This six-inch cylindrical slide rule consists of a chromium-plated holder, a metal cylinder that slides into the holder, and a black metal tube that fits around and slides up and down on the cylinder. The rule is ten inches long when extended and equivalent to a linear slide rule 66 feet in length. Two short white lines on the tube and a black mark on the chrome cap at the end of the cylinder serve as the indicator. A paper spiral logarithmic scale is attached to the top half of the holder. A second, linear and logarithmic, paper scale is attached to the cylinder. The logarithmic scales are used to multiply and divide, and the linear scale is used to find logarithms.
The end of the cylinder is engraved: MADE IN (/) ENGLAND. At the top of the cylinder is printed: PATENT No 183723. At the bottom of the cylinder is printed: OTIS KING'S POCKET CALCULATOR; SCALE No 430. The top of the scale on the holder is printed: SCALE No 429; COPYRIGHT. The bottom is printed: OTIS KING'S PATENT No 183723. The end of the holder is machine engraved: T/0503. Engraved by hand (and upside-down to the serial number) is: C73.
The instrument is stored in a rectangular black cardboard box. A label on one end reads: Otis King's (/) Calculator (/) Model "L" (/) No. T0503. The slide rule arrived with instructions, 1987.0788.06, and an advertising flyer, 1987.0788.07. See also 1989.3049.02 and 1981.0922.09.
Otis Carter Formby King (b. 1876) of Coventry, England, received a British patent (183,723) for this instrument on August 31, 1922, and in 1923 he received patents 207,762 and 207,856 for improvements to the slide rule. From London, King filed a U.S. patent application, which he assigned to Carbic Limited, the London manufacturer of the slide rule, when that patent was granted in 1927. With co-inventor Bruce Hamer Leeson, King received U.S. Patent 1,820,354 for an "electrical remote control system" on August 25, 1931.
The serial number indicates that this example of Otis King's calculator was manufactured around 1960 to 1962. Howard Irving Chapelle (1901–1975), a naval architect, maritime historian, and curator of what was then the National Museum of History and Technology, donated it to the Smithsonian around 1969 to 1970.
References: Peter M. Hopp, Slide Rules: Their History, Models, and Makers (Mendham, N.J.: Astragal Press, 1999), 274, 281; Otis Carter Formby King, "Calculating Apparatus," (U.S. Patent 1,645,009 issued October 11, 1927); Richard F. Lyon, "Dating of the Otis King: An Alternative Theory Developed Through Use of the Internet," Journal of the Oughtred Society 7, no. 1 (1998): 33–38; Dick Lyon, "Otis King's Patent Calculator," http://www.svpal.org/~dickel/OK/OtisKing.html.
This is the ninth in a series of models illustrating the volume of solids designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio. The unpainted wooden model is a triangular prism with three rectangular sides and a triangular base and top. It separates into three pyramids of equal volume; two of these are identical. A diagram of the dissection appears on one of two paper stickers glued to the model. A mark on one label reads: Triangular Pris [. . .].
Finding the volume of pyramids was not only important for practical reasons but was central to Ross’s demonstrations for the volume of a cone and of a sphere.
For Ross solids, see 1985.0112.205 through 2012.0112.217. For further information about Ross models, including references, see 1985.0112.190.
This is one of a series of models illustrating the volume of solids designed by William Wallace Ross, a school superintendent and mathematics teacher in Fremont, Ohio. It is a wooden square prism with a base of 1 inch by 1 inch and a height of 3 inches. The object has no maker’s label.
Ross took the fundamental unit of measure of rectangles to be one square inch, and the fundamental unit of measure for solids to be one cubic inch. He argued from there that a 1 inch x 6 inch rectangle had an area of 6 square inches (see 1985.0112.191). Similarly, this solid model consisted of 3 cubic inches. He would go on to consider several square prisms lined up end to end, and may have intended for this to be one of them. See 1985.0112.206 for two closely related models. These are also shown in the photograph.
Compare models 1985.0112.205 through 2012.0112.217.
For further information about Ross models, including references, see 1985.0112.190.
