#
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 2770 items.

Page 9 of 277

## Chronograph

- Description
- From its infancy, timekeeping has depended on astronomy. The motion of celestial bodies relative to the rotating Earth provided the most precise measure of time until the mid-twentieth century, when quartz and atomic clocks proved more constant. Until that time, mechanical observatory clocks were set and continuously corrected to agree with astronomical observations.

- The application of electricity to observatory timepieces in the late 1840s revolutionized the way American astronomers noted the exact movement of celestial events. U.S. Coast Survey teams devised a method to telegraph clock beats, both within an observatory and over long distances, and to record both the beats and the moment of observation simultaneously. British astronomers dubbed it the "American method of astronomical observation" and promptly adopted it themselves.

- Transmitting clock beats by telegraph not only provided astronomers with a means of recording the exact moment of astronomical observations but also gave surveyors a means of determining longitude. Because the Earth rotates on its axis every twenty-four hours, longitude and time are equivalent (fifteen degrees of longitude equals one hour).

- In 1849 William Cranch Bond, then director of the Harvard College Observatory, devised an important improvement for clocks employed in the "American method." He constructed several versions of break-circuit devices—electrical contracts and insulators attached to the mechanical clock movement—for telegraphing clock beats once a second. The Bond regulator shown in the forground incorporates such a device. Bond's son Richard designed the accompanying drum chronograph, an instrument that touched a pen to a paper-wrapped cylinder to record both the beats of the clock and the instant of a celestial event, signaled when an observer pressed a telegraph key.

- Location
- Currently not on view

- Date made
- ca 1868

- maker
- William Bond & Son

- ID Number
- ME*318759

- catalog number
- 318759

- accession number
- 230288

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

## Microscope

- Location
- Currently not on view

- date made
- 1968

- maker
- Bausch & Lomb Optical Company

- ID Number
- MG*M-12196

- accession number
- 272522

- catalog number
- M-12196

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

## Felsenthal FAO-44 Artillery Protractor

- Description
- This clear plastic semicircular protractor is divided by twenties and marked by two hundreds from 0 to 3,200 and from 3,200 to 6,400. A pinhole is at the origin point. The interior is labeled: ANGULAR MILS; 8016738. This protractor was item no. FAO-44. Felsenthal Instruments Company manufactured it for the U.S. Army about 1958.

- The Felsenthal Instruments Company was the leading supplier of mathematical instruments to the U.S. Army Air Force and the U.S. Navy Bureau of Aeronautics, particularly during World War II (when the firm was known as G. Felsenthal & Sons). After the company ceased operations in approximately 1976, it provided a large sample of its products to the Smithsonian.

- See also 1977.1141.01, 1977.1141.02, 1977.1141.03, 1977.1141.05, 1977.1141.08, 1977.1141.09, 1977.1141.11, 1977.1141.12, 1977.1141.18, 1977.1141.19, 1977.1141.20, 1977.1141.21, 1977.1141.22, 1977.1141.23, 1977.1141.24, 1977.1141.30, and 1977.1141.39.

- Location
- Currently not on view

- date made
- ca 1958

- maker
- Felsenthal

- ID Number
- 1977.1141.10

- accession number
- 1977.1141

- catalog number
- 336394

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

## Felsenthal A-10 Protractor and Map Coordinator

- Description
- This clear plastic semicircular protractor is divided by ten mils and marked by hundreds from 100 to 3,100 in both the clockwise and counterclockwise directions. It is also divided by single degrees and marked by tens from 0° to 180° in both directions. Diagonal lines extend some of the measurement markings out to the edges of the rectangle surrounding the protractor. Pinholes are at the origin point and in the upper left and right corners. The interior of the protractor has cutout stencils for a circle, triangle, square, and two oblong shapes. The middle also contains scales placed at right angles to each other. They are divided and marked by hundreds from 1,000 to 2[00]. The scales are labeled: 1:21120.

- The left edge of the rectangular plastic piece is divided by tenths of an inch and marked by ones from 1 to 3. Inside the 3-inch ruler is a scale for mils divided by hundreds and marked by thousands from 5,000 to 1,000. The scale continues on the top of the rectangle, again divided by hundreds and marked by thousands from 5,000 to 1,000. The scale is labeled: 1:62500. On the right side of the top is a scale labeled: 1:20,000. It is divided and marked by hundreds from 1,000 to 2[00]. This scale also repeats on the right side of the rectangle. On the right edge of the rectangle, there is a scale divided by millimeters and marked by ones from 1 to 7. It is labeled: METRIC.

- The bottom of the protractor bears a scale divided by hundreds and marked by thousands from 1,000 to 8,000. It is labeled: 1:62500. The bottom edge has a second scale, divided by hundreds and marked by five hundreds from 500 to 3,000. It is labeled: 1:21120. The name of the instrument is printed on the very bottom edge: MAP COORDINATOR AND PROTRACTOR - A-10. Donor Ben Rau dated the object to 1942.

