Surveying

Since the first protractors appeared near the turn of the 17th century, around the same time that the technique of triangulation was developed for surveying, their utility for this activity appeared evident from early on. Surveyors typically carried at least one protractor in their field kits. The instrument might be combined with another drawing instrument, such as a set of parallel rules. By the 19th century, makers tried to blend convenience with multi-functionality, offering rectangular protractors that fit easily in a case or pocket and that were packed with aids for reducing real-world distances to proportional scales. They also showed off their improving craftsmanship with fine objects that retained accuracy in measurement. (See also the page on Engineering & Drafting.)

This brass semicircular protractor is divided by single degrees and marked by fives from 5° to 180°. The letter X is at the 90-degree mark. The upper right side of the protractor contains a shadow square.
Description
This brass semicircular protractor is divided by single degrees and marked by fives from 5° to 180°. The letter X is at the 90-degree mark. The upper right side of the protractor contains a shadow square. This is divided on both sides into sets of four units, each approximately 3/8" long and numbered from 1 to 12, for a total of 48 units on each side. The vertical side is marked: OMBRA VERSA. The horizontal side is marked (upside down): OMBRA RETTA.
The scale on the "ombra versa" side measured tangents from 0 to 45°. The scale on the "ombra retta" (or "recta") side measured tangents from 45° to 90°. The lines for degrees and on the shadow square appear to be made by hand, perhaps by placing the instrument next to a pattern. The instrument is decorated with floral and solar motifs. The protractor rests in a brass base that unfolds to form a limb, which is chipped. There are two holes in the limb; the numbers 2 and 1 are scratched next to the holes. There are four holes in the base; the numbers 3 and 1 are scratched next to the outermost holes, which align with the holes on the limb. This instrument is Italian in origin and was likely made before 1800. New York University donated the object in 1963.
Reference: J. A. Bennett, The Divided Circle (Oxford, 1987), 42–43.
Location
Currently not on view
date made
18th century
ID Number
MA.326978
catalog number
326978
accession number
1990.0646
This brass semicircular protractor is graduated by single degrees and marked by tens, from left to right and from right to left, from 10° to 180°.
Description
This brass semicircular protractor is graduated by single degrees and marked by tens, from left to right and from right to left, from 10° to 180°. The degree lines are probably stamped rather than engraved by hand and thus represent a notable increase in workmanship over MA.326978 and MA.316861. Higher levels of accuracy were not reached until machine division was achieved by instrument makers such as Jesse Ramsden, who worked approximately fifty years after this protractor was manufactured.
The inner edge of the base of the protractor is slanted, and there is a notch at the origin point. The base carries a maker's mark: Delure À Paris. The protractor is very similar to one depicted in the famous manual on mathematical instruments by Jean-Baptiste Delure's son-in-law, Nicolas Bion. The protractor dates to about 1720. It was purchased in 1959 from the estate of Henry Russell Wray via an auction conducted by Maggs Bros. Ltd. of London.
References:
Nicolas Bion, Traité de la construction et des principaux usages des instruments de mathematique (Paris, 1709), 25–27.
Peggy Aldrich Kidwell, Amy Ackerberg-Hastings, and David Lindsay Roberts, Tools of American Mathematics Teaching, 1800–2000 (Baltimore: Johns Hopkins University Press, 2008), 166–168.
Maya Hambly, Drawing Instruments: 1580–1980 (London: Sotheby's Publications, 1988), 120–121.
Jean-Dominique Augarde, "La fabrication des instruments scientifiques du XVIIIe siècle et la corporation des fondeurs," in Christine Blondel et al., eds., Studies in the History of Scientific Instruments (London, 1989), 62–63.
Reference:
Sotheby & Company, Catalogue of a Collection of Scientific Instruments, the Property of the Late Henry Russel Wray, London, 1959 (a copy of the catalogue is in the accession file).
Location
Currently not on view
date made
ca 1720
maker
Delure, Jean-Baptiste-Nicolas
ID Number
MA.316930
accession number
228694
catalog number
316930
This brass parallel rule has a semicircular protractor attached to the top blade. The protractor is divided to degrees and marked by tens from 10 to 90 to 10.
Description
This brass parallel rule has a semicircular protractor attached to the top blade. The protractor is divided to degrees and marked by tens from 10 to 90 to 10. A movable arm attached to the origin point of the protractor contains a vernier, which was intended to permit the measurement of angles to 5 minutes of accuracy. The hinges connecting the blades of the rule are straight. There is no maker’s mark.
Mathematician James McKenna gave this measuring instrument to the Smithsonian. He reported that an ancestor used it at Bedford, Pa., before 1800. A name, scratched on one of the tools in the set of drawing instruments (310891) that accompanied this protractor, suggests that the ancestor was John A. Stuart, who surveyed a line in Bedford County on Wills Mountain that continues to bear his name.
Compare this instrument to 1978.2110.06.
Reference: Peggy A. Kidwell, "American Parallel Rules: Invention on the Fringes of Industry," Rittenhouse 10, no. 39 (1996): 90–96.
Location
Currently not on view
date made
late 18th century
ID Number
MA.310890
catalog number
310890
accession number
131549
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.
