Complete Mathematical Chart Designed by C. W. Goodchild

This object consists of paper laminated to both sides of two wooden boards that are held together by two brass hinges and fastened with a brass hook. The front gives instructions for using the 100-line logarithmic table that appears on the inside two pages. To multiply, the user looked up the first multiplicand, noted the number of the line on which the multiplicand appeared, and measured the distance from the left of the line to the multiplicand. Then, the user repeated the process with the second multiplicand. The product appeared on the sum of the line numbers at the sum of the distances. (For instance, the number 4 is on line 60 and the number 2 is on line 30, so the number 8 is on line 90.)
The table could also be used for division, calculations of interest, finding logarithms, and finding the numbers when the logarithm is known. A diagonal scale at the bottom of page three allowed for interpolation of values. A card or ruler was necessary for recording the distances. The back of the object has a 31-line chart of trigonometrical ratios for finding logarithmic sines and cosines. The bottom of the back is marked: Copyrighted September, 1893, by C. W. GOODCHILD.
Cecil Wray Goodchild (1847–1900) was born in England but lived in central California by 1880. By 1893, he was a civil engineer and attorney in San Luis Obispo. He designed this chart to meet the needs of those surveyors, engineers, and accountants who required greater accuracy in their work than that provided by an ordinary slide rule, but who did not wish to purchase an expensive instrument such as the Thacher cylindrical slide rule.
In 1903 and 1906, Keuffel & Esser advertised his invention as the Goodchild Mathematical Chart, model 4019. It sold on paper for 75¢ and on a flat board for $2.75. For an additional $5.00, K&E offered a sliding triangular rule for recording and adding the line numbers and distances.
References: Library of Congress, Catalogue of Title-Entries of Books and Other Articles Entered . . . Under the Copyright Law, no. 116 (18–23 September 1893): 19; "A Slide Rule Fifty Feet Long," The Cornell Daily Sun 14, no. 83 (31 January 1894); Catalogue and Price List of Keuffel & Esser Co., 31st ed. (New York, 1903), 298; Catalogue and Price List of Keuffel & Esser Co., 32nd ed. (New York, 1906), 317.
Currently not on view
Object Name
scale rule
logarithmic chart
date made
Goodchild, C. W.
Physical Description
wood (overall material)
paper (overall material)
brass (overall material)
overall: 1.7 cm x 21.8 cm x 24.6 cm; 21/32 in x 8 19/32 in x 9 11/16 in
place made
United States: California, San Luis Obispo
ID Number
catalog number
accession number
Scale Rules
Science & Mathematics
Rule, Calculating
See more items in
Medicine and Science: Mathematics
Scale Rules
Data Source
National Museum of American History, Kenneth E. Behring Center
Credit Line
Gift of Keuffel & Esser Co.

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