- See also 1977.1141.01, 1977.1141.02, 1977.1141.03, 1977.1141.05, 1977.1141.08, 1977.1141.09, 1977.1141.10, 1977.1141.11, 1977.1141.12, 1977.1141.18, 1977.1141.19, 1977.1141.20, 1977.1141.22, 1977.1141.23, 1977.1141.24, 1977.1141.30, and 1977.1141.39.

- Location
- Currently not on view

- date attributed by donor
- 1942

- maker
- Felsenthal

- ID Number
- 1977.1141.21

- accession number
- 1977.1141

- catalog number
- 336405

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

## Kern Semicircular Protractor

- Description
- This German silver semicircular protractor bears the distinctive italic engraved numbers of Kern & Co. of Aarau, Switzerland. It is graduated by quarter-degrees and marked by tens from 10 to 170 both from left to right and from right to left. There are no other marks. The lower edge of the protractor is beveled, with a groove at the origin point.

- Ruth E. Crownfield, the widow of Albert C. Crownfield Jr., a mechanical engineer from Mohawk, N.Y., donated this protractor in 1978. The instrument is quite tarnished and scratched, suggesting Crownfield used it frequently. Similar protractors cost $3.50 in the first decade of the 20th century and $4.50 in 1936.

- See also ID numbers MA*247966 and 1977.0460.02.

- References: “(Product No.) 1248,”
*Catalogue of Keuffel & Esser Co.*(New York, 1909), 172;*Catalogue of Keuffel & Esser Co.*(New York, 1936), 201.

- Location
- Currently not on view

- date made
- early 20th century

- maker
- Kern & Co.

- ID Number
- 1978.2291.01

- accession number
- 1978.2291

- catalog number
- 336875

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

## Geometric Model of a Regular Icosahedron by A. Harry Wheeler or One of His Students

- Description
- Greek mathematicians knew in ancient times that there are only five polyhedra that have identical faces with equal sides and angles. These five regular surfaces, called the Platonic solids, are the regular tetrahedron (four equilateral triangles as sides), the cube (six square sides), the regular octahedron (eight equilateral triangles as sides), the regular dodecahedron (twelve regular pentagons as sides) and the regular icosahedron (twenty equilateral triangles as sides). This is an early 20th-century model of a regular icosahedron. The sides are covered with sateen and brocade fabrics of various designs and colors, in the style of late 19th-century piece work. Catch stitches are along the edges.

- The model is unsigned, but associated with the Worcester, Massachusetts, schoolteacher A. Harry Wheeler. Wheeler taught undergraduates at Wellesley College, a Massachusetts women’s school, from 1926 until 1928. It is possible that one of his students there made the model.

- Reference:

- Judy Green and Jeanne LaDuke,
*Pioneering Women in American Mathematics: The Pre-1940 PhD’s*, Providence: American Mathematical Society, 2009, p. 21.

- Location
- Currently not on view

- date made
- ca 1926

- ID Number
- 1979.0102.188

- accession number
- 1979.0102

- catalog number
- 1979.0102.188

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

## Geometric Model of a Deltahedron (also a Form of Stellated Icosahedron) by A. Harry Wheeler and His Students

- Description
- Polyhedra in which all faces are equilateral triangles are called deltahedra. The regular tetrahedron, octahedron, and icosahedron are the simplest deltahedra. It also is possible to replace each face of a regular dodecahedron with a “dimple” having five equilateral triangles as sides. This is a model of such a surface. It also may be considered as one of the polyhedra formed by extending the sides of—or stellating—a regular icosahedron.

- This deltahedron is folded from paper and held together entirely by hinged folds along the edges. Fifteen of the sixty faces have photographs of students of A. Harry Wheeler at North High School in Worcester, Massachusetts. All are boys. Another face reads: 1927 (/) Stanley H. Olson. A seventeenth face reads: Royal Cooper. Cooper is also shown on one of the sides with a photograph. There is a photograph of Lanley S. Olson, but not Stanley H. Olson. Yet another face of the model has a pencil mark that reads: June – 1927.

- Reference:

- Magnus J. Wenninger,
*Polyhedron Models*, Cambridge: The University Press, 1971, p. 48.

- Location
- Currently not on view

- date made
- 1927

- ID Number
- 1979.0102.308

- accession number
- 1979.0102

- catalog number
- 1979.0102.308

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

## Clark Refracting Telescope

- Description
- Alvan Clark & Sons were the leading telescope opticians in the United States in the second half of the 19th century. The firm came to prominence in 1865 when their 18½-inch refractor, then the largest in the world, was installed in the Dearborn Observatory in Chicago. Other notable achievements included the 26-inch telescope installed in the U.S. Naval Observatory in Washington, D.C., in 1873; the 30-inch objective lens installed in the Imperial Russian Observatory at Pulkowa in 1883; the 36-inch objective lens installed in the Lick Observatory in California in 1887; and the 40-inch objective lens installed in the Yerkes Observatory in Williams Bay, Wisconsin, in 1897.