The Omicron Ellipsograph Model 17 was manufactured by the Omicron Company of Glendale, CA, in the 1950s. An oval shape, the ellipse is one of the four conic sections, the others being the circle, the parabola, and the hyperbola. Ellipses are important curves used in the mathematical sciences. For example, the planets follow elliptical orbits around the sun. Ellipses are required in surveying, engineering, architectural, and machine drawings for two main reasons. First, any circle viewed at an angle will appear to be an ellipse. Second, ellipses were common architectural elements, often used in ceilings, staircases, and windows, and needed to be rendered accurately in drawings. Several types of drawing devices that produce ellipses, called ellipsographs or elliptographs, were developed and patented in the late 19th and early 20th centuries. The U.S. Army purchased several examples of this device for use in surveying and mapping.
The Omicron Ellipsograph is not an elliptic trammel like many of the other ellipsographs in the Smithsonian’s collections. This ellipsograph is a linkage, in particular a Stephenson type III linkage. A linkage is a mechanical device made of rigid bars connected by hinges or pivot points that move in such a way as to produce smooth mathematical curves. The most common types of linkages are used to draw true straight lines. See the Kinematic Models in the Smithsonian’s online collections for examples of other linkages.
In this ellipsograph, a metal bar is attached to two sliding brackets. One is on the stationary bar that runs horizontally across the device and is the major axis of the ellipse. The other sliding bracket is attached to a curved arm. A pencil is inserted through the hole at the top end of the bar. As the pencil is moved, the linkage articulates at five pivot points (the two adjustable sliders and three pivots as seen in the image). This constrains the pencil to move in an elliptic arc. Unlike the elliptic trammel, only half an ellipse can be drawn with this device, making it a semi-elliptic trammel. It can be turned 180 degrees to draw the other half of the ellipse. Although this device cannot draw a complete ellipse in one motion, it does have the advantage of being able to draw very small ellipses. By adjusting the distance between the two slider brackets, the eccentricity of the ellipse can be changed. Eccentricity is a number between zero and one that describes how circular an ellipse is. By moving the slider brackets closer together, the eccentricity of the ellipse is reduced, creating a more circular ellipse. As the brackets are moved farther apart, the eccentricity is increased and a more elongated ellipse is produced.
Several demonstrations of how an elliptic trammel works are available online. Comparing the slider motion of the elliptical trammel and the linkage ellipsograph highlights the similarities of the motion of these two ellipsographs. Both devices constrain the motion of the sliders so that as one moves inward on a straight line, the other slider moves outward on a straight line perpendicular to the first. Thus both types of ellipsographs produce an elliptic curve using the same mathematical theory, but incorporating different physical configurations.
The Omicron Ellipsograph is made of aluminium and steel on an acrylic base. The base is 18.5 cm by 8.5 cm (7 1/4 in by 3 3/8 in). The top bar is 18 cm (7 in) long. The whole linkage rests on the central pivot directly above the company logo. It can draw ellipses with major axes up to 12 inches long.
This white plaster model of the outer shell of a Fresnel wave surface for a biaxial crystal consists of two pieces that fit together. It is hollowed out and missing an octant and a half-octant. Parts of two small and two larger circles are drawn on the surface. The elliptical wooden stand is painted black. A paper tag on the model reads: Fresnel'sche Wellenfläche. (/) Verl. v. L. Brill. 6. Ser. Nr. 1a. A mark on the bottom of the stand reads: VI.1a
An example of the inner shell of this wave surface, L Brill No. 160. Ser. 6 No. 1b, is the collection as 1982.0795.24, which is part of another copy of Brill No. 160.
This example of the model was exhibited at the Columbian Exposition, a World’s Fair held in Chicago in 1893.
This set of tables was published by the Project for the Computation of Mathematical Tables (later the Mathematical Tables Project) in New York City. During the 1930s. an agency of the United States government known as the Works Project Administration sought to create jobs for employable workers, Malcolm Morrow, a statistician at the W.P.A.’s Washington, D.C., office, proposed a project that would hire people to compute useful mathematical tables. The program came to be under the sponsorship of Lyman Briggs, the director of the National Bureau of Standards, and operated from 1938 until 1942 in New York City, under the direction of physicist Arnold Lowan, with immediate supervision of the (human) computers by the mathematician Gertrude Blanch.
