#
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 2655 items.

Page 165 of 266

## Felsenthal Graphical Site Table

- Description
- This one-sided wooden instrument, similar to a slide rule, was designed in 1964 by Felsenthal Instrument Company but, according to the accession file, made at the Fort Sill Bookstore in Oklahoma. It was used to position a 155 mm howitzer armed with high-explosive M107 shells. The indicator is clear plastic with wooden edges held together with brass screws.

- The bottom of the base has a scale labeled Site and Vertical Interval. The lower right corner of the base is marked: Rule 2 (/) Apr 64. On one side, the slide has a scale for range and scales for the Target Above Gun (TAG) and Target Below Gun (TBG) with charges of 5 or 6. The other side of the slide has another scale for range and TAG/TBG scales for charges of 3, 4, and 7. Tables for the observer's position are on the left and right ends of the slide on both sides. Both sides are marked: HOW 155 mm (/) FT 155-AH-1 (/) PROJ, HE, M107 Rule 2 (/) Apr 64.

- Tables for angling guns to the left and right at various distances are printed under the slide. The back of the instrument has instructions and examples of use. The markings suggest that this rule was distributed in a white bag. Compare to 1977.1141.26, which may be an earlier version of the instrument.

- Location
- Currently not on view

- date made
- 1964

- maker
- Felsenthal Instrument Co.

- ID Number
- 1977.1141.27

- catalog number
- 336411

- accession number
- 1977.1141

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

## Pickett 14 Military Duplex Slide Rule

- Description
- This ten-inch aluminum linear slide rule is coated with yellow plastic and has a flat nylon indicator. The back of the base has LL1, LL2, A, D, LL3, and LL4 scales, with B, T, ST, S, K, and C scales on the slide. The left end of the slide is marked: MODEL 14 (/) U.S. The right end has the Pickett triangular logo used between 1958 and 1962. The style of the grooved stamped aluminum posts is also consisted with this timeframe.

- The top front of the base has scales for "opposite angle" (sine) in both degrees and mils; the top bottom of the base has "Distance D" and A scales. The front of the slide has scales for apex angle (in both mils and degrees), tangent, sine-tangent, sine, and base. The top center of the base is marked: U.S. MILITARY SLIDE RULE.

- Pickett & Eckel, Inc., of Chicago and Alhambra, Calif., made this instrument for computations related to the use of field artillery. It fits in an orange-red leather case that has the Pickett logo and US stamped in gold on the front and a metal loop on the back for suspension from a belt. The case is lined with white plastic. A white plastic "data strip" slides into a slot on the case. The strip contains diagrams and equations for trigonometric functions, traverse computations, azimuth and distance from coordinates, triangle computation, and the distance to an artillery target.

- The case fits in a brown, black, white, and yellow paper box. The box and its insert are repeatedly marked: ALL METAL SLIDE RULE a rule for every need. The Pickett logo appears between the two segments of the mark. The end of the box once bore a paper tag: 1 UNIT - FSN - 7520 - 656 - 0660 (/) Slide Rule – Military, Field Artillery (/) With Data Strip and Case MIL-S-20195B (/) Mfg. Contr.; PICKETT & ECKEL, INC. Model No. 14.

- The object comes from the Felsenthal Collection of computing devices. (See Felsenthal's company history with 1977.1141.02.) Donor Ben Rau suggested a date of 1965 for this slide rule, but it was probably made a few years earlier. Compare to the box collected with 1995.0126.02.

- References: Accession File; Tom Bullock, "Pickett 14 U.S. military slide rule," December 8, 2009, http://www.tbullock.com/sliderule.html; Clark McCoy, "Highlights of the A. J. Boardman Collection of Pickett Slide Rules,"
*Journal of the Oughtred Society*16, no. 2 (2007): 10–14.

