Keuffel & Esser 4105 Webb's Stadia Cylindrical Slide Rule

This instrument consists of a wooden cylinder covered with paper scales, wooden handles at the ends of the cylinder, and a metal sleeve lined with felt. The sleeve, which is painted maroon, holds the cylinder. Running the length of the sleeve are a slot 1.5 cm wide and a paper scale.

The instrument is marked on the paper covering the cylinder: “WEBB’S STADIA SLIDE RULE”, (/) DESIGNED BY WALTER LORING WEBB, C. E. (/) MANUFACTURED BY KEUFFEL & ESSER CO., N.Y. It also is marked there: DIRECTIONS. SLIDE THE CYLINDER UNTIL ONE END OF THE CYLINDER IS SET AT THE DISTANCE MARK ON THE SCALE AND SO THAT THE GIVEN ANGLE OF ELEVATION ALSO COMES TO SOME PART OF THE SCALE. THE REQUIRED QUANTITY IS 1/10 (1/100 or 1/1000, AS SHOWN BY THE MARK ON CYLINDER) OF THE SCALE READING AT THAT ANGLE MARK.

The stadia slide rule was used in topographical surveying to determine the elevation and geographical position of points and objects. Initially, a chain and compass or transit had been used to determine geographical position, with a level employed to obtain relative elevations. Greater efficiency in these measurements was then found by using a plane-table.

In about 1864, the U.S. Lake Survey adopted a third system, first used in Italy about 1820. A stadia rod was placed at the point of interest and sighted through the telescope of a transit. The distance to this point was found by observing the portion of the graduated rod shown between certain cross-hairs of the telescope. To find the elevation of the point, one examined the vertical angle on the vertical circle of the transit when the telescope was aimed at a point on the stadia rod that was the same height off the ground as the telescope. A stadia slide rule was then used for data reduction.

Keuffel & Esser of New York introduced a 20-inch linear stadia slide rule in 1895. It sold under various model numbers (1749, 4101, N-4101) until 1952. In 1897, the firm introduced a 50-inch linear stadia slide rule designed by Branch H. Colby of St. Louis. Colby's stadia slide rule (model number 1749-3, later 4125) sold until 1903. Textbook authors such as John Butler Johnson endorsed the rule, but it was awkward to carry in the field.

Walter Loring Webb (1863–1941), a civil engineer who graduated from Cornell University and taught there and at the University of Pennsylvania, proposed a rule that had parallel scales arranged on a cylinder, reducing the length of the instrument to about 16 inches. K&E sold Webb's stadia slide rule for $5.00 from 1903 to 1923.

One end of the sleeve is painted: 1803. This may be an inventory number from the University of Missouri's Department of Civil Engineering, which donated the instrument in 1972. The university began teaching civil engineering in 1859, and its School of Engineering was renamed the College of Engineering in 1877.

See also 1983.0472.01. For circular stadia slide rules, see MA.336425, 1987.0221.01, and 2002.0282.01.

References: John Butler Johnson, The Theory and Practice of Surveying, 16th ed. (New York: John Wiley & Sons, 1908), 237ff; Walter Loring Webb, Railroad Construction: Theory and Practice, 7th ed. (New York: John Wiley & Sons, 1922), 22–23; Wayne E. Feely, "K & E Slide Rules," The Chronicle of the Early American Industries Association 49, no. 5 (1996): 50–52; Catalogue and Price List of Keuffel & Esser Co., 31st ed. (New York, 1903), 308; Mark C. Meade, "A History of the College of Engineering at the University of Missouri – Columbia," Archives of the University of Missouri, http://muarchives.missouri.edu/c-rg9-eng.html.

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