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 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.
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).
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.
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.
These hollow wooden stands are painted black. They are for Brill models once part of the Wesleyan University collections that did not survive to be given to the Smithsonian. The first model is elliptical and is for Brill model #2. The second is also elliptical and is for model #3. The third is elliptical and for model #102. The fourth, received in 2 pieces, is elliptical and for model 103. The fifth and sixth are elliptical and for models 105 and 107. The seventh is elliptical and for model 108. The eighth is elliptical and for model 161. The ninth is circular and is the stand for model 204. Four of these stands have dimensions: 19.5 cm. x 16 cm. x 2 cm. Three of these stands have dimensions: 16 cm. x 12 cm. x 1 cm. One stand measures: 12.5 cm. x 10.5 cm. x 1.5 cm. One stand measures: 10.2 cm. x 10.2 cm. d. x 1.4 cm. h.
This white plaster model of a third order surface (Hesse's surface) has a nearly square base on which a four-sided curved surface sits in the center. Above this are three symmetrically arranged pieces held up by metal rods. Two pieces detached from the center are intended to go at the top. One of these is broken. An incomplete paper tag reads: [ . . .] 6.
The model is one in a series designed by Carl Rodenberg of the technical high school in Darmstadt that was first published in 1880.
This example of the model was exhibited at the Columbian Exposition, a world’s fair held in Chicago in 1893.
References:
L. Brill, Catalog mathematischer Modelle. . ., Darmstadt: L. Brill, 1892, p. p. 15, 64
Groeningen University website, accessed September 3, 2019.
This ten-key printing electric adding machine has a bright orange and brown plastic frame, plastic keys, metal workings, and a paper tape. In addition to a block of ten numeral keys, the keyboard has an “x” key on the left, and - (/) T”and + (/) S bars on the right. The printing mechanism is behind the keyboard, with a narrow 2-1/4” (5.7 cm.) paper tape. Numbers up to eight digits long may be printed. There is a plastic serrated edge for tearing the paper tape. One type bar prints special characters. An orange button in the back of the machine can be pressed to release the lid for access to the mechanism and the black ribbon. Parts include a clear plastic cover and a black cord.
The machine is marked on the right: Sears. It is marked on the bottom: MODEL 888.58801 (/) 120 V 60 W 0.5A (/) SERIAL # 8263820 (/) MADE IN JAPAN. It is marked on the cord: KAWASAKI (/) KP-50 (/) JAPAN.
For manual, see 1988.0265.03. A receipt inside the manual indicates that the donor purchased the machine on May 28, 1973, for $46.68 (including tax).
During the 1950s, the Belgian teacher Emile-Georges Cuisenaire designed a set of rods to teach about numbers and basic arithmetic. Caleb Gattegno popularized his methods in Great Britain and the United States. This small paperback, Book A of Gattegno’s explanation, was copyrighted in 1958 and 1961.
For a set of Cuisenaire rods, see 1987.0542.01. For related documentation see 1987.0542.02 through 1987.0542.07.
For further information about the donor of the materials, see 1987.0542.01.
The instrument shown in this document resembles the perspective tracing instrument patented in Great Britain by Francis Ronalds in 1825. Behind this text, written in ink, are instructions that relate to the used of the "French Diagraph," quite possibly the Gavard perspectograph.
Protropin is an injectable, recombinant pharmaceutical that is used to treat children with growth problems stemming from an inability to produce their own growth hormone.
Recombinant pharmaceuticals are created by inserting genes from one species into a host species, often yeast or bacteria, where they do not naturally occur. The genes code for a desired product, and therefore the genetically modified host organisms can be grown and used as a kind of living factory to produce the product. In this case, genes coding for human growth hormone are inserted into bacteria. Bacteria produce the growth hormone, which is harvested and used as the active ingredient in Protropin.
Object consists of a plastic box with three glass vials: two vials Protropin (Recombinant growth hormone) and one vial Bacteriostatic Water for Injection.