Gurley Cox's Stadia Computer Circular Slide Rule

Some slide rules reveal transformations in materials. A later version of this paper circular slide rule was made from celluloid (1987.0221.02). Both were designed to reduce data obtained with a surveyor's transit.
On the base, just outside the disc, is a logarithmic scale for readings of a stadia rod used with a transit telescope, in feet. The edge of the disc has two scales involving functions of angles. One scale allows for multiplying the stadia reading by 1/2 sin 2 A, where A is the vertical angle of the transit telescope. This multiplication gives the difference in elevation of the transit and the stadia rod, in feet. The second scale represents multiplying the stadia reading by the square of the cosine of A, to find the horizontal distance of the rod in feet. The instrument bears a copyright date of 1899. Compare this instrument to Webb’s stadia rule (MA*333636) as well as to 1977.1141.41 and 2001.0282.01.
The slide rule has a cloth-covered cardboard cover. Pasted on the inside of the cover is an image of the Light Mountain Transit sold by W. & L. E. Gurley of Troy, N.Y., from 1897 to 1908. The image of the transit in the 1910 Gurley catalog is different, but it is not the same as the image on rule 1987.0221.02. Cox’s stadia computer is not mentioned in any of these catalogs; the device was probably given away as a promotional item.
In 1904, W. M. Beaman, a topographer in the U.S. Geological Survey, devised the “Beaman stadia arc,” a transit attachment that obviated the need for separate computing rules. Beaman obtained a patent for his instrument in 1906, and it was offered in Gurley catalogs from at least 1908.
References: W. & L. E. Gurley, A Manual of the Principal Instruments Used in American Engineering and Surveying, 42nd ed. (Troy, N.Y., 1908), 62–63; Florian Cajori, "A Stadia Slide-Rule," Engineering News 43 (April 5, 1900): 232; Richard Smith Hughes, "Stadia or Tacheometric Slide Rules, Part II," Journal of the Oughtred Society 16, no. 2 (2007): 32–41.
Currently not on view
Object Name
slide rule
date made
after 1899
W. & L. E. Gurley
Physical Description
paper (overall material)
cloth (case material)
overall: .6 cm x 16.8 cm x 16.5 cm; 1/4 in x 6 5/8 in x 6 1/2 in
place made
United States: New York, Troy
ID Number
accession number
catalog number
Rule, Calculating
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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