- Location
- Currently not on view

- date made
- 1958-1962

- maker
- Pickett & Eckel, Incorporated

- ID Number
- 1977.1141.29

- catalog number
- 336413

- accession number
- 1977.1141

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

## Koehler Trim-Numeral Calculator

- Description
- This plastic green and white slide rule carries out calculations related to the capacity, draft, and resistance of cargo tankers able to carry up to 26,700 deadweight metric tons of petroleum or petroleum products. Eight metal rivets hold the rule together. The front is marked: KOEHLER TRIM-NUMERAL CALCULATOR (/) 26700 D.W.T. TANKERS. The bottom of the front of the slide is marked: MARKETED BY JEFKO PRODUCTS COMPANY, 100 OAKLAND ROAD, MAPLEWOOD, NEW JERSEY. The back of the rule and the back of the slide are both marked: COPYRIGHT 1954 BY J. F. KOEHLER.

- According to the accession file, this instrument was made by Felsenthal Instrument Company in 1954 as model number FDJ-23. For company history, see 1977.1141.01 and 1977.1141.02. The address for JEFKO Products is a single-family home constructed in 1925. A New Jersey engineer named J. Franklin Koehler (b. 1927) earned a B.S. in naval architecture and marine transportation from the Massachusetts Institute of Technology in 1951 with a thesis titled "Influence of Rising Operating Costs on Relative Economic Operation of Higher Speed Cargo Vessels."

- Location
- Currently not on view

- date made
- 1954

- maker
- Felsenthal Instrument Co.

- ID Number
- 1977.1141.38

- catalog number
- 336422

- accession number
- 1977.1141

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

## Felsenthal FAE-15 Stadia Computer Circular Slide Rule

- Description
- This white plastic circular slide rule consists of a disc riveted to a square backing. The backing has a logarithmic scale of readings of a stadia rod used with a transit telescope, in feet. The disc has two logarithmic scales of angles. The first scale gives the difference in elevation of the transit and the stadia rod, in feet. It represents multiplying the stadia reading by 1/2 sin 2A, where A is the vertical angle of the transit telescope. The second scale finds the horizontal distance of the rod in feet and represents multiplying the stadia reading by the square of cos A. There is no indicator.

- The instrument is marked on the front: STADIA COMPUTER. The interior of the disc has DIRECTIONS FOR USE and a table providing the quantity to be added when a constant is used in measuring stadia. On the back, the rule is marked: 6675-664-4676 (/) CONTRACT NO. DSA 700-68-M-AF86 (/) FELSENTHAL INSTRUMENTS CO. (/) CHICAGO, ILLINOIS (/) 22040 (/) MFR'S PART NO. FAE-15. It has a blue plastic case with snaps and a holder for a label. This object was donated with a second, duplicate Felsenthal stadia computer, which was assigned the same catalog number.

- The instrument resembles Cox's Stadia Computer (see 1987.0221.01 and 1987.0221.02). Donor Ben Rau dated the object to 1968, which is consistent with the form of the company name on the instrument. For Felsenthal company history, see 1977.1141.01 and 1977.1141.02.

- References: Deborah J. Warner, “Browse by Maker: Felsenthal,”
*National Museum of American History Physical Sciences Collection: Navigation*, http://americanhistory.si.edu/collections/navigation/maker.cfm?makerid=173; accession file.

- Location
- Currently not on view

- date made
- ca 1968

- maker
- Felsenthal Instrument Co.

- ID Number
- 1977.1141.41

- catalog number
- 336425

- accession number
- 1977.1141

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

## Range Correction Chart, Felsenthal FAS-3

- Description
- This white plastic chart was designed for the U.S. Army Signal Corps. It is a nomogram for finding the range correction in yards of a weapon, by lining up the meteorological correction as a percentage of the range and the range.

- On the left is a scale marked “Range Correction in Yds.” On the right is a scale marked “Percentage Meteorological Correction” and on the diagonal between the two is a scale marked “Range in Yds.” According to a label received with the object and stored in the accession file, the object was made in 1945.

- The meteorological correction is found from the temperature and wind speed using a related chart called a “sound velocity corrector” (for an example, see 1977.1141.42) .

- A mark on the object reads: Range Correction Chart PT-63/TSS-1.

- For an explanation of the mathematical theory of this kind of nomogram, see Lipka. For a similar device used for another purpose, see 1985.0636.01.

- References:

- Joseph Lipka,
*Graphical and Mechanical Computation. Part I. Alignment Charts*, New York: John Wiley & Sons, 1921, pp. 65–

- 67.

- Accession file.