Not long after the outbreak of World War II in 1941, President Roosevelt ended the W.P.A. The computing work continued in New York, partly as an office of the U.S. Navy and also as part of the U.S. Office of Scientific Research and Development. After the war ended, the two projects were reunited under the National Bureau of Standards. In 1959, the project moved to Washington, D.C. as the Computation Laboratory of the National Bureau of Standards. Some of the staff would work on the SEAC computer built there.
According to the preface to this document, it was one of the first publications of the Project for the Computation of Mathematical Tables. It was proposed at a January, 1938, conference held in Washington, D.C., that was attended by members of the Committee on Bibliography of the Mathematical Tables and Aids to Computation of the National Research Council as well as representatives of the W.P.A. and N.B.S. At the Same time, a committee of the British Association for the Advancement of Science undertook a more extensive project of computing powers of integers. Hence only a small number of mimeographed copies of this W.P.A. table were prepared.
Reference:
David Alan Grier, “Table making for the relief of labour,” in The History of Mathematical Tables: From Sumer to Spreadsheets, Oxford: Oxford University Press, 2003, pp. 265-292.
According to the preface to this document, it was one of the first publications of the Project for the Computation of Mathematical Tables. It was proposed at a January, 1938, conference held in Washington, D.C., that was attended by members of the Committee on Bibliography of the Mathematical Tables and Aids to Computation of the National Research Council as well as representatives of the W.P.A. and N.B.S. At the Same time, a committee of the British Association for the Advancement of Science undertook a more extensive project of computing powers of integers. Hence only a small number of mimeographed copies of this W.P.A. table were prepared.
This example of the publication was owned by the German- American statistician, mathematician and computer pioneer Carl Hammer (1914-2004).
Reference:
David Alan Grier, “Table making for the relief of labour,” in The History of Mathematical Tables: From Sumer to Spreadsheets, Oxford: Oxford University Press, 2003, pp. 265-292.
By 1880, German-speaking chemists, physicist, mineralogists, chemical engineers, and pharmacists were willing to purchase an annual update of technical information in their discipline. That year Rudolf Bidermann (1844-1929) began publishing his Chemiker-Kalendar. By 1914, when this thirty-fifth edition of the book appeared, it took up two volumes. This is the first of the two volumes. It includes a calendar for the year (including notes on events important to the history of science that occurred on different dates), advertisements for apparatus and publications, and extensive information on chemical elements and compounds.
This example of the book was owned by the German- American statistician, mathematician and computer pioneer Carl Hammer (1914-2004).
A College Algebra is typical of mathematics textbooks at the turn of the twentieth century in that the book echoes earlier algebra textbooks with its reliance on vocabulary and rules - the only structural improvement Wentworth included from Elements of Geometry is use of boldface - while it at the same time included pre-calculus topics such as series, the binomial theorem, and derivatives. There is also an extensive section on combinations and permutations. Exercises emphasizing repetitive drill (Wentworth would have called it "learning by doing") are scattered throughout the book. The word problems are contrived but do not impart the moral lessons common of earlier textbooks. There are no illustrations in A College Algebra until functions are graphed on page 432 and following. Some oddities in the book include: a nonstandard technique of summation (p. 57), a process for computing square roots (pp. 93-95), and an alternative symbol for factorials (p. 256). There are no owners' marks in this copy, although there are jottings giving hints on some exercises and marking others as assigned or completed. The book was donated to NMAH by Mrs. Chauncey Brockway Schmeltzer, whose husband earned a B.S. (1919) and M.S. (1920) from the University of Illinois and taught surveying there from 1920 to 1926. Wentworth was memorialized with a highway marker on Route 16 in his birthplace, North Wakefield, NH.
References:
David E. Smith, "Wentworth, George Albert," in Dictionary of American Biography, vol. 19, part 2, pp. 655-656.
Clark A. Elliott, Biographical Index to American Science.
www.newhampshire.com/pages/HistmarkerLake.cfm#georgeawentworth [accessed 23 August 2001].
