Proportional Dividers

A collection of dividers and compasses in the Division of Medicine and Science's Mathematics collection.

Unlike regular dividers, proportional dividers have points at both ends. A screw and nut slide along a slot within the legs to allow the instrument to be opened into an "X" shape. The user then tightens the screw at a particular proportion in order to make scale drawings, such as for engineering or architecture. Proportional dividers are especially helpful when the drafter must change between several different scales. However, for one of these objects, there was only one desirable proportion, the so-called "universal ratio" of 5.333:1. Maurice Kidjel, a Hawaiian artist and inventor, sought out and received publicity for his device in the 1960s.

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Japanese Proportional Dividers

These brass dividers have metal points, short at one end and longer at the other. The legs are slotted to allow a brass set screw to be placed at one of several positions on two proportional scales that are engraved on one of the legs.
Description
These brass dividers have metal points, short at one end and longer at the other. The legs are slotted to allow a brass set screw to be placed at one of several positions on two proportional scales that are engraved on one of the legs. The scales are labeled with Japanese characters, but they are presumably for drawing lines and circles at different ratios.
The Japanese Empire Department of Education displayed this instrument at the 1876 World's Fair, the Centennial Exhibition in Philadelphia, in order to demonstrate its nation's modernity and progress. In fact, the Department of Education had just been established in 1870 to replace an Educational Board and assume a more active role in the management of primary, middle, and secondary schools. John Eaton, the U.S. Commissioner of Education, arranged for the transfer of the entire exhibit in which these dividers appeared to the Bureau of Education (then part of the Department of the Interior) for a planned museum. The museum closed in 1906 due to high maintenance costs, and much of the collection was transferred to the Smithsonian in 1910.
Other educational mathematical objects exhibited by Japan in 1876 include MA.261301, MA.261305, and MA.261306.
References: Michael Scott-Scott, Drawing Instruments (Aylesbury, England: Shire Publications Ltd., 1986), 14–15; Japan. Department of Education, An Outline History of Japanese Education: Prepared for the Philadelphia International Exhibition, 1876 (New York: D. Appleton, 1876), 121–122, 191–202; U.S. Centennial Commission, International Exhibition, 1876. Reports and Awards , ed. Francis A. Walker (Washington, D.C.: Government Printing Office, 1880), viii:143, 335; U.S. Bureau of Education, Annual Report of the Commissioner (1876), ccxi–ccxii.
Location
Currently not on view
date made
before 1876
ID Number
MA.261313
accession number
51116
catalog number
261313

Fosse Proportional Dividers

This oversized wooden instrument has two slotted arms, with corroded steel points at both ends of each arm. The end of the slot by the short point on the back arm is broken. A screw, anchored by two rectangular metal pieces and adjusted with a wing nut, holds the arms together.
Description
This oversized wooden instrument has two slotted arms, with corroded steel points at both ends of each arm. The end of the slot by the short point on the back arm is broken. A screw, anchored by two rectangular metal pieces and adjusted with a wing nut, holds the arms together. A proportional scale labeled 1/4, 1/3, 2, 3, 4, and 5 is on one arm. Both arms are marked: Fosse. The mark is inside an oval, and the letters E and O appear on either side of the mark on the back arm. No information was found for a maker or brand named Fosse. The object may have been used for classroom demonstrations.
Location
Currently not on view
date made
ca 19th century
ID Number
MA.319792
accession number
239772
catalog number
319792

Proportional Dividers

This instrument has brass slides with steel points. On one end, the points are 3/8" long; on the other, they are 1-3/4" in length. The longer points are corroded.
Description
This instrument has brass slides with steel points. On one end, the points are 3/8" long; on the other, they are 1-3/4" in length. The longer points are corroded. Thumbscrews on both sides adjust the instrument along a gear and tooth mechanism (or "rack movement") on the back slide. The front slide is marked on both sides of the slot with what appears to be a single proportional scale for lines: 1/2, 1/3, 1/4, 1/5, 1/6, 7, 8, 9, 10. A wooden case fastened with brass hooks is lined with dark blue velvet. Red lines and numbers are on the bottom of the case. No legible maker's mark is present.
Location
Currently not on view
date made
ca 1900
ID Number
1986.0316.01
accession number
1986.0316
catalog number
1986.0316.01

