Rectangular Protractor Sold by McAllister & Co.

This ivory rectangular protractor is three times larger in area than many surviving ivory rectangular protractors from the nineteenth century, which tend to be short and narrow enough to fit in a pocket. (See MA*335349, MA*321754, and MA*321014.) Catalogs of the time period advertise foot-long rectangular protractors comparable to this one, but at approximately $12 each, they were 3 to 8 times as expensive as 6-inch versions. Thus, surveyors probably did not purchase and use the large protractors as often.
This protractor is graduated to half-degrees and marked by tens from 10 to 170 in both the clockwise and counterclockwise directions. The interior of the protractor contains a maker's mark: LONDON MADE. FOR MCALLISTER & CO. PHILADELPHIA. The front of the protractor also contains a diagonal scale; a scale of chords which is divided by half-degrees and marked by tens from 10 to 90; and scales for dividing 1 inch into 10, 20, and 30 parts. These scales were used to create drawings in which 1 inch represented 1, 2, and 3 feet, respectively.
A chain scale is on the bottom edge of the protractor, facing outwards (i.e., appearing upside-down as one looks at the front of the protractor). The scale is graduated to half-units and marked by ones from 1 to 44 and from 44 to 1. The numbers from 44 to 1 are called an "offset." Ten units on the scale total 1/4" in length. A surveyor's chain was 66 feet long and contained 100 links. Thus, this chain scale represented 4 links to each inch. The number 40 (described as a "line of 40" or a "scale of 40" in trade catalogs) is marked at the midpoint of the protractor, in between the chain scale and the scale dividing 1 inch into 30 parts. The markings are worn off the protractor in a few places.
The back of the protractor bears scales for dividing the inch into 80, 60, 55, 50, 45, 40, 35, and 30 parts. There are also scales for 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8, and 1 inch to the foot. The protractor is stored in a black and red leather and cardboard case that is badly worn.
William Young McAllister (1812–1896) was a third-generation optician and dealer of mathematical instruments in Philadelphia. His firm was known as McAllister & Co. between 1836 and 1853. From 1830 to 1836, he partnered with his father, John McAllister Jr., and between 1853 and 1865 he partnered with his brother, Thomas, who subsequently worked as an optician in New York City. This protractor is slightly different from the 12-inch ivory protractor described in McAllister's 1867 catalog: this object is 1/4" wider; there are eleven scales of equal parts instead of ten; there are eight scales of feet and inches instead of twelve; there is one scale of chords instead of two; and there is a chain scale. John C. Armstrong of Washington, D.C., donated the protractor to the Smithsonian in 1933.
References: William Ford Stanley, Mathematical Drawing and Measuring Instruments 6th ed. (London: E. & F. N. Spon, 1888), 227–230; Catalogue of Keuffel & Esser, 33rd ed. (New York, 1909), 176; "McAllister Family Business Timeline," The John A. McAllister Collection, Library Company of Philadelphia,; A Priced and Illustrated Catalogue of Mathematical Instruments . . . Sold Wholesale and Retail by William Y. McAllister (Philadelphia, 1867), 25; Peggy A. Kidwell, "James Prentice's Rectangular Protractor," Rittenhouse 1, no. 3 (1987): 61–63.
Currently not on view
Object Name
date made
McAllister, William Young
Physical Description
paper (overall material)
ivory (overall material)
leather (overall material)
overall: .3 cm x 30.5 cm x 27.5 cm; 1/8 in x 12 in x 10 13/16 in
place made
United Kingdom: England, London
Associated Place
United States: Pennsylvania, Philadelphia
ID Number
accession number
catalog number
Drafting, Engineering
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Data Source
National Museum of American History, Kenneth E. Behring Center


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