Description
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, http://www.librarycompany.org/mcallister/pdf/McAllister%20family%20business%20timeline.pdf; 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.
Location
Currently not on view
date made
1836-1853
maker
McAllister, William Young
ID Number
MA.310743
accession number
127352
catalog number
310743
This brass circular protractor was manufactured in the mid-19th century and made available for sale by the New York City firm headed by Benjamin Pike (1777–1863).
Description
This brass circular protractor was manufactured in the mid-19th century and made available for sale by the New York City firm headed by Benjamin Pike (1777–1863). Pike, a dealer of optical, mathematical, and philosophical instruments whose firm serviced the entire United States, partnered at various times with his sons, Benjamin Jr., Daniel, and Gardner. The business was called “Benjamin Pike & Son,” as is marked on the vernier limb of this protractor, between 1831 and 1841 and between 1843 and 1850.
This protractor likely would have been of interest to surveyors and engineers. The object is divided by single degrees. It bears two sets of markings by tens in the clockwise direction: from 0° to 90° to 0° to 90° to 0°, and from 10° to 360°. Brass arms extend into the center to divide the protractor into quadrants. The arms are not placed at the 0° and 90° points, as one might expect, but rather at the 50/50, 40/140, 50/230, and 40/320 markings. There are rounded, beveled notches at the 90/90 and 90/270 markings. A round hole (5/8" diameter) is at the center. Crosshairs would typically have been placed in this hole to mark the origin point for measuring angles, but no crosshairs are present. Instead, a brass piece fills about one-third of the hole.
An arm pivoted from the center carries a vernier, which allows the user to read off angles to 10 minutes of arc. The vernier is marked by 30s from 60 to 0 to 60. The vernier arm is marked: Benj-n Pike & Son New York. The arm extends beyond the vernier. A brass strip, fastened on top of the arm, contains a sharp metal pin that pokes through a hole near the end of the arm. The pin was used to prick, or mark, angle points.
This protractor has some notable differences from the circular protractor depicted in Pike catalogs of 1848 and 1856: its outer edge is smooth instead of appearing to bear gear teeth; it has one vernier arm instead of two; and it has two sets of markings instead of one.
References: Deborah J. Warner, “Browse by Maker: Pike,” National Museum of American History Physical Sciences Collection: Surveying and Geodesy, http://americanhistory.si.edu/collections/surveying/maker.cfm?makerid=22; Benjamin Pike Jr., Pike’s Illustrated Descriptive Catalogue of Optical, Mathematical, and Philosophical Instruments (New York, 1848), 43–45; Benjamin Pike Jr., Pike’s Illustrated Descriptive Catalogue of Optical, Mathematical, and Philosophical Instruments (New York, 1856), 43–45; facsimile with historical introduction by Deborah J. Warner (Dracut, Mass., and San Francisco, 1984).
Location
Currently not on view
date made
1831-1850
maker
Pike, Jr., Benjamin
ID Number
MA.304826.059
accession number
304826
catalog number
304826.059
Protractors, devices for measuring and drawing angles, were used in professional practice as well as by schoolchildren. The instruments manufactured for surveyors, draftsmen, and the like could be of quite high quality.
Description
Protractors, devices for measuring and drawing angles, were used in professional practice as well as by schoolchildren. The instruments manufactured for surveyors, draftsmen, and the like could be of quite high quality. This circular protractor is one of at least three in the Smithsonian collections that were produced by Kern & Co. of Aarau, Switzerland. Made of German silver, an alloy of 60% copper, 20% nickel, and 20% zinc, it is graduated along the outer edge to one-quarter degree and marked by tens from 0 to 350 in both the clockwise and counter-clockwise directions.
A center cross-plate, which instrument dealers called a "horncentre," contains crosshairs to assist with placing the protractor on a drawing. A movable arm attached to the center contains a vernier scale that allows the user to read angles to one minute of arc. The arm also has a blade-like extension of 3 inches. There are indentions on the interior of the protractor at 0, 90/270, 180, and 270/90 degrees.
Across its diameter, the protractor is engraved: U.S.G.S. No. 8. Stamped on the back of the vernier arm is the number 88. The protractor was purchased by the U.S. Geological Survey between 1879 and 1907, when it was transferred to the Smithsonian. According to the accession record, it was already "badly tarnished" in 1907. Protractors of this style were manufactured by Kern at least as early as 1867. In 1878 and 1881, respectively, the Troy, N.Y., factory of W. & L. E. Gurley, and New York dealer William Y. McAllister sold Kern circular protractors of this size (10" diameter) for $20.00.
See also ID numbers 1977.0460.02 and 1978.2291.01.
References: William Y. McAllister, A Priced and Illustrated Catalogue of Mathematical Instruments . . . Particular Attention is Called to the Swiss Drawing Instruments (Philadelphia, 1867), 23; W. & L. E. Gurley, A Manual of the Principal Instruments Used in American Engineering and Surveying (Troy, N.Y., 1878), 166; William Y. McAllister, A Priced and Illustrated Catalogue of Mathematical Instruments (Philadelphia, 1881), 35.