This is a full- keyboard printing manual adding machine. It has a black metal frame, a metal mechanism, glass sides, and a metal handle with a wooden knob. Each of the six columns of black and white plastic number keys has a red key at the top. The repeat and error keys are right of the number keys. The subtotal and total keys are to the left. There is no paper tape. The printing mechanism and paper tape are not visible to the operator. A collapsible metal stand is attached to the left side of the machine. The overall dimensions with the stand up are: 49 cm. w. x 37 cm. d. x 32.9 cm. h.
The machine is marked at the bottom of the front: STYLE No. 7. It is marked on a metal tag below this: No 7-66878. According to the donor, this machine was used in a grocery store in Hopewell, Virginia, in 1917 or earlier.
Like several other models made by the Jesuit mathematician Joseph F. MacDonnell of Fairfield University, this model shows a surface swept out by a moving straight line. Such a surface is called a ruled surface. It is represented by the cylindrical coordinates (r, t, z) by the equation r = a + z tan (pt/q). The model has a clear plastic cylindrical exterior, with pink plastic threads inside it that represent the surface. Here the ratio p/q = ¼ and the fraction 1 /4 is marked on the outside of the cylinder.
This ten-inch yellow plastic duplex linear slide rule has a clear plastic indicator. The posts holding the rule together are also yellow plastic. The front of the base has LL2, LL3, and DF scales at the top and D, LL2, and LL3 scales at the bottom. The front of the slide has CF, CIF, L, CI, and C scales. The left end of the slide is marked: PickETT (/) MICROLINE (/) 140. The right end is stamped with the Pickett logo used between 1964 and 1975.
The back of the base has LL1, K, and A scales at the top and D, DI, and LL1 scales at the bottom. The back of the slide has B, S, ST, T, and C scales. The right end of the slide is also stamped with the 1964–1975 Pickett logo, featuring block letters with a triangle over the "I".
The rule slides into a black imitation leather stitched sheath. Earlier Pickett rules that were also intended for use by middle and high school students include 1991.0445.02 and 1984.1068.03.
This white plaster model has a rectangular base, four concave sides, and a flat top. No curves are indicated on it. It goes with 1985.0112.120.
The model was designed in 1877 by Walter Dyck under the supervision of Ludwig Brill at the technical high school in Munich. It shows the locus of centers of principal curvature of a one-sheeted hyperboloid (that is to say, the envelope or caustic of reflected rays). A tag on the base of the model reads: 153. Another tag reads Centrafläche des Hyperboloids. (/) Verl. v. L. Brill. 1. Ser. Nr. IIIa.
This example of the model was exhibited at the German Educational Exhibit at the Columbian Exposition, a World’s Fair held in Chicago in 1893. It there was purchased by Wesleyan University in Connecticut, and subsequently was donated to the Smithsonian.
References:
L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 3, 86.
Allen Wales Adding Machine Division, the National Cash Register Company
ID Number
1988.0488.01
catalog number
1988.0488.01
accession number
1988.0488
Description
This full-keyboard printing manual adding machine has a tan metal frame, a metal mechanism, and green and white plastic keys on a light green plastic keyboard. It has eight columns of keys and has an operating by a handle on the right side. Subtraction and repeat levers are next to the keyboard, as is a clearing button. Total/subtotal and non-add levers are next to the handle.
The ribbon and the printing mechanism are exposed. The paper tape is released by a lever on the right, advanced by a roller on the right, and torn off using a serrated edge along the top of the paper guide. The machine prints results up to eight digits long. Using a lever on the tip left side, paper advance may be set at nonprint, one space, two spaces or total space.
The machine is marked at the front: National. The serial number, impressed on a metal tag attached to the front at the base is: 9H 309035. A mark on the back reads: MANUFACTURED AT (/) ITHACA, NEW YORK U.S.A. BY THE (/) ALLEN-WALES ADDING MACHINE DIVISION OF (/) THE NATIONAL CASH REGISTER COMPANY (/) DAYTON, OHIO, U.S.A. (/) National.
