Science & Mathematics

Chemical Balance

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.

Date: 1940s

Psychological Test, Stanford Achievement Test, Primary Battery: Form D

After their widespread use during World War One, experts increasingly used psychological tests as a tool to rank and sort people in contexts including (but not limited to) education and employment. The Stanford Achievement Test was written by Truman L. Kelley, Giles M.
Description
After their widespread use during World War One, experts increasingly used psychological tests as a tool to rank and sort people in contexts including (but not limited to) education and employment. The Stanford Achievement Test was written by Truman L. Kelley, Giles M. Ruch, and Lewis M. Terman. This version is the primary battery: form D. It was published by the World Book Company and was copyrighted in 1940. The test included questions about: paragraph meaning, word meaning, spelling, arithmetic reasoning, and arithmetic computation. It appears to be a more basic version of the Advanced Battery-Complete Form D. It is eight pages long.
Location
Currently not on view
date made
1940
ID Number
1983.0168.12
catalog number
1983.0168.12
accession number
1983.0168

Booklet, Instruction Book LA Models Monroe Adding-Calculator

This illustrated instruction book explains the use of the LA-X line of Monroe calculating machines. It was received with a Monroe LA 200 (1986.0131.01).Currently not on view
Description
This illustrated instruction book explains the use of the LA-X line of Monroe calculating machines. It was received with a Monroe LA 200 (1986.0131.01).
Location
Currently not on view
date made
1947
ID Number
1986.0131.02
accession number
1986.0131
catalog number
1986.0131.02

Burroughs Series P Adding Machine

This full-keyboard printing electric adding machine has a black metal case, black and white color-coded round plastic keys, a rubber carriage, rubber feet, and a metal paper tape holder at the back. There is a hole for a handle but no handle.
Description
This full-keyboard printing electric adding machine has a black metal case, black and white color-coded round plastic keys, a rubber carriage, rubber feet, and a metal paper tape holder at the back. There is a hole for a handle but no handle. There are ten columns of keys, with nine keys in each column, as well as a column with five function keys and a large “+” bar.
A red paper tag attached to the machine reads: PATENT DEPT. (/) #208. A metal tag attached to the keyboard reads: 139-243. The machine is marked on the front: Burroughs. A white paper tag attached to the object reads: STY 10 (/) TALLY ROLL (/) MACH (/) TAG (/) 139-243. A metal tag attached to the object reads: DONATED TO (/) The Smithsonian Institution (/) by (/) Burroughs Corporation.
This example was #208 in the collection of the Patent Division of Burroughs Corporation. The Burroughs Series P was introduced in 1949, and this machine presumably dates from about that time.
Location
Currently not on view
date made
ca 1949
maker
Burroughs Adding Machine Company
ID Number
1982.0794.39
catalog number
1982.0794.39
accession number
1982.0794

Acreage Worked Circular Slide Chart by Perrygraf for Allis-Chalmers

The base of this orange, black, and white cardboard circular chart has scales for the number and size of plows and for the size of combines, planters, or harrows. Riveted to the rectangular base is a disc with a scale of tractor speed in miles per hour.
Description
The base of this orange, black, and white cardboard circular chart has scales for the number and size of plows and for the size of combines, planters, or harrows. Riveted to the rectangular base is a disc with a scale of tractor speed in miles per hour. Setting the dial for the appropriate tractor speed opposite the size and type of machinery employed reveals the approximate number of acres worked per day.
According to its markings, Perry Graf Corporation of Maywood, Ill., copyrighted this "Tractor Calculator" in 1938 and made it for the Allis-Chalmers Manufacturing Company's Tractor Division in Milwaukee, Wis. A curator's note indicates the copyright was not issued until November 27, 1941. Perrygraf (spelled variously as "Perrygraf" and "Perry Graf") designed special purpose "slide charts," which were often distributed by manufacturers to their customers.
The back of the calculator contains an advertisement for Allis-Chalmers, titled: WORK-PER-DAY THE A-C WAY. For other rules distributed by Perrygraf, see 1983.3009.06 and 1996.3029.01.
Location
Currently not on view
date made
ca 1941
maker
Perry Graf Corporation
ID Number
1983.3009.04
catalog number
1983.3009.04
nonaccession number
1983.3009

Lightning Adding Machine

This small seven-wheeled stylus-operated non-printing adding machine has a metal case painted green and covered with felt on the back. It sits in a brown bakelite stand. A stylus fits in the ten holes in each wheel.
Description
This small seven-wheeled stylus-operated non-printing adding machine has a metal case painted green and covered with felt on the back. It sits in a brown bakelite stand. A stylus fits in the ten holes in each wheel. Placing the stylus in the proper hole and and rotating it enters a digit. The sum appears in seven windows above the holes. The two rightmost and the two leftmost wheels are brass. The three middle ones are steel. The device has no zeroing mechanism and the stylus is missing.
The instrument is marked on the front: THE (/) Lightning (/) ADDING (/) MACHINE (/) CO. (/) LOS ANGELES (/) CALIF. U.S.A.. It is marked with intertwined letters on the back of the stand: GIM.
This machine is from the calculating machine collection of Myron R. Smith.
References:
Office Appliances, January, 1948, vol. 87, p. 225 - sold for $12.95 - also March, 1948, vol. 87, p. 208.
Location
Currently not on view
date made
1948
maker
Lightning Adding Machine Company
ID Number
1989.0325.02
accession number
1989.0325
catalog number
1989.0325.02

