#
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 37 items.

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## Trigonometric Calculating Instrument

- Description
- This square card has a rotating pointer attached at the center. A movable mechanism shows the length of the sine in various sectors of a circle.

- Marks indicate the sign of various other trigonometric functions. Thus the tangent, cotangent, and cosine are positive in the first quadrant; the cosine, cotangent, and tangent are negative in the second quadrant; the cosine is negative and the tangent and cotangent are positive in the third quadrant; and the cosine is positive, and the tangent and cotangent are negative in the fourth quadrant.

- Location
- Currently not on view

- date made
- 1919

- 1919-02-15

- associated dates
- 1919 02 15 / 1919 02 15

- unspecified
- Wheeler, Albert Harry

- maker
- Wheeler, Albert Harry

- ID Number
- 1979.3002.113

- catalog number
- 1979.3002.113

- nonaccession number
- 1979.3002

- 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

## Patenta Multiplication Table

- Description
- This simple German table was intended as an aid to multiplication and division. Each side of the blue and white paper disc has a blue and white paper arm pivoted from the center. The disc has a diameter of 15 cm.; with the arm, the width is 15.6 cm.

- Going in from the circumference, each arm has printed on it the numbers from 1 to 20 in a column. On each side of the disc there are 19 radial columns. On one side these are numbered from 2 to 20; on the other from 21 to 39. The “2” column contains multiples of 2, the “3” column multiples of 3, etc. To find, say, the product of 35 and 19, one lines up the arm next to the 35 column on the disc. Next to 19 on the arm is 665 (the desired product) on the disc.

- The instrument is marked on both sides: PATENTA. It is also marked on both sides: D.R.G.M. (/) 145,796. The initials D.R.G.M. stand for Deutsches Reichgebrauchmuster, a temporary form of German intellectual property protection (not a full patent). D.R.G.M. numbers were first issued in 1891 and continued to be used through World War II. This number was issued in about 1901. A second form of the instrument, with more numbers, was issued later.

- The object is described briefly in a column in the
*Zeitschrift für Mathematischen und Naturwissenschaftlichen Unterricht*in 1903. This example was found in the collections of the National Museum of American History’s Division of Transportation around 1980.

- References:

- “Besprechung von Lehrmitteln, Mathematik”
*Zeitschrift für Mathematischen und Naturwissenschaftlichen Unterricht*34, 1903, p. 67.

- D. von Jezierski, trans. R. Shepherd,
*Slide Rules: A Journey through Three centuries*, Mendham, N.J.: Astragal Press, 2000, p. 102. This reference indicates that D.R.G.M. registered design 148526 was issued in 1901 and 173095 in 1902.

- Location
- Currently not on view

- date made
- ca 1901

- ID Number
- 1988.0579.01

- catalog number
- 1988.0579.01

- accession number
- 1988.0579

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

## Multiplication Table

- Description
- Printed multiplication tables have long been included as parts of general introductions to arithmetic and its applications in business. This table, which shows multiples of integers from 1 times 1 through 25 times 25, contains larger numbers than those found in most elementary texts. It also has no printing on the back. This suggests that it may have been printed as a broadside to be used separately.

- An inscription in pencil on the back reads: Francis Lincoln (/) Fiskale (/) Mass.” Fiskale (known also as Fiskdale) is an area of Sturbridge, Massachusetts. The object was a donation of George H Watson of Sturbridge.

- Location
- Currently not on view

- date made
- ca 1850

- ID Number
- 72.5

- accession number
- 280076

- catalog number
- 72.5

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

## Mathematical Table, J. D. Smith Machine For Multiplying Numbers

- Description
- This is the United States patent model for a multiplication table. It consists of a wooden disc pivoted to a wooden handle on which it revolves. The front of the part of the handle above the disc is a metal rod with the numbers 1/4, 1/2, 3/4, 1 through 10, and 20 engraved on it. The top of the disc has numbers engraved over its surface such that one can line up the handle with a number on the edge of the disc and find multiples of that number on the disc next to the engraved numbers on the handle.

- A mark painted on the back of the handle and written on the back of the disc reads: J.D. SMITH.

- This invention was patented in 1857 by James D. Smith (1834-1908), a native of Chatham, New York, who had moved to Brantingham in that state in 1841. He worked there in various businesses. In addition to this patent, Smith took out patents for an improvement in tool sharpeners (#87,212, February 12, 1869) and an improvement in station-indicators (#161170, March 23, 1875). No evidence has been found indicating that any of these inventions led to products.

- In 1881, Smith moved to Albany to study law. He spent the rest of his career as an attorney.

- References:

- James D. Smith, “Machine for Multiplying Numbers,” U. S. Patent 18711, November 24, 1857.

- “James D. Smith,”
*The Journal and Republican*, Lowville, New York, June 4, 1908, p. 1.

- Location
- Currently not on view

- date made
- 1857

- patentee
- Smith, James D.

- maker
- Smith, James D.

