Circular Slide Rules

An image of various slide rules from the collection of the Division of Medicine and Science at the National Museum of American History.

Slide rules that are round offer the length of a 10" rectangular slide rule in a pocket-sized (roughly 3.6") format, since the scales are on the circumference of circles. The scales are also continuous, so there is no need to make adjustments, such as folded and inverse scales, for results of calculations that go off the ends of the scales. Furthermore, these instruments are relatively easy to construct: the scales are printed on one or more disks, and the disks or a single disk and cursor are fastened together with a pin at the center. However, this simple construction is also not very durable, and so circular slide rules may get out of position and thus they lack accuracy, compared to linear slide rules with slides that move along carefully grooved channels.

This collection suggests the diverse appearances and functions of circular slide rules that were manufactured between the mid-19th and late 20th centuries. For example, before Mannheim-type linear slide rules became popular in the late 19th century, American inventors patented a variety of circular designs. Some circular slide rules were made to look like pocket watches, while others were intended to promote particular businesses—Whitehead & Hoag and Perrygraf were especially influential American manufacturers of promotional items. Inventors and makers such as Albert Sexton, Louis Ross, Claire Gilson, Norman Albree, and Ross Pickett wanted their circular slide rules to compete with linear instruments in the engineering and education markets. Other circular slide rules were designed specifically for surveying, such as stadia computers, or for navigation, such as Dalton instruments that may also be seen in the Smithsonian's exhibition, Time and Navigation. Even more specialized in purpose were slide rules for grading earthworks, determining the effects of nuclear bomb explosions, writing efficient computer programs, and betting on horse races.

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Patent Model for Circular Slide Rule Invented by John W. Nystrom

The expansion of American engineering in the nineteenth century created a new market for aids to computation.
Description
The expansion of American engineering in the nineteenth century created a new market for aids to computation. The Swedish-born Philadelphia engineer, John William Nystrom (1824–1885), contributed to this movement by inventing a circular slide rule in 1848 and writing a pocket book of mathematical tables that was reprinted at least 21 times between 1854 and 1895.
This is the patent model for Nystrom's calculator. The surface is a brass disc that rests on three wooden feet. It has two graduated brass arms, pivoted about a central spindle, which may be clamped to any desired angular separation and rotated together. Glass magnifiers are attached to both arms. A small dial on the top of the central knob can be moved to record rotations of more than one full circle.
There are four unlabeled circles on the calculating rule, here called a, b, c, and d. They go from the outer rim inward. Circle b is divided into 20 equal parts. Subdivisions of these parts are represented by a series of parallel curves extending between the outer rim and circle b. These, in combination with scales marked on the rim of the arms, allow one to measure subdivisions of the distance between equal parts. The outermost circle (a) is a logarithmic scale ranging from 1 to 10 twice. A series of lines between the two outer circles give intermediate values, which are read from the rotating arms. The circle c, just inside b, is divided from 0 to 90 degrees so that the sine of an angle indicated is given on the outer circle a. The parts of the scale are unequal, with the tens value of degrees from 10 to 49 indicated by large digits. The innermost circle d is divided for finding cosines.
Nystrom promoted the device and solicited a manufacturer in the May 17, 1851, issue of Scientific American. By 1852, he offered the device at three price points, $10.00, $15.00, and $20.00. He was likely making the instrument himself. From 1864 to 1887, the Philadelphia firm established by William J. Young sold Nystrom calculators that were probably handcrafted by George Thorsted. It is unlikely that more than one hundred of these devices ever existed.
References: J. W. Nystrom, "Calculating-Machine" (U.S. Patent 7,961 issued March 4, 1851); Description and Key to Nystrom's Calculator (Philadelphia, 1854), http://history-computer.com/Library/Nystrom's%20Calculator.pdf; "Nystrom's New Calculating Machine," Scientific American 6, no. 35 (May 17, 1851): 273; "Nystrom's Calculating Machine," Scientific American 7, no. 36 (May 22, 1852): 284; John W. Nystrom, Pocket-Book of Mechanics and Engineering, 10th ed. (Philadelphia, 1867); Robert C. Miller, "Nystrom's Calculator," Journal of the Oughtred Society 4, no. 2 (1995): 7–13; Peggy A. Kidwell, "Nystrom's Calculating Rule," Rittenhouse 1 (1987): 102–105.
Location
Currently not on view
date made
before 1851
patentee
Nystrom, John William
maker
Nystrom, John William
ID Number
MA.252682
catalog number
252682
accession number
49064