Underwood Sundstrand 8120P Adding Machine

This ten-key printing electric adding machine has a gray metal case with ten white plastic number keys arranged in a block. Left of the number keys are CORRECTION, B’K (/) SPACE, and REPEAT keys. Right of the number keys are SUB- (/) TRACT, ADD and N.ADD (/) TOTAL keys.
Description
This ten-key printing electric adding machine has a gray metal case with ten white plastic number keys arranged in a block. Left of the number keys are CORRECTION, B’K (/) SPACE, and REPEAT keys. Right of the number keys are SUB- (/) TRACT, ADD and N.ADD (/) TOTAL keys. Above the keyboard is a place indicator for up to eight places, which moves from left to right as up to eight digits are entered. The 2-3/8” (6 cm.) paper tape is in the back, A black ribbon is underneath a metal plate held down by thumbscrews. The machine prints up to eight digits, and the rightmost type bar prints symbols. One lever on the top right releases the position of the carriage and the second releases tension on the platen. The motor is on the left.
Gustav David Sundstrand, the son of Swedish immigrants to the United States and a resident of Rockford, Illinois, applied for a patent for an adding machine in 1912, and was granted it in 1920 (U.S. Patent 1,329,028). He applied for a second patent in 1914, which was granted in 1916 (U.S. Patent 1,198,487). The Sundstrand originally was produced by the Rockford Milling Machine Company - by 1920 it was a product of Sundstrand Corporation, a closely related firm. Oscar Sundstrand, a brother of Gustav David, took over primary responsibility in improvements in the adding machine. During the 1920s, several business machine companies consolidated. The Elliott-Fisher Company acquired rights to the Sundstrand adding machine in 1926, and soon merged with the Underwood Typewriter Company. Hence the adding machine was renamed the Underwood Sundstrand.
This example is from considerably later in the history of the machine. The “8” in the model number indicates that the machine has a capacity of listing eight-digit totals, while the “P” signifies a portable electric machine with “Multiflex” control, allowing more rapid repeat addition and subtraction. According to the accession file, the donor acquired this machine secondhand in about 1953.
References:
American Office Machines Research Service, III.
Fédération Nationale des Chambres Syndicales de la Mécanographie, Fédération de Reprise officielle des Machines à Ecrire, Machines à Calculer . . ., Lyon, 1970, p. 86.
Underwood Sundstrand, “Underwood Sundstrand presents the right machine with the right keyboard . . . The only complete line of ten key adding machines,” [no date], 1990.3188.07.
Location
Currently not on view
date made
1940
maker
Underwood Elliot Fisher Company
ID Number
1985.0655.01
maker number
336139
accession number
1985.0655
catalog number
1985.0655.01

Slide Chart, Slide Selector for Elastic Machinery Steels

This slide chart advertises the properties of the ELASTUF machinery steels manufactured by Beals, McCarthy & Rogers, Incorporated, of Buffalo, New York. It consists of a paper envelope with metal rivets and a paper slide.
Description
This slide chart advertises the properties of the ELASTUF machinery steels manufactured by Beals, McCarthy & Rogers, Incorporated, of Buffalo, New York. It consists of a paper envelope with metal rivets and a paper slide. Lining up an arrow on the slide with a type of steel listed along the top of the front reveals in a window of the envelope a general description of the properties of the steel. The other side of a chart shows the physical properties of that type of steel (its tensile strength, yield point, elongation and reduction) for different bar sizes.
A mark along the bottom right of the back reads: COPYRIGHT 1947 BEALS, McCARTHY & ROGERS, INC. A mark on the slide reads: MANUFACTURED BY (/) GRAPHIC CALCULATOR CO. (/) CHICAGO 5, ILL. (/) MADE IN U.S.A.
For other products of Graphic Calculator Company, see 2000.3029.02 and 2000.3029.13.
Graphic Calculator Company was a slide rule and slide chart manufacturing and design company founded in Chicago in 1940 by Capron R. Gulbransen, and apparently still in business at the time of Gulbransen’s death in 1969. By 1965, the firm had moved to Barrington, Illinois.
Reference:
Obituaries, Chicago Tribune, August 11, 1969, p. A6
Location
Currently not on view
date made
1947
maker
Beals-McCarthy & Rogers
ID Number
1988.3076.02
catalog number
1988.3076.02
nonaccession number
1988.3076