- ID Number
- MA*252687

- catalog number
- 252687

- accession number
- 49064

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

## Replica of a Babylonian Clay Tablet - Plimpton 322

- Description
- Both written language and written tables originated in the ancient Middle East. Scribes kept lists of numerical data, such as the number of sheep and goats transferred on different days of the month. A few of the clay tablets on which they wrote survive to this day. A tiny number of these tablets have rows and columns arranged in tables.. The rows may give totals of number of various forms of livestock transferred over time, with a column for the animals that were the responsibility of each person charged with such matters. Such documents date from around 2020 BCE.

- Those learning and teaching mathematics in ancient Iraq rarely displayed information in tabular form. However, in 1922 the American collector George Plimpton purchased such a tablet. This replica of that unusual object was made in 1957 by L. C. Eichner. Plimpton donated the original object to Columbia University in the 1920s. The original dates from about 1800 BCE, and reportedly was excavated in what is now Iraq at the side of the ancient city of Lasra. The portion of the tablet that survives has four columns of numbers written in the sexagesimal (base 60) system of numbers.

- Otto Neugebauer and A. J. Sachs offered a modern mathematical interpretation of the tablet in 1945. They noted that the numbers in the second and third columns of the table might represent the squares of the length of the shortest side and of the hypotenuse of right triangles, and interpreted the table as relating to Pythagorean triples. As the name Pythagorean suggests, such numbers had previously only been associated with later Greek mathematics. Other scholars have suggested that this was a part of a larger table of reciprocal numbers and related geometric figures, compiled by a teacher wishing to have examples of such reciprocals available for use in assignments.

- References:

- A. Aaboe,
*Episodes from the Early History of Mathematics*, New Haven: Yale University Press, 1964, pp. 30–31.

- O. Neugebauer and A. J. Sachs,
*Mathematical Cuneiform Texts*, New Haven: American Oriental Society and American Schools of Oriental Research, 1945.

- O. Neugebauer,
*The Exact Sciences in Antiquity*, Providence, R.I.: Brown University Press,1957, pp. 36–40 and Plate 7a.

- E. Robson, “Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322,”
*Historia Mathematica*, 28 (2001), pp. 167–206.

- E. Robson, “Words and Pictures: New Light on Plimpton 322,” American Mathematical Monthly, 109 (Feb 2002), pp. 105–120.

- E. Robson, “Tables and Tabular Formatting in Babylon and Assyria, 2500 BCE–50 CE,”
*The History of Mathematical Tables from Sumer to Spreadsheets*, eds. M. Campbell-Kelly, M. Croarken, R. Flood and E. Robson, Oxford: Oxford University Press, 2003, pp. 18–47.

- Location
- Currently not on view

- date made
- 1957

- maker
- L. C. Eichner Instruments

- ID Number
- MA*315226

- catalog number
- 315226

- accession number
- 218473

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

## Rotating Multiplication Table

- Description
- This device is a rotating multiplication table. It consists of a wooden box containing a cylinder of sheet steel, which is rotated by turning a metal knob on the left side. A lid at the front of the box opens to reveal rows of numbers on a paper table pasted to the cylinder, and a paper strip with three horizontal rows of numbers pasted to the box in front of the cylinder. The numbers are handwritten in pen.

- The leftmost numbers on the cylinder, indicated in red, increase from 1 to 75 as a knob on the side is rotated. The numbers in the top row, also indicated in red, increase from .05 5/11 to .35. From .05 5/11 through .10, these numbers increase by about .018 from one column to the next (each number at the head of a column is .01 9/11 larger than the previous one. Thus the second column has the heading .07 3/11), and from .10 through .35 they increase by .0125. The three rows of numbers on the sheet attached to the box are labeled 1/1, 1/2, and 1/4. Entries in the table are in black ink, and represent the product of the number in the uppermost row by that in the leftmost column, rounded off to the nearest hundredth (e.g., to cents). What the numbers in the table signify is unclear.

- The instrument was collected in 1966 from Howard S. Pellatt, President of Dudley Shuttles. Dudley Shuttles was the descendent of a firm founded in 1825 in Wilkinsonville, Massachusetts, that made wooden shuttles for textile mills.

- Compare MA*389100.

- Location
- Currently not on view

- ID Number
- MA*328416

- accession number
- 272524

- catalog number
- 328416

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

## Pencil-Multiplier, a Multiplication Table

- Description
- Inventors have arranged multiplication tables on cylinders and on discs to ease use. This set of tables is designed to fit over the end of a pencil.

- Near the top of this red pencil, just below the eraser, is a table of multiples of the numbers from 13 to 24 by the numbers 1 through 12. A metal cap numbered from 13 to 24 fits over the table at the top. A rotating metal cylinder fits into the cap, and is numbered 1 to 12 around the top. There is a small window in the cylinder below each of these numbers; the distance of the hole from the top varies with the size of the number. The “1” hole reveals multiples of 1 in the table, the “2” hole multiples of 2, etc. To find, say, 15 times 9, one sets the 9 column of the cylinder under the 15 of the cap and reads off 135.