Location
Currently not on view
date made
1879-1907
maker
Kern & Co.
ID Number
MA.247966
accession number
47736
catalog number
247966
This steel semicircular protractor is divided by half-degrees and is marked by tens from 360 to 180 and from 180 to 0, both in the counterclockwise direction. A 3/8" line is engraved at the origin point. On its left side, the protractor slides along a steel bar or straight edge.
Description
This steel semicircular protractor is divided by half-degrees and is marked by tens from 360 to 180 and from 180 to 0, both in the counterclockwise direction. A 3/8" line is engraved at the origin point. On its left side, the protractor slides along a steel bar or straight edge. Two thumbscrews at the top of the protractor hold in place a removable scale, which is divided into units of four and marked by 40s from 0 to 720. Forty units correspond to approximately one centimeter. The bottom of each screw is marked "2." The scale moves approximately 60 units to the left or right by turning a third screw against a serrated edge on the scale.
An additional scale accompanies the object. This scale is divided by fifties and marked by thousands from 0 to 12,000. Ten units correspond to approximately 1.5 centimeters. The protractor was originally stored in a mahogany case, apparently discarded by 1959. The protractor was purchased by the U.S. Geological Survey between 1879 and 1907.
See also ID number MA.247968.
Location
Currently not on view
date made
1879-1907
maker
W. & L. E. Gurley
Gurley, Lewis E.
Gurley, William
ID Number
MA.247967
accession number
47736
catalog number
247967
According to the accession record, this "special protractor and scale" is attributed to the factory operated by William and Lewis Ephraim Gurley in Troy, N.Y.
Description
According to the accession record, this "special protractor and scale" is attributed to the factory operated by William and Lewis Ephraim Gurley in Troy, N.Y. No examples of this protractor could be identified in Gurley catalogs, although the "special" may refer to a special order placed by the U.S. Geological Survey, which in 1907 declared this instrument "obsolete" and transferred it to the Smithsonian.
This semicircular steel protractor within a rectangular frame is exactly like ID number MA.247967, except that there is no second scale to replace the sliding scale screwed to the top of the protractor. The number 1 is marked on the bottom of each of these two screws. This instrument also retains the bottom half of its original mahogany case, which is lined with blue velvet and bears two brass hooks for latching the case. The protractor is disassembled from the straight edge on which it slides so that both pieces fit in the case.
Reference: Deborah J. Warner, "Browse by Maker: Gurley," National Museum of American History Physical Sciences Collection: Surveying and Geodesy, http://americanhistory.si.edu/collections/surveying/maker.cfm?makerid=14.
Location
Currently not on view
date made
1879-1907
maker
W. & L. E. Gurley
Gurley, Lewis E.
Gurley, William
ID Number
MA.247968
accession number
47736
catalog number
247968
This circular German silver protractor is divided to quarter-degrees and marked by tens from 0° to 350° in the clockwise direction and from 10° to 360° in the counterclockwise direction. The inner edge has indentations at the 0/360, 90/270, 180/180, and 270/90 degree points.
Description
This circular German silver protractor is divided to quarter-degrees and marked by tens from 0° to 350° in the clockwise direction and from 10° to 360° in the counterclockwise direction. The inner edge has indentations at the 0/360, 90/270, 180/180, and 270/90 degree points. A transparent horn center allows positioning on an engineering drawing. A vernier, which may be adjusted with a micrometer screw, permits readings to one minute of accuracy. A clamp screw is adjacent to the micrometer screw. A magnifying glass that may be raised and rotated is screwed to the vernier arm near the center of the protractor. A 6-inch blade extends from the vernier.
Although there is no maker's mark, the protractor is similar to a Gem Union protractor marketed by Dietzgen of Chicago and Stieren of Pittsburgh for $23.50 in the early 20th century. Gem Union was a Dietzgen brand and represented the highest grade of drawing instruments manufactured or sold by Dietzgen. By 1911, every Gem Union instrument was stamped with the Dietzgen monogram. There is no such stamp on this protractor, so it likely either was manufactured earlier or was a copy.
This protractor was apparently used by employees of the Calumet & Hecla Mining Company, which operated highly profitable copper mines in northern Michigan in the late 19th and early 20th centuries. Universal Oil Products (UOP, Inc.; now a division of Honeywell) purchased the company in 1968, while its productivity was declining. The mines closed in 1970, and UOP donated at least three dozen objects, including this one, to the Smithsonian in 1982.
References: Catalogue & Price List of Eugene Dietzgen Co., 7th ed. (Chicago, 1904), 45–49, 191; Catalogue & Price List of Eugene Dietzgen Co., 8th ed. (Chicago, 1907), 47–51, 214; Catalogue & Price List of Eugene Dietzgen Co., 9th ed. (Chicago, 1910), 63–67, 244; Catalogue & Price List of Eugene Dietzgen Co., 12th ed. (Chicago, 1926), 56–57, 204; The Wm. E. Stieren Co., Catalogue and Price List (Pittsburgh, n.d.), 209.
Location
Currently not on view
date made
ca 1900
maker
Eugene Dietzgen Company
ID Number
1986.0662.01
accession number
1986.0662
catalog number
1986.0662.01

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