Psychological Test, Iowa Placement Examinations, Foreign Language Aptitude

After their widespread use during World War One, experts increasingly used psychological tests as a tool to rank and sort people in contexts including (but not limited to) education and employment. The Foreign Language Aptitude was constructed by G.D.
Description
After their widespread use during World War One, experts increasingly used psychological tests as a tool to rank and sort people in contexts including (but not limited to) education and employment. The Foreign Language Aptitude was constructed by G.D. Stoddard and was revised by Grace Cochran, J.R. Nielson, and D.B. Stuit. It appears to be a part of the larger Iowa Placement Examinations (New Series, Revised). According to the instructions, the test aimed to “see how quickly and accurately you can think in the field of language.” The test contained three parts including inference, construction, and grammar. The inference questions use the language Esperanto. The test is eight pages long. It was published by the Bureau of Educational Research and Service, State University of Iowa, and was copyrighted in 1941.
For a general discussion of testing at the University of Iowa, see 1990.0034.086.
Location
Currently not on view
date made
1941
ID Number
1983.0168.14
catalog number
1983.0168.14
accession number
1983.0168

Psychological Test, Stanford Achievement Test, Advanced Battery - Complete, Form D

After their widespread use during World War One, experts increasingly used psychological tests as a tool to rank and sort people in contexts including (but not limited to) education and employment. The Stanford Achievement Test was written by Truman L. Kelley, Giles M.
Description
After their widespread use during World War One, experts increasingly used psychological tests as a tool to rank and sort people in contexts including (but not limited to) education and employment. The Stanford Achievement Test was written by Truman L. Kelley, Giles M. Ruch, and Lewis M. Terman. Ruth E. Myer’s name appears in the upper right hand corner. This version is the Advanced Battery-Complete Form D. It was published by the World Book Company and was copyrighted in 1940. The test included questions about: paragraph meaning, word meaning, language usage, arithmetic reasoning, arithmetic computation, literature, social studies (two parts: I and II) elementary science, and spelling. The test is twenty-four pages long.
References:
For more on Terman, see John Carson, The Measure of Merit: Talents, Intelligence, and Inequality in the French and American Republics (Princeton: Princeton University Press, 2007).
John C. Flanagan, “Truman Lee Kelley,” Psychometrika 26 (1961): 343–45.
“Truman Kelley, 76, Taught at Harvard,” New York Times, May 3, 1961.
Location
Currently not on view
date made
1940
ID Number
1983.0168.11
catalog number
1983.0168.11
accession number
1983.0168

Carborundum Grinding Wheel Calculator Slide Rule

Some slide rules were used to do calculations relating to industrial safety. The Carborundum Company, a manufacturer of abrasives founded in Pennsylvania in 1890 and moved in 1895 to Niagara Falls, N.Y., distributed this instrument.
Description
Some slide rules were used to do calculations relating to industrial safety. The Carborundum Company, a manufacturer of abrasives founded in Pennsylvania in 1890 and moved in 1895 to Niagara Falls, N.Y., distributed this instrument. It consists of a tan and black plastic envelope and a paper slide colored green, red, and tan. The rule has scales for the diameter of the grinding wheel in inches, the angular velocity in revolutions per minute, and surface feet per minute (a measurement combining diameter and velocity). Knowing two of these variables, one can find the third. At the same time, a table under the scales lists types of wheels according to their size, shape, and type of bond holding an abrasive to the wheel. If the surface feet or number of revolutions per minute becomes too large for a type of wheel to operate safely, a hole in the envelope shows red.
Grit and grade scales on the reverse side of the slide indicate the uses appropriate for various granularities and hardnesses of abrasives and bonding agents. The back of the instrument shows the Carborundum Company main office and factory in Niagara Falls, N.Y.
The front of the rule is marked: GRINDING WHEEL (/) SPEED AND SAFETY INDICATOR (/) PATENT APPLIED FOR (/) THE CARBORUNDUM COMPARNY, NIAGARA FALLS, N.Y. (/) REG. U.S. PAT. OFF. The front of the slide is marked (between logos for Bastian Bros. and the International Photo-Engravers' Union of North America): BASTIAN BROS. CO. ROCHESTER, N. Y. The slide is also marked: COPYRIGHT 1939 BY (/) THE CARBORUNDUM COMPANY.
Bastian Bros., a maker of plastic objects and memorabilia, was an early firm to unionize. For other slide rules by this company, see 1987.0183.01 and 1998.3050.02. Harrison Bucklin (b. 1881 or 1882), a resident of Rochester, N.Y., received at least three patents between 1914 and 1942. He applied for a patent on this device in 1940 and assigned it to Carborundum after it was granted.
References: Library of Congress Copyright Office, Catalog of Copyright Entries: Part 1, Books, Group 2, Pamphlets, Etc., n.s. 37 (1940): 920; Harrison Bucklin, "Indicating Device" (U.S. Patent 2,303,018 issued November 24, 1942); "Bastian Company Profile," http://www.bastiancompany.com/about.shtml; Carborundum Abrasives Products, "More Than a Century of Pacesetting Innovation," http://www.carborundumabrasives.com/aboutCarborundum.aspx.
Location
Currently not on view
date made
1940-1941
maker
Bastian Brothers Company
ID Number
1988.0323.03
accession number
1988.0323
catalog number
1988.0323.03