The machine was given to the Smithsonian by Leona T. Feldman of Philadelphia, and used by her father in his law office. Her father was most probably lawyer David N. Feldman (1896-1987).
This machine-embroidered cloth arm patch was worn around 1944 by a US Navy Specialist I, Third Class. Navy Specialist is a rating that refers to an enlisted sailor's job specialty and the letter I inside the diamond indicates that the sailor who wore this patch had been trained to be a machine operator for a punch-card accounting machine, an electric accounting machine, or a tabulating machine. The single red chevron below the diamond indicates that the specialist's rate, or pay grade, was equivalent to that of a Petty Officer Third Class.
Grace Murray Hopper (1906-1992), a mathematician who became a naval officer and computer scientist during World War II, donated this patch to the Smithsonian. Hopper joined the U.S. Naval Reserves in December 1943. From July 1944 she worked with the Navy’s Computation Project at Harvard University’s Cruft Laboratory writing computer code for the Mark I computer, formally known as the Automatic Sequence Controlled Calculator.
Similar patches (with white background) are shown on World War II images of specialists working on the Computation Project. Hopper herself had been commissioned a lieutenant (junior grade) before she was assigned to the project, so she would not have worn this patch.
In 1881, Gottlieb Herting, then a student in the technical high school in Munich where he worked under the direction of Alexander Brill, designed a set of eleven plaster models of surfaces of revolution. Herting would spend the rest of his career teaching mathematics and physics at an advanced high school (gymnasium) in Augsburg. The models would be published by Ludwig Brill of Darmstadt in 1885 as his Series 10, 30 (lettered a through l and given Brill numbers 113 to 123). A twelfth model in the series was designed by another Brill student, Sievert. This is letter “k” in that series. This example was exhibited at the German Educational Exhibit at the Columbian Exposition held in Chicago, where it was purchased by Wesleyan University.
The plaster model shows a surface of revolution generated by the revolution of a cubic parabola. The equation of the surface is z3 = a3 (x - a). The fragments of a number tag remaining on the model are illegible.
References:
Ludwig Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. 22,76.
J. C. Poggendorff, J.C. Poggendorffs biographisch-literarisches Handwörterbuch zur Geschichte der exacten Wissenschaften . . ., vol. 4, Barth, 1904, p. 626.
“Asymptotic Curves,” website of the Mathematical Institute, Oxford University, accessed September 5, 2017.
This control panel is a small part of a very large programmable calculator built by Bell Telephone Laboratories of New York for the U.S. Army. By the mid-twentieth century, improving communications required complicated calculations. In order to improve the clarity and range of long distance voice signals, George Stibitz, a research mathematician at Bell Labs, needed to do calculations using complex numbers. Stibitz and Bell Labs engineer Sam Williams completed a machine for this purpose in 1939–it later was called the Bell Labs Model I. With the outbreak of World War II, Stibitz and Bell Labs turned their attention to calculations related to the aiming and firing of antiaircraft guns. Stibitz proposed a new series of relay calculators that could be programmed by paper tape to do more than one kind of calculation. The BTL Model 5 was the result. The machine consisted of 27 standard telephone relay racks and assorted other equipment. It had over 9000 relays, a memory capacity of 30 7-digit decimal numbers, and took about a second to multiply 2 numbers together. Two copies of the machine were built. This one was used by the U.S. Army for ballistics work at Aberdeen, Maryland and then at Fort Bliss, Texas. Machines that used relays were reliable, but slower than those using vacuum tubes, and soon gave way to electronic computers.
The perspectograph (also called a diagraph) was used to make enlarged or reduced two-dimensional drawings of three-dimensional objects. This example consists of a metal bar at the base, with an ivory plate which holds a pencil with weight cup. A hollow brass tube on a wheel and pivot fits into this base with screws. A mark on the connection for this tube reads: GAVARD. An eyepiece would be attached to the tube, but the linkage is missing. The assembled tube and bar rolls along a metal guide piece which has prickers to secure it to the paper. Another brass tube may attach to a brass slider on the base bar. A rectangular sight would attach to this tube if the necessary parts were there. Both tubes have spools for thread, which is wound around a card in the case. The case also contains two hollow rectangular joiners, two keys on a white ribbon, and a stone weight.