Fowler's Long Scale Calculator Circular Slide Rule

In the late 19th and early 20th centuries, several circular slide rules were made to resemble pocket watches. Fowler & Co., of Manchester, England, was a particularly notable manufacturer of this type of slide rule.
Description
In the late 19th and early 20th centuries, several circular slide rules were made to resemble pocket watches. Fowler & Co., of Manchester, England, was a particularly notable manufacturer of this type of slide rule. The company was in business from 1898 to 1988 and made a large variety of calculators, although the labor-intensive nature of its manufacturing process produced expensive instruments that never sold in large numbers.
This example is the "long scale" model, consisting of a metal case with a ring, two knobs, and two rotating paper discs covered with glass. The front has a short logarithmic scale and a long logarithmic scale, laid out in six concentric circles rather than in a spiral. These scales are rotated by the knob on the left. The glass is marked with two hairlines. The interior of the disc reads: FOWLER'S (/) LONG SCALE CALCULATOR (/) PATENT (/) FOWLER & Co MANCHESTER.
The other knob rotates the seven scales on the back of the instrument: multiplication and division, reciprocals, logarithms, square roots, logarithmic sines, logarithmic tangents, and a second scale for logarithmic sines. The interior is marked: FOWLER'S (/) CALCULATOR (/) PATENT (/) FOWLER & Co MANCHESTER. There is one hairline indicator on the glass. The slide rule is with a tarnished square metal case, lined with purple velvet. The outside of the case is engraved: Fowler's (/) CALCULATOR. The inside is stamped: Fowler & Co. (/) CALCULATOR (/) SPECIALISTS (/) Manchester (/) ENGLAND.
William Henry Fowler (1853–1932) and his son, Harold Fowler, took out several British patents for improvements to circular calculators between 1910 and 1924. The first Fowler calculator with two knobs on the rim was patented in 1914. In 1927, Fowler & Co. introduced the Magnum Long Scale Calculator, which extended the scale length to 50 inches. Thus, this example is dated between 1914 and 1927.
Charles Looney (1906–1987), the donor of this slide rule, catalogued engineering drawings and trade literature at the Smithsonian after he retired from the University of Maryland–College Park, where he served as chair of the Department of Civil Engineering. He also donated his library of books and pamphlets to the Museum.
References: Peter M. Hopp, "Pocket-Watch Slide Rules," Journal of the Oughtred Society 8, no. 2 (1999): 45–51; Richard Blankenhorn and Robert De Cesaris, "The Fowler Calculators: A Catalogue Raisonné," Journal of the Oughtred Society 11, no. 2 (2002): 3–11; Museum of History and Science in Manchester, "Fowler & Co.," http://www.mosi.org.uk/media/33870536/fowlerandco.pdf; accession file.
Location
Currently not on view
date made
1914-1927
maker
Fowler & Co.
ID Number
MA.333849
catalog number
333849
accession number
303780