Perrygraf Enamel Coating Calculator Slide Rule for Armco

This blue, tan, and white cardboard rule consists of an envelope held together by six metal rivets and a paper slide.
Description
This blue, tan, and white cardboard rule consists of an envelope held together by six metal rivets and a paper slide. The rule calculates the weight of an enamel coating, given the area of a metal sample; the surface area of metal, given its thickness and weight; and the weight of enamel per square foot of surface coated, given the weight of enamel used, the thickness of the metal sample, and the weight of the metal.
Perrygraf Corporation of Maywood, Ill., made this instrument (copyrighted in 1941) for the American Rolling Mill Company of Middletown, Ohio. ARMCO produced and enameled coils of sheet steel at plants in Middletown and Ashland, Ky. Since 1999, the company has been part of AK Steel. For more on Perrygraf, see 1979.3074.03.
Reference: "American Rolling Mill Company," Ohio History Central: An Online Encyclopedia of Ohio History, July 1, 2005, http://www.ohiohistorycentral.org/entry.php?rec=840.
Location
Currently not on view
date made
1941
maker
Perry Graf Corporation
ID Number
1983.3009.05
catalog number
1983.3009.05
nonaccession number
1983.3009

Barrett Model 123E Adding Machine

This full-keyboard printing electric adding machine has a metal case painted black and nine columns of black and white color-coded keys. The steel keyboard is painted green. To the left of the keyboard are a non-print lever and a subtract lever.
Description
This full-keyboard printing electric adding machine has a metal case painted black and nine columns of black and white color-coded keys. The steel keyboard is painted green. To the left of the keyboard are a non-print lever and a subtract lever. To the right are a subtotal key, a total key, an add bar, a repeat key, a correction key, and a non-add key. Above the keyboard is a set of small dials that indicates totals. Next to these on the left is a crank that may be used to shift the dials to the left or to the right in multiplication.
Behind the dials are the ribbon, printing mechanism, and narrow fixed carriage. This example has no paper tape. There are 13 type bars, and 12-digit results may be shown. The spools for the ribbon are under metal covers which are screwed down. At the back of the machine, outside the case, is the motor. The cord is cloth-covered. The legs at the back of the machine are longer than those in front, so that the machine sits at an angle.
The machine is marked on the front: Barrett Desk Electric (/) REG. U.S. PAT. OFF. (/) LANSTON MONOTYPE MACHINE COMPANY (/) PHILADELPHIA, PA. U.S.A.; It is marked on a metal tag attached to the front of the machine: MODEL ROOM. It is also marked there: 133820-123E; It is marked on a white paper tag attached to the machine: to E. Racz 11-22-44K. It is marked on a red paper tag attached to the machine: PATENT DEPT. (/) #149. The machine is from the Patent Division of Burroughs Corporation.
References:
American Office Machines Reference Services, May, 1939, 3.21, p. 1-6 describes this model.
Ernst Martin, The Calculating Machines, pp. 240-243, indicates that a manual Barrett machine was introduced in 1910, with production passing to Lanston Monotype in 1922. No electric Barrett machines are shown in McCarthy, American Digest of Business Machines, 1924 or in the Business Machines and Equipment Digest for 1928.
Location
Currently not on view
date made
1940
maker
Lanston Monotype Machine Company
ID Number
1982.0794.26
catalog number
1982.0794.26
accession number
1982.0794

TASCO Adder

This stylus-operated steel notched band adder has seven crook-shaped columns and one straight one, with eight notched bands below. Eight windows show results, and a narrow clearing lever is at the top.
Description
This stylus-operated steel notched band adder has seven crook-shaped columns and one straight one, with eight notched bands below. Eight windows show results, and a narrow clearing lever is at the top. A steel plate slides over seven columns in the shape of inverted crooks, as well as an eighth straight column. These are used in subtraction. Instructions accompany the instrument. Compare to MA.313629.
The TASCO pocket arithmometer closely resembles an adder sold by the Gray Arithmometer Company of Ithaca, New York, in the early 20th century and distributed by the Morse Chain Company of Ithaca in the 1920s. In 1929, the Morse Chain Company became part of Borg-Warner Corporation. Distribution of the adder soon shifted to the Tavella Sales Company of New York City.
References: P. Kidwell, “Adders Made and Used in the United States,” Rittenhouse, 8, (1994): pp. 78-96.
Advertisements in Popular Mechanics 83 (March 1945), p. 178, (April 1945): 180, and (May, 1945), p. 178. Popular Science 152 (January 1948), p. 34.
Utility Supply Company, Office Supply Catalog (Chicago, 1946), p. 285.
Location
Currently not on view
date made
ca 1945
distributor
Tavella Sales Company
maker
Tavella Sales Company
ID Number
1986.0663.01
accession number
1986.0663
catalog number
1986.0663.01