- Location
- Currently not on view

- date made
- 1945

- author
- G. Felsenthal & Sons

- ID Number
- 1977.1141.43

- catalog number
- 336427

- accession number
- 1977.1141

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

## Hemmi Duplex Slide Rule Retailed by Post (Versalog 1460)

- Description
- The Frederick Post Company, a 20th-century manufacturer and retailer of scientific instruments based in Chicago, did not make its own slide rules. From 1932, its exclusive supplier of linear slide rules was Hemmi, a Japanese firm. Hemmi was known for using a large-diameter variety of bamboo grown in Kagoshima Prefecture on the island of Kyushu. Company founder Jiro Hemmi (1878–1953) patented this innovation in several nations, including the United States in 1920.

- While Post usually sold standard Hemmi models, around 1951 Hemmi created two ten-inch slide rules solely for Post, which sold in the United States as the model 1450 Versatrig and model 1460 Versalog. The Versalog was especially popular, selling several hundred thousand copies.

- This example is bamboo, coated on all sides (except the ends) with white celluloid. The rule is held together with metal posts, one of which is engraved on the front: Wm. Krutz. The glass indicator has a metal frame with plastic sides. One side is marked: HEMMI JAPAN. The other side bears a Post logo in red, which has largely been rubbed away. The red Post logo and the serial number 015836 appear on the right front of the slide. The serial number indicates the rule was manufactured in 1959. This is confirmed by the date code JI on the bottom edge of the rule, which corresponds to a manufacturing date of September 1959.

- The top edge of the rule is marked: CAT. NO. 1460; VERSALOG; FREDERICK POST CO.; HEMMI BAMBOO – JAPAN. The front of the base has LL0, LL/0, K, DF, D, R1, R2, AND L scales. The front of the slide bears CF, CIF, CI, and C scales. The LL/0, CIF, and CI scales are numbered in red. The back of the base has LL/1, LL/2, LL/3, D, LL3, LL2, AND LL1 scales. The back of the slide has T, Sec T and ST, Cos and S, and C scales. The LL/1, LL/2, LL/3, T, and Sec T scales are numbered in red. All the other scales are navy.

- The rule fits into a black Fabrikoid case with a leather flap (stamped POST). The case could be hung from the user's belt, and it is labeled: W. K. KRUTZ. The case is stored in a red, white, and black cardboard box, along with a guarantee from Post and a ruler-sized white plastic set of conversion tables, copyrighted in 1950 by the Eugene Dietzgen Co., another prominent slide rule manufacturer. The rule also arrived with an instruction booklet, 1978.0800.02.

- References: Jiro Hemmi, "Slide-Rule" (U.S. Patent 1,329,902 issued February 3, 1920); Walter Shawlee II, Ted Hume, and Paul Ross, "The Post Slide Rule Archive," Sphere Research Corporation, http://www.sphere.bc.ca/test/post.html; Bob Otnes, "Notes on Frederick Post Slide Rules,"
*Journal of the Oughtred Society*7, no. 1 (1998): 7–10; Paul Ross and Ted Hume, "Slide Rules of the Frederick Post Company,"*Journal of the Oughtred Society*9, no. 2 (2000): 37–46; Ted Hume, "The Popular Post Versalog Slide Rule,"*Journal of the Oughtred Society*15, no. 1 (2006): 53–55; William Lise, "Japanese Slide Rules," 19 August 2004, accessed via Internet Archive Wayback Machine; E. I. Fiesenheiser,*The Versalog Slide Rule: An Instruction Manual*(Chicago: The Frederick Post Company, 1951).

- Location
- Currently not on view

- date made
- 1959

- maker
- SUN HEMMI JAPAN CF

- inventor
- Frederick Post Co.

- ID Number
- 1978.0800.01

- catalog number
- 336682

- accession number
- 1978.0800

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

## Polyhedron Model by Martin Berman, Regular Tetrahedron

- Description
- This painted and varnished paper object is the first in a series of models of convex polyhedra with regular faces constructed by Martin Berman. The faces are four regular triangles.

- In 1970 Berman (1938-1984), a physicist at the Pittsburgh Energy Technology Center, constructed a set of models of regular-faced convex polyhedra. A polyhedron is said to be uniform if its faces are regular and its vertices are all alike (so that it has the same arrangement of polygons at each vertex). A polyhedron (uniform or not) is convex if a line segment joining any two of its points lies entirely on or inside it.

