Slide RulesCylindrical Slide Rules
Writing a logarithmic scale in a spiral that is then imprinted around the outside of a cylinder allows instrument makers to lengthen the scale. Since a logarithmic scale only needs to run to 10 twice to include all possible results from adding or subtracting two logarithmic numbers, this means that the distance between the points on the scale may be increased. When any two numbers on the scale are further apart, the user may read a fractional position between these numbers (expressed as a decimal) to a finer level of granularity. For example, on a 10" linear slide rule, results generally may be calculated to only three significant figures (0.123, 1.23, 12.3, 123, 1230, and so on). A cylindrical slide rule may provide results of up to seven significant digits (0.1234567, 1.234567, 12.34567, 123.4567, 1234.567, and so on).
On the other hand, cylindrical slide rules were typically about twice as expensive to produce as linear slide rules, and the provenances for the objects on this page indeed suggest that, in the main, only corporate and government offices could afford them. A number of the objects in this category were received with instruction manuals and advertising pamphlets, which may be viewed in the Index by Makers & Retailers. The collection includes multiple examples for several of the objects, as the 23 items below represent only eight different slide rules, half developed in Europe and half invented by Americans. The cylindrical slide rule by Edwin Thacher, a Pennsylvania railroad bridge designer, also illustrates the 19th-century shift in production from Europe to the United States, as originally William Ford Stanley's London firm made the entire instrument. Then, Keuffel and Esser of New York City began constructing the wooden drum and brass and wood stand while continuing to import the scales printed on paper and pasted around the drum. Finally, K&E developed its own dividing engine for printing the scales and henceforth manufactured the entire instrument in the United States.
"Slide Rules - Cylindrical Slide Rules" showing 1 items.
- This cylindrical calculating rule was designed to solve problems in spherical trigonometry encountered in navigation. For example, it could be used to compute the altitude and azimuth of a celestial body, knowing the latitude of the observer and the hour angle and declination of the body. Such a slide rule was patented by the Englishman Leonard C. Bygrave in 1921. This example, serial number 90143, was manufactured in Germany by Dennert and Pape at about the time of World War II.
- The instrument consists of three concentric cylinders. The innermost cylinder can be extended, and the outermost cylinder then slides up and down on part of the extended tube. Tightening a knob at the top fixes the relative position of the two inner cylinders. The innermost cylinder has a helical scale divided from 0 to 90 degrees (also from 180 down to 90). The middle cylinder has a helical scale marked from 0 to 90 and also from 145 to 90. At the bottom, the middle cylinder has instructions for using the instrument. The outermost cylinder has two marks for reading results, declination tables, formulas, and a window that allows for reading the second scale. The instrument fits in a cylindrical metal case painted black and lined with cloth near the top.
- This object was found in the Naval History collections of the National Museum of American History some time before August 1984.
- References: U.S. Hydrographic Office, American Practical Navigator (Washington, D.C., 1958), 559; L. C. Bygrave, "Improvements in Calculating Apparatus," (U.K. Patent 162,895 issued May 12, 1921); Serge Savoysky, "Calcul de navigation: État courant de l'étude de l'hélice logarithmique MHR1 de Dennert et Pape," http://serge.savoysky.pagesperso-orange.fr/Calcul%20de%20navigation,%20v2%20(WEB).pdf.
- Currently not on view
- date made
- ca 1940
- Dennert and Pape
- ID Number
- accession number
- catalog number
- Data Source
- National Museum of American History, Kenneth E. Behring Center