Keuffel & Esser 4097C Ever-There Simplex Slide Rule

This five-inch solid Xylonite (celluloid) slide rule is one of several "Ever-There" pocket slide rules made by Keuffel & Esser. This line was noted for its light weight and small size.
Description
This five-inch solid Xylonite (celluloid) slide rule is one of several "Ever-There" pocket slide rules made by Keuffel & Esser. This line was noted for its light weight and small size. There are A, D, and K scales on the base, with B, CI, and C scales on one side of the slide and S, L, and T scales on the other side of the slide. The glass indicator has a metal frame, plastic edges, and metal screws. The top of the base is marked: KEUFFEL & ESSER CO. N.Y.; PAT. 1,875,927; MADE IN U.S.A. The right end of the slide is marked: < 4097C >.
The back of the slide rule has a scale of 5 inches divided to sixteenths of an inch and a scale of 13 centimeters divided to millimeters. The left ends of the back of the rule and of the back of the slide are marked with a serial number: 38642. The rule fits in a leather sheath marked: K&ECO.
After Adolf Keuffel applied for a patent on what became the Ever-There product line on October 29, 1930, K&E introduced this version of slide rule as model 4098 in 1931. It was renamed model 4097C in 1936 and was discontinued around 1951. With a case, it cost $4.15 in 1936 and $5.75 in 1949. By 1959, it was replaced by model 4153-1. Compare to 1981.0933.05 and 1981.0922.08. An instruction booklet, received separately, is 1981.0933.09.
This example was given to the museum by Myron R. Smith (1911–2007), an electronics engineer who used it in a long career at Collins Radio in Cedar Rapids, Ia., then at Honeywell in Minneapolis, and then at Honeywell in Seattle. Smith used the rule to solve problems relating to the testing of broadcast equipment, the design of electronic temperature controls, the design of power transformers, and corporate management.
References: Adolf W. Keuffel, "Slide Rule" (U.S. Patent 1,875,927 issued September 6, 1932); Bob Otnes, "Adolf Keuffel and the Later K&E Slide Rules," Journal of the Oughtred Society 8, no. 1 (1999): 37–38; K&E Slide Rules and Calculating Instruments (New York, 1931), 17; Catalogue of Keuffel & Esser Co., 38th ed. (New York, 1936), 324; K&E Price List Applying to the 41st Edition Catalog (New York, 1949), 32; K&E Price List Applying to the 41st Edition Catalog (New York, 1951), 35; K&E Price List Applying to the 42nd Edition Catalog (New York, 1959), 73; accession file.
Location
Currently not on view
date made
1936-1949
maker
Keuffel & Esser Co.
ID Number
1989.0325.06
accession number
1989.0325
catalog number
1989.0325.06

Geometric Model by A. Harry Wheeler, Spherical Triangles

This cut and taped tan paper model shows two trihedral angles with the same center and radius but differeng angles facing opposite directions. The radii defining the upper triangle appear to be perpendicular to the lower triangle.
Description
This cut and taped tan paper model shows two trihedral angles with the same center and radius but differeng angles facing opposite directions. The radii defining the upper triangle appear to be perpendicular to the lower triangle. The vertices of the upper triangle are labeled A, B, and C and those of the lower triangle are labled A", B", and C".
Location
Currently not on view
date made
ca 1945
maker
Wheeler, Albert Harry
ID Number
MA.304723.688
accession number
304723
catalog number
304723.688

Geometric Model by A. Harry Wheeler, One-Sided Polyhedron

This self-intersecting polyhedron has twelve trapezoidal faces (made out of light turquoise plastic) and twelve triangular faces (made out of dark turquoise plastic).
Description
This self-intersecting polyhedron has twelve trapezoidal faces (made out of light turquoise plastic) and twelve triangular faces (made out of dark turquoise plastic). It has twelve vertices at which two trapezoids and two triangles meet and four vertices at which six trapezoids and three triangles meet. The polyhedron has a total of 42 edges. A mark on one face of the polyhedron reads: 710 (/) e = 16 (/) k = 42 (/) f = 24 (/) e – k + f = -2. The number 710 is that Wheeler assigned to the model. The other marks refer to the Euler characteristic of the polyhedron, which equals the number of vertices, minus the number of edges, plus the number of faces. Hence: 16 – 42 + 24 = -2.
Speaking more mathematically, this model consists of four copies of Wheeler’s model #708 (MA.304723.416) glued together in the pattern of a regular tetrahedron. It is a closed, non-orientable surface; that is to say it has neither inside nor outside. It has 4 x 6 = 24 faces. At first glance, there are 4 x 12 = 48 edges, but six are identified along the edges of the tetrahedron, leaving 42. At first glance, there are 4 x 6 = 24 vertices, Twelve of these (those like v4 – v6 in Figure 1) remain unidentified, but the others are amalgamated into the four vertices of the tetrahedron, for a total of 16 vertices. The Euler characteristic of the model is thus 16 – 42 + 24 = -2.
For a pattern related to this model, which is dated March 1945, see 1979.3002.104.
Reference:
A. H. Wheeler, Catalog of Models, A. H. Wheeler Papers, Mathematics Collections, National Museum of American History.
Location
Currently not on view
date made
ca 1940
maker
Wheeler, Albert Harry
ID Number
MA.304723.410
accession number
304723
catalog number
304723.410