- A polygon (convex or not) is regular if it is uniform and its faces are all alike. The regular convex polyhedra are the five Platonic solids, which have been known since classical Greece. The ancient Greek mathematician Euclid proved in his
*Elements of Geometry*that there are only five Platonic solids. These are the regular tetrahedron (four sides that are equilateral triangles), the cube (six sides that are squares), the regular octahedron (eight sides that are equilateral triangles), the regular dodecahedron (twelve sides that are regular pentagons), and the regular icosahedron (twenty sides that are equilateral triangles).

- The term "semiregular" is used to describe polyhedra that are uniform but not regular. The semiregular convex polyhedra include thirteen solids associated with another ancient mathematician, Archimedes. He lived after Euclid and worked in Syracuse on the Mediterranean island of Sicily. These objects are called Archimedean solids. There also are an infinite number of semiregular prisms. These have like regular polygons on the top and bottom and straight lines joining the vertices of these to form the square sides. A second infinite group of semiregular solids are called antiprisms. These also have like polygons for top and bottom, but twisted so that each vertex of one polygon is joined to two vertices of the other to form an equilateral triangle.

- Besides the regular and semiregular solids, there are just ninety-two other convex polyhedra with regular faces. In 1966 the American mathematician Norman W. Johnson, a student of H. S. M. Coxeter at the University of Toronto in Canada, enumerated them. These polyhedra are sometimes called the Johnson solids. In 1969 the Russian Viktor A. Zalgaller offered a computer-based computational proof that Johnson had completed the enumeration of convex polyhedra with regular faces.

- Berman made paper models of the Platonic solids, the Archimedean solids, the Johnson solids, a prism with a triangular base, and an antiprism with a square base, for a total of 112 models. He published photographs of these and diagrams for making them in 1971, identifying the models with the same names as those used by Johnson. Berman gave the models to the Smithsonian in 1978.

- References:

- Accession File

- Martin Berman, "Regular-faced Convex Polyhedra,"
*Journal of the Franklin Institute*, 291, 1971, pp. 329-352. Includes illustrations of models and of nets for making them.

- Norman W. Johnson, "Convex Polyhedra with Regular Faces,"
*Canadian Journal of Mathematics*, 18, 1966, p. 169-200;

- Viktor A. Zalgaller, “Convex Polyhedra with Regular Faces,” in
*Seminars in Mathematics, V. A. Steklov Math. Inst., Leningrad*, vol. 2, English translation: Consultants Bureau, New York, 1969.

- Online discussion of Johnson solids on Wikipedia and on Wolfram MathWorld (both accessed November 11, 2015).

- Location
- Currently not on view

- date made
- 1970

- maker
- Berman, Martin

- ID Number
- 1978.1065.001

- accession number
- 1978.1065

- catalog number
- 1978.1065.001

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

## Polyhedron Model by Martin Berman, Regular Octahedron

- Description
- The faces of the model are eight equilateral triangles.

- For further information about Berman's models of regular-faced convex polyhedra, see 1978.1065.01.

- Location
- Currently not on view

- date made
- 1970

- maker
- Berman, Martin

- ID Number
- 1978.1065.002

- accession number
- 1978.1065

- catalog number
- 1978.1065.002

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

## Polyhedron Model by Martin Berman, Cube

- Description
- The faces of the model are six squares.

- For further information about Berman's models of regular-faced convex polyhedra, see 1978.1065.01.

- Location
- Currently not on view

- date made
- 1970

- maker
- Berman, Martin

- ID Number
- 1978.1065.003

- accession number
- 1978.1065

- catalog number
- 1978.1065.003

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

## Polyhedron Model by Martin Berman, Regular Icosahedron

- Description
- The faces of the model are twenty equilateral triangles.

- For further information about Berman's models of regular-faced convex polyhedra, see 1978.1065.01.

- Location
- Currently not on view

- date made
- 1970

- maker
- Berman, Martin

- ID Number
- 1978.1065.004

- accession number
- 1978.1065

- catalog number
- 1978.1065.004

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

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