- The Clarks also made many smaller instruments for investigation, education, and recreation. This example is marked "Alvan Clark & Sons 1894 Cambridgeport, Mass." It has a nickel-plated brass tube assembly, an objective lens of 5 inches aperture, an equatorial mount, and a wooden tripod.

- Ref: Deborah Jean Warner and Robert B. Ariail,
*Alvan Clark & Sons. Artists in Optics*(Washington, D.C., 1996).

- Location
- Currently not on view

- date made
- 1894

- maker
- Alvan Clark & Sons

- ID Number
- 1979.1017.01

- accession number
- 1979.1017

- catalog number
- 79.1017.1

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

## Painting -

*Proof of the Pythagorean Theorem (Euclid)*- Description
- The Pythagorean theorem states that in any right triangle, the square of the side opposite the right angle (the hypotenuse), is equal to the sum of the squares of the other two sides. This painting depicts the “windmill” figure found in Proposition 47 of Book I of Euclid’s
*Elements*. Although the method of the proof depicted was written about 300 BC and is credited to Euclid, the theorem is named for Pythagoras, who lived 250 years earlier. It was known to the Babylonians centuries before then. However, knowing a theorem is different from demonstrating it, and the first surviving demonstration of this theorem is found in Euclid’s*Elements*.

- Crockett Johnson based his painting on a diagram in Ivor Thomas’s article on Greek mathematics in
*The World of Mathematics*, edited by James R. Newman (1956), p. 191. The proof is based on a comparison of areas. Euclid constructed a square on the hypotenuse BΓ of the right triangle ABΓ. The altitude of this triangle originating at right angle A is extended across this square. Euclid also constructed squares on the two shorter sides of the right triangle. He showed that the square on side AB was of equal area to the rectangle of sides BΔ and Δ;Λ. Similarly, the area of the square on side AΓ was of equal area to the rectangle of sides EΓ and EΛ. But then the square of the hypotenuse of the right triangle equals the sum of the squares of the shorter sides, as desired.

- Crockett Johnson executed the right triangle in the neutral, yet highly contrasting, hues of white and black. Each square area that rests on the sides of the triangle is painted with a combination of one primary color and black. This draws the viewer’s attention to the areas that complete Euclid’s proof of the Pythagorean theorem.

*Proof of the Pythagorean Theorem*, painting #2 in the series, is one of Crockett Johnson’s earliest geometric paintings. It was completed in 1965 and is marked: CJ65. It also is signed on the back: Crockett Johnson 1965 (/) PROOF OF THE PYTHAGOREAN THEOREM (/) (EUCLID).

- Location
- Currently not on view

- date made
- 1965

- referenced
- Euclid

- painter
- Johnson, Crockett

- ID Number
- 1979.1093.01

- catalog number
- 1979.1093.01

- accession number
- 1979.1093

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

## Painting -

*Reciprocation*- Description
- In this oil or acrylic painting on masonite, Crockett Johnson illustrates a theorem presented by the Greek mathematician Pappus of Alexandria (3rd century AD). Suppose that one chooses three points on each of two line straight segments that do not intersect. Join each point to the two more distant points on the other lines. These lines meet in three points, which, according to the theorem, are themselves on a straight line.

- The inspiration for this painting probably came from a figure in the article "The Great Mathematicians" by Herbert W. Turnbull found in the artist's copy of James R. Newman's
*The World of Mathematics*(p. 112). This figure is annotated. It shows points A, B, and C on one line segment and D, E, and F on another line segment. Line segments AE and DB, AF and DC, and BF and EC intersect at 3 points (X, Y, and Z respectively), which are collinear. Turnbull's figure and Johnson's painting include nine points and nine lines that are arranged such that three of the points lie on each line and three of the lines lie on each point. If the words "point" and "line" are interchanged in the preceding sentence, its meaning holds true. This is the "reciprocation," or principle of duality, to which the painting's title refers.

- Crockett Johnson chose a brown and green color scheme for this painting. The main figure, which is executed in seven tints and shades of brown, contains twelve triangles and two quadrilaterals. The background, which is divided by the line that contains the points X, Y, and Z, is executed in two shades of green. This color choice highlights Pappus' s theorem by dramatizing the line created by the points of intersection of AE and DB, AF and DC, and BC and EC. There wooden frame painted black.

*Reciprocation*is painting #6 in this series of mathematical paintings. It was completed in 1965 and is signed: CJ65.

- Location
- Currently not on view

- date made
- 1965

- referenced
- Pappus

- painter
- Johnson, Crockett

- ID Number
- 1979.1093.02

- catalog number
- 1979.1093.02

- accession number
- 1979.1093

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