Puzzle, TRI'-N'-DO-IT

John D. Boyle (1891-1968), an English-born New York advertising executive who lived in Greenwich, Connecticut, patented several mechanical puzzles.. At least two of these were produced, including this one, which sold under the name TRI'-N'-DO-IT.
Description
John D. Boyle (1891-1968), an English-born New York advertising executive who lived in Greenwich, Connecticut, patented several mechanical puzzles.. At least two of these were produced, including this one, which sold under the name TRI'-N'-DO-IT. The puzzle consists of three wooden cylinders held together by three wooden dowels and a shaped metal piece. The goal of the puzzle is to take apart the pieces.
A mark on one of the cylinders reads: TRI'-N'-DO-IT (/) TR.MK. (/) US PAT 2207778 (/) IT COMES APART (/) WITHOUT FORCE. Boyle applied for a patent for this puzzle August 30, 1939, and received it July 16, 1940.
Compare MA.333295 and MA.333289.
References:
John D. Boyle, “Puzzle,” U.S. Patent 2,207,778, August 30, 1939.
“John D. Boyle, 77, Ex-Head of an Advertising Agency,” New York Times, May 30, 1968, p. 25.
Jerry Slocum and Jack Botermans, Puzzles Old & New: How to Make and Solve Them, Seattle: University of Washington Press, 1986, p. 52.
Location
Currently not on view
date made
ca 1940
ID Number
MA.335295
catalog number
335295
accession number
314637

Rule Advertising Marchant Calculators

This promotional black plastic six-inch ruler is divided along the top edge to sixteenths of an inch and numbered from 1 to 6. The bottom edge has six one-inch sections, divided to 1/10", 1/12", 1/16", 1/24", 1/32", and 1/64", respectively.
Description
This promotional black plastic six-inch ruler is divided along the top edge to sixteenths of an inch and numbered from 1 to 6. The bottom edge has six one-inch sections, divided to 1/10", 1/12", 1/16", 1/24", 1/32", and 1/64", respectively. The center of the ruler is marked: MARCHANT CALCULATORS. Between these words is marked: NORMAN G. HOUGH (/) 1412 Eye St., N.W. Washington, D. C. (/) Republic 1673-74-75. A 1946 calendar is on the back of the ruler. Compare to MA.293320.2816.
The Marchant Calculating Machine Company of Oakland, Calif., was the oldest and one of the most influential American manufacturers of mechanical and electronic calculators. Established in 1911, the firm quickly built up a national sales network, with receipts of $12,000,000 in 1946. In 1958, the company merged with Smith-Corona, Inc., a manufacturer of typewriters, adding machines, and cash registers. A slow decline resulted for the combined firm, as electronic computers began performing the tasks of Smith-Corona Marchant's machines. SCM stopped selling calculators in 1973. Over 150 of Marchant's products and related documentation are in the Smithsonian collections.
Norman G. Hough, Sr., presumably distributed Marchant calculating machines in Washington, D.C. It is not known whether he was the same Norman G. Hough who directed a trade organization for lime and concrete from the 1910s to the 1930s.
References: "Marchant Calculator," http://en.wikipedia.org/wiki/Marchant_Calculator; Nigel Tout, "Marchant," Vintage Calculators Web Museum, http://www.vintagecalculators.com/html/marchant.html; Ernie Jorgenson, "My Years with Marchant," December 1987, Xnumber World of Calculators, ed. James Redin, http://www.xnumber.com/xnumber/marchant.htm.
Location
Currently not on view
date made
1946
distributor
Marchant Calculating Machine Company
maker
Marchant Calculators
ID Number
MA.293320.2811
catalog number
293320.2811
accession number
293320

Geometric Model by A. Harry Wheeler, Model for the Pythagorean Theorem

This is A. Harry Wheeler’s visual representation of the Pythagorean Theorem. The wooden base has a right triangle at the center with square holes cut out along each side of the triangle.
Description
This is A. Harry Wheeler’s visual representation of the Pythagorean Theorem. The wooden base has a right triangle at the center with square holes cut out along each side of the triangle. The two vertices of the triangle next to the long side are cut out so that metal filings can run from the smaller squares into the larger one. A clear plastic top and bottom hold the filings within the model. In theory, one can fill either the large square or the two smaller squares with filings—according to the Pythagorean Theorem, the area of the large square is the sum of the area of the small ones.
The model is unsigned and undated.
Location
Currently not on view
date made
1915-1945
maker
Wheeler, Albert Harry
ID Number
MA.304723.480
catalog number
304723.480
accession number
304723

Geometric Model by A. Harry Wheeler, Six Tetrahedra Inscribed in Regular Tetrahedron

This transparent green plastic model of a regular tetrahedron has six smaller tetrahedra shown inside it. The smaller tetrahedra are outlined in thread, held at the ends by beads. The model has no maker's marks.A.H. Wheeler, the maker of this model, lived from 1873 to 1950.
Description
This transparent green plastic model of a regular tetrahedron has six smaller tetrahedra shown inside it. The smaller tetrahedra are outlined in thread, held at the ends by beads. The model has no maker's marks.
A.H. Wheeler, the maker of this model, lived from 1873 to 1950. Models made by him are marked with dates ranging from 1910 to 1949, hence the rough date assigned.
Location
Currently not on view
date made
1910-1949
maker
Wheeler, Albert Harry
ID Number
MA.304723.741
accession number
304723
catalog number
304723.741