Proportional Dividers by Kern

Engineers and surveyors have long used proportional dividers to mark off equal segments on a line or the circumference of a circle. This instrument also permits a draftsman to proportionally enlarge or reduce a portion of a drawing while reproducing the drawing.
Description
Engineers and surveyors have long used proportional dividers to mark off equal segments on a line or the circumference of a circle. This instrument also permits a draftsman to proportionally enlarge or reduce a portion of a drawing while reproducing the drawing. Although drawing instruments such as dividers were the first objects produced when Jakob Kern established his workshop in Switzerland in 1819, this example dates from the early 20th century, by which time Kern & Co. of Aarau was internationally prominent.
The two main slides are nickel silver, and the points are steel. On one end, the points are 1/2" long; on the other, they are 3" in length. The longer points are quite rusted. The slides are connected with a screw. A smaller steel slide is attached by two screws to the slide for planes and solids. There are two scales, each divided proportionally, on each slide. On one slide, the first scale is marked by ones from 2 to 10 and engraved SOLIDS. The second scale is marked by ones from 2 to 10 and engraved PLANES. On the second slide, one scale is marked by ones from 6 to 20, with a division marked GS at the lower end of the scale and CIRCLES engraved at the upper end of the scale. The second scale is marked irregularly (11/12; 9/10; 7/8; 5/6; 4/5; 3/4; 2/3; 3/5; 2; 2/5; 3; 4; 5; 6; 7; 8; 9; 10) and engraved LINES.
The maker’s mark—KERN & CO. [/] AARAU SWISS—is obscured by a museum mark. The number 640 is engraved near the maker’s mark and above the company logo, a K within a pair of dividers. The dividers are housed in a case of morocco leather over wood, lined with green velvet and locked by a button on the side. The top of the case is imprinted with a rectangle that has a fleur-de-lis at each corner. Inside the case, the Museum number (321-781) is written on a ribbon pasted over the maker’s mark, which reads: SWISS; KERN & CO. A word precedes “Swiss,” but it is illegible. The Interstate Commerce Commission transferred these dividers to the Smithsonian in 1963.
Location
Currently not on view
date made
early 20th century
maker
Kern & Co.
ID Number
MA.321781
accession number
246883
catalog number
321781

Tacro Proportional Dividers

The pointers on this German silver drawing instrument are held in place with screws, meaning that they can be adjusted and replaced. The points are 1-1/8" and 1/2" long.
Description
The pointers on this German silver drawing instrument are held in place with screws, meaning that they can be adjusted and replaced. The points are 1-1/8" and 1/2" long. The front slide has scales for lines, running by ones from 1 to 10, and for circles, irregularly numbered from 6 to 36. Thumbscrews on both sides adjust the instrument along a gear and tooth mechanism (or "rack movement") on the back slide. The front slide is marked: TACRO INC. (/) GERMANY. The case is covered with black leather and lined with blue velvet. It is unlocked by pulling out a button on the right side of the case. The case is marked on the top: TACRO. It is also marked: 4130. The case is marked on the bottom: Made in Germany.
Tacro is a manufacturer of drawing instruments apparently established in the 20th century. According to online auction records, it marked its products as made in West Germany from about 1950 to 1991. Thus, this object probably dates to the 1930s or 1940s. As of 2012, Tacro continues to make these proportional dividers.
Location
Currently not on view
date made
ca 1940
maker
Tacro
ID Number
1986.0316.02
accession number
1986.0316
catalog number
1986.0316.02