- A mark on the rotating cylinder reads: CHICAGO RECORDING SCALE CO. (/) WAUKEGAN. ILL. (/) PAT. PENDING. A mark on the pencil reads: U.S.A. SOUTHERN CROSS - No 2502.

- The Chicago Recording Scale Company was in business in Waukegan, Illinois, from at least 1895 until at least 1910. I have seen no patent assigned to the company that corresponds to this object. The drawings for U.S. patent 613,432 for an improvement in pencil-boxes show something somewhat similar to this device, although the numbers included and the arrangement of windows is different. That patent was taken out by Stanislas Szenhak of “Warshaw, Russia,” and assigned to Julius Witkowski of Yokohama, Japan. Szenhak applied for a patent on August 19, 1898, and received it November 1, 1898. He also obtained a patent in Great Britain, where his invention was called a “toy for teaching arithmetic.”

- This example of the device was given to the Museum by John William Christopher Draper and James Christopher Draper. Several objects in this gift were once the property of the New York meteorologist Daniel Draper, who took an active interest in the improvement of calculating instruments.

- References:

- Stanislas Szenhak, “Pencil-box,” U.S. Patent 613432, November 1, 1898.

- P. A. Kidwell, “American scientists and calculating machines: from novelty to commonplace,”
*Annals of the History of Computing*, 12, 1990, pp. 31–40.

- Location
- Currently not on view

- date made
- ca 1900

- maker
- Chicago Recording Scale Company

- ID Number
- MA*335350

- catalog number
- 335350

- accession number
- 304826

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

## Rotating Multiplication Table

- Description
- This device is a rotating multiplication table, probably intended as a currency converter.

- The wooden box contains a cylinder that is rotated by turning a metal wheel on the left side. A lid at the front of the box opens to reveal a paper strip with a horizontal row of numbers pasted to the box, a window below that shows a row of numbers on a paper pasted to the cylinder, and a paper strip with three horizontal rows of numbers pasted to the box below the window. The leftmost number on the cylinder increases as it is turned from 1 to 30. Numbers on the row of numbers above this window increase from 2 to 11, including intermittent values such as 2/3, 2/6, and 2/9.

- Supposing that these numbers are in feet and inches, the product shown on the cylinder is given in fathoms [1 fathom = 6 feet = 72 inches]. Supposing that these numbers are in Massachusetts shillings and pence (6 shilling = $1 in 1818), the tables give the dollar and cents equivalents of multiples of Massachusetts currency.

- The three rows of numbers below the window are labeled 1/4, 1/2, and 3/4. They give fractional values of the numbers in the top row, in the converted units (e.g. if the numbers in the top row represent shillings, they give values of fractions of that number of shillings, in cents).

- The device is marked faintly in pencil on the bottom. This mark reads in part: May 1814.

- According to the Ethnology catalog card, this object is American. It came with a large collection of Americana, particularly with school apparatus from New England.

- Compare MA*328416.

- Reference:

- Zacariah Jess,
*The American Tutor’s Assistant*, Philadelphia, 1818, p. 18.

- Location
- Currently not on view

- date made
- 1814

- ID Number
- MA*389100

- catalog number
- 389100

- accession number
- 182022

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

## Leavitt Calculating Disc

- Description
- Printed tables have long offered bankers, businesspeople, and customers a way to calculate interest. This example consists of two interest tables, printed on paper, arranged radially and pasted to the two sides of a pine disc. A slotted piece pivoted at the center of the disc rotates, so that one can select the appropriate column of the tables. The first table gives the interest on sums ranging from 2 cents to $1,000 at a rate of 6 percent, for periods of from 1 to 7 days, 1 to 11 months, and 1 year. The second table gives the total value of an amount compounded at 6% annually for periods of 1 to 6 years.

- A mark on the front and the back reads: Entered according to act of Congress, in the Year 1845, by Wm. B. LEAVITT, in the Clerk’s Office of the District Court of New Hampshire. A mark on the front reads: Stereotyped by Morrill, Silsby & Co.

- William B Leavitt is probably the astronomer and almanac author William B. Leavitt (1812–1895) of North Grantham, New Hampshire. He studied with his uncle, Dudley Leavitt, and took over Dudley’s popular almanac when he died in 1851. William B. Leavitt carried out the calculations for
*Leavitt’s Almanac*until his own death.

- Reference:

- “Life Sketches of Leading Citizens of Merrimack and Sullivan Counties, New Hampshire,”
*Biographical Review*vol. 22, Boston: Biographical Review Publishing Company, 1897, p. 475.

- Location
- Currently not on view

- date made
- ca 1845

- maker
- Leavitt, William B.

- ID Number
- 1980.0588.02

- catalog number
- 1980.0588.02

- accession number
- 1980.0588

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