Geometric Model by A. Harry Wheeler, Moebius Polyhedron (Polyhedron of Musical Chords)

This plastic model is in roughly the shape of a torus. All the faces are triangles. Twelve are turquoise and twelve white, with the colors alternating. The surface has thirty-six edges and twelve vertices.
Description
This plastic model is in roughly the shape of a torus. All the faces are triangles. Twelve are turquoise and twelve white, with the colors alternating. The surface has thirty-six edges and twelve vertices. This would give an Euler characteristic of vertices – edges + faces = 12 – 36 + 24 = 0, which is appropriate for a surface with one hole. Four of the white triangles are numbered. Face 1 also has a tag that reads: 739. Another tag on this side reads: A. Harry Wheeler. Another mark on this side reads: MP. Face 2 is a congruent white triangle on the lower left side, face 3 is a white triangle on the bottom of the back, and face 4 is a triangle on the bottom of the right side.
Wheeler called the surface a “polyhedron of musical chords,” following the German mathematician August F. Moebius, who described the surface in the second volume of his collected works. Wheeler made two other versions of the model, a paper version of the same size with museum number MA.304723.508 and a larger plastic version in yellow and white with museum number MA.304723.404. Musical notes are not indicated on this larger version of the model.
Wheeler’s model shows relationships between the twelve notes in a chromatic musical scale. In the Germanic system, going up by semitones, these are C, C#, D, D#, E, F, F#, G, G#, A , B, H (no flats are used). On a piano, C#, D#, F#, G#, and B would be black keys and the rest white.
If one raises pitches by a major third (four semitones) and keeps going until the original note returns (one octave higher), there are four cyclic sequences:
C E G# C, C# F A C#, D F# B D, D# G H D#
Each note of the chromatic scale appears in exactly one of these sequences.
Similarly, if one raises pitches by a minor third (three semitones), there are three cyclic sequences, each one note longer:
C D# F# A C, C# E G B C#, D F G# H D
Again, each note of the chromatic scale appears in one sequence.
Since three and four are divisors of twelve, the sequences of major and minor thirds all take place within one octave. The third musical interval studied is the perfect fifth, consisting of seven semitones. Since seven and twelve are relatively prime, raising the pitch by a fifth produces one multi-octave cycle:
C G D A E H F# C# G# D# B F C
Moebius and Wheeler sought to label the twelve vertices of the torus with notes of the chromatic scale in such a way that edges and triangles represent interesting musical relationships. Recall that two of the most common musical chords are the major triad (such as C E G) and the minor triad (such as C D# G). Any note of the chromatic scale can be the low note in a major triad or a minor triad, making a total of twenty-four triads, which are to be paired up with the twenty-four triangles of the model. The blue triangles of the model represent major triads and the white triangles represent minor triads.
In a major triad, the low and middle note are a major third apart and the middle and high note are a minor third apart, making the low and high note a perfect fifth apart. In a minor triad, the low and middle note are a minor third apart, and the middle and high note are a major third apart, again making the low and high note a perfect fifth apart. It follows that the thirty-six edges in the model need to be divided into three groups of twelve, one group representing a minor third, one group a major third, and the last group a perfect fifth. Each vertex should be incident to two edges of each type, and opposite edges should be of the same type.
We now discuss how the cycles of major thirds, minor thirds, and fifths discussed above are situated on the torus. For a topologist, one of the most significant features of a torus is that there are simple closed curves that cannot be shrunk to a point without leaving the torus. The four edge cycles representing major triads are of this type; they are commonly called meridians of the torus. (There are three edges in each cycle, but they do not bound a triangle on the torus.) The three cycles of minor thirds go the other way around the torus. The cycle of perfect fifths wraps itself around the torus in one continuous band that appears to form a trefoil knot in three-space.
Suppose the model is cut along the four meridians representing major triads (that is to say, cut into four parts at the corners). It is divided into four shapes, each with a six triangles around the edge in a zigzag pattern (an anti-prism). Gluing a triangle onto the top and bottom of a set of triangles would produce an octahedron. Thus the model can be thought of as four octahedra glued together in a ring.
Compare MA.304723.508. For patterns, see 1979.3002.060. For an undated English translation of the relevant pages from Moebius, see 1979.3002.110. Some patterns for this model are labeled in Wheeler’s hand and dated July 1939.
References:
A. H. Wheeler, Catalog of Models, A. H. Wheeler Papers, Mathematics Collections, National Museum of American History.
August F. Moebius, Gesammelte Werke, vol. 2, ed. F. Klein, Leipzig: S. Hirzel, 1886, pp. 553–554.
Location
Currently not on view
date made
ca 1940
maker
Wheeler, Albert Harry
ID Number
MA.304723.405
accession number
304723
catalog number
304723.405