The wooden case has a metal handle, lock, and two hooks. The braces in the case are lined with felt.
J.D.C. Gavard made the first perspectograph on a design patented in England for him Jean-Marie Etienne Ardit in 1831, and in France by Gavard himself in 1834. His business, which passed to Adrien Gavard, manufactured perspectographs and pantographs which were sold in the United States, and was active until about 1900.
A pamphlet entitled "Rules for Using the Diagraph" was received with the object. It is for a different instrument, but handwritten hints in the back relate to the "French Diagraph." The pamphlet is catalogued as 1987.0923.03.
References:
Howard Dawes, "Scientific Instruments in Perspective," Bulletin of the Scientific Instrument Society, no. 17 (1988): pp. 4-6.
Deborah J. Warner, "French Instruments in the United States," Rittenhouse, 8, (1993): p. 23.
Susan C. Piedmont-Palladino, ed., Tools of the Imagination: Drawing Tools and Technologies from the Eighteenth Century to the Present, New York: Princeton Architectural Press, 2007, p. 67. this is an illustration of a complete version of the apparatus.
Comments by David Bryden at the collections web page of the National Museum of American History.
This rule has a cylindrical hollow brass drum, which is covered with paper printed with 40 A scales. The first A scale runs from 100 to 112; the fortieth runs from 946 to 100 to 105. The paper is also printed in italics on the right side: Patented by Edwin Thatcher [sic], C.E. Nov. 1st 1881. Divided by W. F. Stanley, London, 1882. A wooden handle is attached to each end of the drum, and the drum slides in both directions.
The drum fits inside an open rotating frame to which 20 brass slats are fastened. The slats are lined with cloth and covered with paper. The paper on each slat is printed with two B and two C scales. The first B scale runs from 100 to 112; the fortieth runs from 946 to 100 to 105. The first C scale runs from 100 to 334; the fortieth runs from 308 to 325. The frame is attached to a mahogany base, and the object is housed in a mahogany case. A paper label appears to have been removed from the top of the case.
A paper of directions and rules for operating THACHER'S CALCULATING INSTRUMENT is glued to the top front of the base. A metal tag attached to the top back of the base is engraved: Keuffel & Esser (/) New York. The front right corner of the frame is stamped with numbers: 57 and 35. Presumably one of these is the serial number, but which one is not clear. In either case, the low number and the shape of the frame suggest that this example is the earliest Thacher cylindrical slide rule in the collections. Model 1740 sold for $30.00 in 1887.
Robert B. Steffes of the U.S. Bureau of Labor Statistics donated this instrument to the Smithsonian in 1970.
See also MA.312866 and 1987.0107.08.
References: Wayne E. Feely, "Thacher Cylindrical Slide Rules," The Chronicle of the Early American Industries Association 50 (1997): 125–127; Catalogue of Keuffel & Esser (New York, 1887), 128. This was the first K&E catalog to list the model 1740.
This white plaster model of a third order surface has a square base and three peaks, one larger than the other two. Various lines are indicated. A paper tag on the base reads: 41. Another paper tag reads: Fl. 3 Ord. mit bipl. Knotenpunkt B4 (/) Verl. v. L. Brill 7. Ser. Nr. 12. Brill's catalog indicates that model 41 (series 7, No. 12 - 1985.0112.032) is the real part of the surface and model 42 (Series 7, No. 13 - 1985.0112.033) is the imaginary part.
This model, along with all the models of Series 7, is on the design of Carl Rodenberg of the technical high school in Munich.. It was first published by Brill in 1881.
The object was exhibited at the German Educational Exhibit at the Columbian Exposition, a World’s Fair held in Chicago in 1893. It there was purchased by Wesleyan University in Connecticut, and subsequently was donated to the Smithsonian.
References:
L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill,1892, p.14, 61.
Accession file.
G. Fischer, Mathematical Models, Braunschweig: Vieweg, 1986, vol. 1, p. 24, vol. 2, pp. 12-14. This object is presently missing a piece shown in Fishcer's photograph.