Kidjel Ratio Cali-Pro Proportional Dividers

This metal instrument has two long arms and two short arms, all colored gold and arranged as in a pantograph. Needle points are bolted to both ends of the long arms. The arms are fixed at a desired distance with a thumbscrew on a central rod.
Description
This metal instrument has two long arms and two short arms, all colored gold and arranged as in a pantograph. Needle points are bolted to both ends of the long arms. The arms are fixed at a desired distance with a thumbscrew on a central rod. Unlike a pantograph or standard proportional dividers, the instrument is not marked so that it may be set for a variety of proportional relationships and thus be used to create scale drawings at a variety of sizes. Instead, the inventor, Honolulu portrait artist Maurice Kidjel (1888–1976), designed the instrument so that it always preserved a ratio of 5.333 : 1. To create drawings in this "universal ratio," the user set the long needles at the width of the large part of the drawing and then turned the dividers over to use the short needles to make a small part of the drawing in proportion to the large part of the drawing.
A large white cardboard box is marked in maroon on the top and both ends: THE KIDJEL RATIO (/) CALI-PRO. According to a mark on the bottom, the box was manufactured by Christian & Co., Inc., of North Hollywood, Calif. Cardboard and yellow foam inside the box provided support and cushioning to the dividers and related documentation.
Russian-born Kidjel and his business partner, Kenneth W. K. Young, began selling this device for $25.00 around 1960. According to the advertising flyer received with the object (MA.304213.04), the dividers were used only to lay out designs in the "universal ratio." However, Kidjel also believed that this ratio was the key to solving the three classic construction problems of Greek antiquity. His solutions, constructed with a compass and straight edge, appeared in the textbook distributed with the Cali-Pro (MA.304213.03). His work depended on a false definition of pi and thus is not mathematically valid. Nonetheless, Daniel Inouye read a tribute to Kidjel's ratio system into the U.S. Congressional Record on June 3, 1960. Although Kidjel's foray into mathematical proof was not successful, the dividers were relatively popular with draftsmen in the 1960s and 1970s. Kidjel was also widely respected as an artist, and his artwork was exhibited at the Smithsonian in June 1947.
References: Maurice Kidjel, The Two Hours that Shook the Mathematical World (Hawaii Art Publishing Co., 1958); Maurice Kidjel and Kenneth W. K. Young, Challenging and Solving the "3 Impossibles" (Honolulu: Kidjel-Young Associates, [1961]); Advertisement for Kidjel Cali-Pro, Art Education 15, no. 4 (1962): 2; Maurice Kidjel, "Proportional Calipers" (U.S. Patent 3,226,835 issued January 4, 1966; UK Patent 1,039,636 issued August 17, 1966); Martin Gardner, "Mathematical Games," Scientific American 214 (June 1966): 116–122.
Location
Currently not on view
date made
ca 1962
maker
Kidjel, Maurice
ID Number
MA.333876
accession number
304213
catalog number
333876

The Kidjel Ratio System Instruction Manual

The citation information for this spiral-bound book is: Maurice Kidjel, The Kidjel Ratio System 5.333/1 (Honolulu, 1962).
Description
The citation information for this spiral-bound book is: Maurice Kidjel, The Kidjel Ratio System 5.333/1 (Honolulu, 1962). It was received with an example of Kidjel's Cali-Pro proportional dividers (MA.333876), and a warranty card for the Cali-Pro is inside the front cover of the book. After a biographical note, Kidjel provided supposed solutions to the three classic construction problems of Greek antiquity (trisecting the angle, squaring the circle, and doubling the cube).
Although the Cali-Pro was not needed for these attempted solutions, in part two of the book Kidjel explained how to make these and other, more standard, solutions with the device. Next, he discussed how his ratio applied to the human body. Finally, he explained how to use the Cali-Pro in various fields of industrial design, such as architecture and publishing. A brief biography of Kidjel's business partner, Kenneth W. K. Young, is found inside the back cover. The back cover reproduces a portion of then-U.S. Representative Daniel Inouye's remarks about the Kidjel ratio system, read into the Congressional Record of the 86th Congress.
Location
Currently not on view
date made
1962
author
Kidjel, Maurice
Young, Kenneth W. K.
ID Number
MA.304213.03
accession number
304213
catalog number
304213.03

Advertising Leaflet for Kidjel Ratio Cali-Pro

This yellow fold-out leaflet was received with 333876. It provides instructions for the Cali-Pro, a proportional divider developed by Maurice Kidjel for making drawings in what Kidjel believed was the "universal ratio," 5.333 : 1. Kidjel and his business associate, Kenneth W. K.
Description
This yellow fold-out leaflet was received with 333876. It provides instructions for the Cali-Pro, a proportional divider developed by Maurice Kidjel for making drawings in what Kidjel believed was the "universal ratio," 5.333 : 1. Kidjel and his business associate, Kenneth W. K. Young, filled orders for the device from an office in Honolulu, Hawaii. The leaflet contains examples of applications and testimonials. It was copyrighted in 1962.
Location
Currently not on view
date made
1962
maker
Young, Kenneth W. K.
ID Number
MA.304213.04
accession number
1973.304213
catalog number
304213.04

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