Geometric Model by A. Harry Wheeler, One-Sided Polyhedron

In the late 1930s and early 1940s, A. Harry Wheeler took great interest in polyhedra with interpenetrating sides, such as had been discussed by the German mathematician August F. Moebius. In this example, each of the two like-colored quadrilaterals (e.g.
Description
In the late 1930s and early 1940s, A. Harry Wheeler took great interest in polyhedra with interpenetrating sides, such as had been discussed by the German mathematician August F. Moebius. In this example, each of the two like-colored quadrilaterals (e.g. the two yellow sides) on the top pass through the model and appear as a white quadrilateral on the bottom. These three figures thus contribute only one side to the polygon.
A mark on the model reads: 695. This was Wheeler’s number for the model. Models MA.304723.413, MA.304723.397, and MA.304723.398 fit together. Model MA.304723.409 is a compound of four models like MA.304723.413.
Reference:
Kurt Reinhardt, “Zu Moebius’ Polyhedertheorie,” Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig. Mathematisch-Physische Classe, 37, pp. 106-125. Wheeler referred to this article.
Location
Currently not on view
date made
ca 1940
maker
Wheeler, Albert Harry
ID Number
MA.304723.413
accession number
304723
catalog number
304723.413

R.C.Allen Model 35 Calculating Machine

This ten-key, non-printing electric pinwheel calculating machine has a black metal frame that is painted green under the keys.
Description
This ten-key, non-printing electric pinwheel calculating machine has a black metal frame that is painted green under the keys. Two rows of black plastic keys are in front, a metal bar is on the left, three registers are above the keyboard, and a rod with sliding decimal markers is above the result and revolution registers. One may enter numbers up to nine digits long, record up to eight digits in the revolution register, and computer results of up to 13 digits.
The machine has an electric cord.
A mark on the front reads: “World FAMOUS” [/] 10 KEY CALCULATOR (/) AMERICAN AND SWEDISH PATENTS. Another mark there reads: R.C. Allen (/) MODEL ‘35’. A mark on the back reads: R.C.Allen (/) 10 KEY (/) CALCULATOR (/) FACIT SYSTEM (/) R.C. ALLEN BUSINESS MACHINES, INC. (/) GRAND RAPIDS, MICH.,U.S.A. (/) PATENTED (/) MANUFACTURED IN THE UNITED STATES (/) LICENSED UNDER FACIT PATENTS. A mark on the bottom reads: 29433 (/) MODEL 35
R. C. Allen, Inc. (later R. C. Allen Business Machines) was founded by Ralph C. Allen (1884–1967) in Grand Rapids, Michigan, in 1932. By 1938 Allen was a distributor of Facit machines. It would distribute and manufacture cash registers, calculating machines, and typewriters. During World War II the firm began manufacturing aircraft instruments, and would come to focus on this business.
According to the donor, this machine was manufactured in 1948 and had an original cost of $397. It came from his personal collection of calculating machines.
References:
American Office Machines Research Service, vol. 3, 1938.
Location
Currently not on view
date made
1948
maker
R. C. Allen Business Machines, Inc.
ID Number
MA.335417
maker number
29433
accession number
319049
catalog number
335417

Keuffel & Esser N4053 Polyphase Slide Rule Manual

The citation information for this paperback book is: William E. Breckenridge, The Polyphase Slide Rule No. N4053: A Self Teaching Manual, 3rd ed. (New York: Keuffel & Esser Co., 1944).
Description
The citation information for this paperback book is: William E. Breckenridge, The Polyphase Slide Rule No. N4053: A Self Teaching Manual, 3rd ed. (New York: Keuffel & Esser Co., 1944). According to Clark McCoy, this example comes from the first of two printings of the manual with the 1944 copyright date; the cover and first few pages were changed in the second printing, which was also marked with the K+E logo that was introduced in 1949. This example has the earlier K&E lion logo.
Breckenridge earned an A.M. in mathematics from Columbia University in New York City, was chair of the mathematics department at Stuyvesant High School around 1909–1910, served as an associate editor of The Mathematics Teacher from 1913 to 1928, and apparently also taught at Columbia. He first wrote this manual in 1924. It has 88 pages that describe the uses of slide rules and explain processes for making calculations and locating the decimal point. Breckenridge also discussed the history and theory of the slide rule before providing worked-out examples and exercises for readers to solve. There are also "advanced problems," material on plane trigonometry and triangles, and problems specific to certain occupations and tasks.
At the back of the book, there are advertisements for K&E's specialty slide rules, the all-plastic Ever-There line of slide rules, and surveying instruments such as transits. This manual was received with MA.321780.
References: Clark McCoy, ed., "The Polyphase Slide Rule No. N4053," http://www.mccoys-kecatalogs.com/KEManuals/4053-1944/4053-1944.htm; William E. Breckenridge, The Polyphase Slide Rule, [3rd ed.] (New York: Keuffel & Esser Co., 1944), http://sliderulemuseum.com/SR_Library_KE.htm.
Location
Currently not on view
date made
1944
author
Breckenridge, William E.
ID Number
MA.304213.05
accession number
304213
catalog number
304213.05

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