MHR1 Höhenrechenschieber Cylindrical Slide Rule

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,",%20v2%20(WEB).pdf.
Currently not on view
Object Name
calculating rule
slide rule
date made
ca 1940
Dennert and Pape
Physical Description
metal (overall material)
paper (part material)
plastic (part material)
cloth (part material)
overall: 28.5 cm x 7.5 cm x 7.5 cm; 11 7/32 in x 2 15/16 in x 2 15/16 in
place made
ID Number
accession number
catalog number
Rule, Calculating
Naval History
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Slide Rules
Data Source
National Museum of American History, Kenneth E. Behring Center


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