used at the Freda Fish Corporation, a family-owned wholesale and retail fish business in New York City. The motto of the business was “We handle anything that swims, clings, or crawls.”

- References:

*Office Machines Research, Inc*., section 3.21.

- Accession file.

- Location
- Currently not on view

- date made
- 1934

- maker
- Burroughs Adding Machine Company

- ID Number
- 1981.0058.01

- accession number
- 1981.0058

- catalog number
- 1981.0058.01

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

## Friden Model C 10 Calculating Machine

- Description
- The Swedish-born inventor Carl Friden was stranded in Australia during World War I and then, on his way back to Sweden, decided to settle in California. He found a place at the Marchant Calculating Machine Company, taking out several patents for machines manufactured there. By 1933 he had decided to start his own company. The Friden models A (8-digit entries) and B (10-digit entries) appeared in 1934.

- In 1936 the young company introduced this machine, the model C. It featured automatic return clearance for the carriage and dials and was sold in two sizes, one that allowed entry of numbers up to eight digits long (the C 8) and one allowing ten-digit entries (the C 10). This is an early example of the C 10. It has a case painted greenish black. A later version of the model C, introduced in about 1941, had a gray case. It sold until 1949.

- The stepped drum, full-keyboard electric non-printing calculating machine has ten columns of black and white plastic number keys, colored to make it easy to distinguish different units of money. A blank clearance key of red plastic is at the bottom of each column. Metal rods between the columns of keys turn to indicate decimal places. On the right are red and black function keys. The machine has no separate keys for multiplication.

- Behind the number keys is a movable carriage with an 11-digit revolution register and a 21-digit result register. An arrow above the first column of keys assists in setting the carriage. The result register has plastic buttons above it that can be used to set up numbers. Decimal markers slide above the two registers. Zeroing knobs are on the right of the carriage. The cord is missing. The corners of the machine have metal streamlines. It resembles in key color and general appearance the contemporary Marchant keyboard electric machines built on Friden’s patent.

- The machine is marked on the sides: FRIDEN. A second mark, visible through a window at the front of the machine, is: C10-41272. A paper tag glued to the front left of the machine reads: FRIDEN CALCULATIN [...] ACHINE CO. (/) OAKLAND, CALIF. The Friden Calculating Machine Company moved from Oakland to San Leandro in 1936.

- Compare the Marchant ERB calculating machine with museum number 1977.1225.01, as well as a later model C 10 with catalog number MA*335422.

- This machine was transferred to the collections from the Office of Exhibits at the Smithsonian’s National Museum of Natural History in 1982. It had no Smithsonian Institution tag.

- References:

- Carl Holm, “Milestones in the Development of Friden.”

- Ernie Jorgenson,
*Friden Age List*, Office Machine Americana, p. 1

- Location
- Currently not on view

- date made
- 1936

- maker
- Friden Calculating Machine Company

- ID Number
- 1982.0243.01

- catalog number
- 1982.0243.01

- accession number
- 1982.0243

- maker number
- C10 41272

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

## Burroughs Class 5 Adding Machine

- Description
- This full keyboard non-printing manual adding machine is painted black with a green keyboard. It has black and white octagonal plastic keys. The nine columns of keys have nine keys in each column. Odd-numbered keys are concave, even-numbered ones flat. Complementary digits are indicated as well as numbers. Ten windows at the front show the sum of numbers as the numbers are entered. A single key in the upper left corner controls the numeral wheel seen through the tenth window. The machine has two legs at the back which hold it up at an angle. There is a black plastic cover. Compare to Burroughs calculator.

- The Burroughs calculator was sold as the Burroughs Class 5 from 1918 into the 1960s.

- Reference:

*American Digest of Business Machines*, 1924, pp. 70-71.

- Location
- Currently not on view

- date made
- 1934

- maker
- Burroughs Adding Machine Company

- ID Number
- 1986.3039.01

- catalog number
- 1986.3039.01

- nonaccession number
- 1986.3039

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

## Monroe Model 213-11-011 Adding Machine

- Description
- This machine incorporates ideas of Purdue University graduate Clyde Gardner (1881-1923) who had a long career in the adding machine industry. He began as a draftsman at the Pike Adding Machine Company in 1903. By 1909, when Pike was acquired by the Burroughs Adding Machine Company, Gardner was chief engineer. He moved with the Pike plant to Detroit, where he worked as an engineer and patent expert at Burroughs.

- In 1919 Gardner left Burroughs to work on his own design for an adding machine. On April 19, 1923, the Gardner Calculator Company was established in Ebensburg, Pennsylvania. Gardner died only two days later. His patents eventurally were acquired by the Monroe Calculating Machine Company, which manufactured this printing adding machine to complement its line of calculating machines.

- The object has a green-black steel frame, a green keyboard, and 13 columns of black and white color-coded plastic number keys. To the right of the keyboard are total, error, and subtotal keys, and subtraction and addition bars. A non-add key is to the left of the keyboard. In back of the keyboard is a printing mechanism and a fixed carriage for the three-inch paper tape. The machine prints results of up to 14 digits. An asterisk printed next to a number indicates that it is a total. There is a black rubber-covered cord that plugs into the back.

- The machine is marked on the front: MONROE (/) REGISTERED TRADE MARK. It is marked on a white sticker on the bottom of the machine: DATE (/) INSTALLED 10/Apr/57. It is marked on a gold sticker on the bottom of the machine: Licensed under Gubelman Patents. It is also marked there: 213-11-011-D (/) # 15128. According to the National Office Machine Blue Book, the serial number dates a Monroe machine to about 1932.

- References:

*American Office Machines Service*vol. 3, 1937, 3.21. According to this source, the machine was introduced as the Gardner adding machine in 1924.

*National Office Machine Blue Book*, May, 1975, as compiled by Office Machine Americana, January 2002.

- John E. Gable,
*History of Cambria County, Pennsylvania*, Topeka, Kansas: Historical Publishing Company, 1926, pp. 781-782.

- Location
- Currently not on view

- date made
- 1937

- maker
- Monroe Calculating Machine Company

- ID Number
- 1987.0403.01

- catalog number
- 1987.0403.01

- accession number
- 1987.0403

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