Sexton's Omnimetre Circular Slide Rule

This paper circular rule consists of two paper discs, a celluloid indicator, and a metal screw that holds everything together.
Description
This paper circular rule consists of two paper discs, a celluloid indicator, and a metal screw that holds everything together. Going out from the center of the rotating discs, there are scales of versed sines [3 yellow circles labeled from 3 to 80 degrees—the versed sine of an angle x is (1 - sin x)], the fifth power of N (5 white circles labeled from 1 to 9.5), tangents (3 yellow circles labeled from 5 degrees through 84 degrees), N cubed (three white circles labeled from 1 through 9.5), sines (two circles labeled from 6 to 84 degrees), N squared (two circles labeled from 1 to 95), secants (one yellow circle labeled from 10 degrees to 84 degrees), and a logarithmic B scale running from 1 to 10. On the base disc is a logarithmic A scale, running from 1 to 10, and an equally divided scale for finding logarithms that runs from 0 to 10. THoles in the base make it easier to rotate the disc.
The base disc is marked around the edge: SEXTON'S OMNIMETRE; COPYRIGHT IN THE UNITED STATES 1896. ENTERED AT STATIONERS HALL LONDON FOR INTERNATIONAL COPYRIGHT 1896; NUMERI MUNDUM REGUNT; ENTERED ACCORDING TO ACT OF THE PARLIAMENT OF CANADA IN THE YEAR 1896 BY THADDEUS NORRIS, ENLARGED AND REVISED EDITION. The smaller disc is marked near the center: ALL RIGHTS RESERVED (/) PATENT 1895 U.S. CANADA & EUROPE. The back of the instrument is engraved: THEO. ALTENEDER & SONS (/) PHILADELPHIA. DANKERS is handwritten near the center of the back.
Albert Sexton was a resident of Philadelphia who, according to his own account, read a lecture delivered by Colman Sellers at the Franklin Institute on 20 May 1891. Although the subject of the lecture was the utilization of the power of Niagara Falls, Sellers also mentioned the advantages of the slide rule. Intrigued by these comments, Sexton began to acquire slide rules. He concluded that a less expensive, more complete instrument was needed, and he designed one. When he provided samples to gentlemen visiting a local steam engine manufacturer, Southwark Foundry and Machine Company, he found they were most interested. Arthur Marichal, a Belgian civil engineer, wrote on his sample “Sexton’s Omnimetre” and added the Latin phrase “Numeri Mundum Regunt.” Sexton adopted both the name and the motto.
With the assistance of Philadelphia resident Thaddeus Norris, Sexton introduced several versions of his instrument, including the most complete form, which is represented by this object. Sexton (and Norris posthumously) received the John Scott Medal of the Franklin Institute on 4 January 1899. The instrument was manufactured by the Philadelphia firm of Theodore Alteneder & Sons. The different forms sold for $1.00 to $3.00 around 1900, and this version sold for $4.00 by 1940.
The donor acquired this example in 1938, when he joined the U.S. Navy’s Preliminary Ship Design Branch. He used it in the design of ships from PT boats to aircraft carriers, until his retirement in 1968.
References: Peggy A. Kidwell, "Computing Devices, Mathematics Education and Mathematics: Sexton's Omnimetre in Its Time," Historia Mathematica 36 (2009): 395–404; Thaddeus Norris, "Marker for Slide-Rules" (U.S. Patent 540,184 issued May 28, 1895).
Location
Currently not on view
date made
1938
maker
Theodore Alteneder and Sons
ID Number
2008.3041.01
nonaccession number
2008.3041
catalog number
2008.3041.01

Gilson Midget Circular Slide Rule

This two-sided circular slide rule is a white plastic disc with two transparent, pivoting green plastic arms on one side and a third arm on the back.
Description
This two-sided circular slide rule is a white plastic disc with two transparent, pivoting green plastic arms on one side and a third arm on the back. On the front, from the edge to the center, there is a C scale, CI scale, a scale of logarithms, a scale of squares, a "binary" scale, a log-log scale, a scale for the decimal equivalent of fractions, a scale of drill sizes, and a scale of thread sizes. The rule is marked: MADE IN U.S.A. (/) Copyrighted 1936 (/) Patented.
Three concentric circles forming a scale of degrees, sines, and tangents are on the back. Inside this scale is a scale of decimal equivalents for fractions. The back of the instrument is marked: COPYRIGHTED (/) 1931.
The rule has a green synthetic leather case. On the inside of the flap, it is marked in ink: Donald Mela, and stamped in red: Gordon's (/) DRAFTING MATERIALS (/) 162 W. Madison St. Chicago. The instrument was received with a small paper manual, 1998.0119.03. See also 1989.0032.01.
Claire A. Gilson founded the Gilson Slide Rule Company in Niles, Mich., in 1915. The firm moved to Stuart, Fla., in 1927 and remained in business until about 1975. This example of the firm's Midget model was probably manufactured around 1940.
References: Henry Aldinger and Ed Chamberlain, "Gilson Slide Rules," Journal of the Oughtred Society 9, no. 1 (2000): 48–60 and 9, no. 2 (2000): 47–58; Bobby Feazel, "[Letters of] Richard A. Gilson," Journal of the Oughtred Society 2, no. 2 (1993): 8–12; Ross Grable, "Analysis of a Gilson Circular Rule," Journal of the Oughtred Society 7, no. 1 (1998): 53–55; International Slide Rule Museum, "Time Line for Gilson Slide Rule Company," http://sliderulemuseum.com/SR_Dates.htm#Gilson.
Location
Currently not on view
date made
ca 1940
maker
Gilson Slide Rule Company
ID Number
1998.0119.01
catalog number
1998.0119.01
accession number
1998.0119

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