Skip to main content

Search

My Visit
Donate
Home Smithsonian Institution

Site Navigation

  • Visit
    • Museums and Zoo
    • Entry and Guidelines
    • Maps and Brochures
    • Dine and Shop
    • Accessibility
    • Visiting with Kids
    • Group Visits
      • Group Sales
  • What's On
    • Exhibitions
      • Current
      • Upcoming
      • Past
    • Online Events
    • All Events
    • IMAX & Planetarium
  • Explore
    • - Art & Design
    • - History & Culture
    • - Science & Nature
    • Collections
      • Open Access
    • Research Resources
      • Libraries
      • Archives
        • Smithsonian Institution Archives
        • Air and Space Museum
        • Anacostia Community Museum
        • American Art Museum
        • Archives of American Art
        • Archives of American Gardens
        • American History Museum
        • American Indian Museum
        • Asian Art Museum Archives
        • Eliot Elisofon Photographic Archives, African Art
        • Hirshhorn Archive
        • National Anthropological Archives
        • National Portrait Gallery
        • Ralph Rinzler Archives, Folklife
        • Libraries' Special Collections
    • Podcasts
    • Stories
  • Learn
    • For Caregivers
    • For Educators
      • Art & Design Resources
      • Science & Nature Resources
      • Social Studies & Civics Resources
      • Professional Development
      • Events for Educators
      • Field Trips
    • For Students
    • For Academics
    • For Lifelong Learners
  • Support Us
    • Become a Member
    • Renew Membership
    • Make a Gift
    • Volunteer
      • Smithsonian Call Center
      • Ambassador Program
      • Museum Information Desk
      • Docent Programs
      • Behind-the-Scenes
      • Digital Volunteers
      • Participatory Science
  • About
    • Our Organization
      • Board of Regents
        • Members
        • Committees
        • Reading Room
        • Bylaws, Policies and Procedures
        • Schedules and Agendas
        • Meeting Minutes
        • Actions
        • Webcasts
        • Contact
      • Museums and Zoo
      • Research Centers
      • Cultural Centers
      • Education Centers
      • General Counsel
        • Legal History
        • Internships
        • Records Requests
          • Reading Room
        • Tort Claim
        • Subpoenas & Testimonies
        • Events
      • Office of Human Resources
        • Employee Benefits
        • How to Apply
        • Job Opportunities
        • Job Seekers with Disabilities
        • Frequently Asked Questions
        • SI Civil Program
        • Contact Us
      • Office of Equal Opportunity
        • EEO Complaint Process
        • Individuals with Disabilities
        • Small Business Program
          • Doing Business with Us
          • Contracting Opportunities
          • Additional Resources
        • Special Emphasis Program
      • Sponsored Projects
        • Policies
          • Combating Trafficking in Persons
          • Animal Care and Use
          • Human Research
        • Reports
        • Internships
    • Our Leadership
    • Reports and Plans
      • Annual Reports
      • Metrics Dashboard
        • Dashboard Home
        • Virtual Smithsonian
        • Public Engagement
        • National Collections
        • Research
        • People & Operations
      • Strategic Plan
    • Newsdesk
      • News Releases
      • Media Contacts
      • Photos and Video
      • Media Kits
      • Fact Sheets
      • Visitor Stats
      • Secretary and Admin Bios
      • Filming Requests

Arm Protractor and Goniometer Invented by Samuel L. Penfield

National Museum of American History

Object Details

Central Scientific Company
inventor
Penfield, Samuel Lewis
Description
It may seem obvious that surveyors, navigators, and mathematics students would need to measure angles. These practitioners are not the only audiences for protractors, however, since angle measurement is necessary in a variety of other fields. Geologists examine the faces and edges of crystals and recreate the crystals' structures by drawing stereographic projections. In 1900, Samuel Lewis Penfield (1856–1906), a geology professor at Yale University who earned his Ph.B. from Yale in 1877, patented two forms of "contact-goniometer." (A goniometer measures plane angles.) These instruments, along with a stereographic protractor and beam compasses that Penfield patented in 1901, helped establish the technique of stereographic projections in crystallography. Penfield aimed to simplify the work involved in the technique and to produce an inexpensive instrument.
This semicircular paper protractor appears to be an example of the contact-goniometer awarded patent number 655,004 on July 31, 1900. It is printed on a white rectangular card. It is divided by half-angles and marked by tens in both directions (counterclockwise and clockwise) from 0° to 180°. A ruler, divided to millimeters and marked by ones from 0 cm to 14 cm, is printed along the top edge of the card. A diagonal scale and scales for dividing the inch into 10, 12, and 16 parts appear in the interior of the protractor. A celluloid arm is attached at the vertex of the protractor. Users were to set angles according to a horizontal line on the arm but then draw angles along the edge of the arm.
The lower left corner of the card reads: ARM PROTRACTOR AND GONIOMETER (/) Designed by S. L. Penfield. A mark at the lower right corner of the scales of equal parts affirms that the protractor is: ENGINE DIVIDED. The protractor is contained in a paper envelope, which also holds a sheet of instructions written by Penfield. The envelope is imprinted: ARM PROTRACTOR AND GONIOMETER. It is also stamped: Cenco 88210.
The Mineralogical Laboratory of Yale's Sheffield Scientific School offered early versions of this instrument. Central Scientific Company of Chicago (abbreviated Cenco) sold the Penfield arm protractor and goniometer in this form from as early as 1909 (as item 427) to as late as 1950 (as item 88210). In 1914, the instrument cost 67 cents. William C. Marshall (of Bridgeport Works and formerly at the Sheffield Scientific School at Yale) listed it as a required tool in Elementary Machine Drawing and Design (New York: McGraw-Hill, 1912), 8. Edward Salisbury Dana discussed Penfield's instrument in more detail in A Textbook of Mineralogy, With an Extended Treatise on Crystallography and Physical Mineralogy, 3rd ed. rev. William E. Ford (New York: John Wiley & Sons, 1922), 33–40.
References: Samuel Lewis Penfield, "Contact-Goniometer" (U.S. Patent 655,004 filed April 2, 1900), "Contact-Goniometer" (U.S. Patent 655,005 filed April 2, 1900), "Stereographic Protractor" (U.S. Patent 667,570 filed October 25, 1900), and "Beam-Compass" (U.S. Patent 673,687 filed December 31, 1900); S. L. Penfield, "The Stereographical Projection and its Possibilities, from a Graphical Standpoint," American Journal of Science 4th ser. 11 (1901): 1–24, 115–144; Central Scientific Company, Physical and Chemical Apparatus Catalogue M (May, 1914), 42; L. V. Pirsson, "Samuel Lewis Penfield," American Journal of Science, 4th ser. 22 (1906): 353–367; Horace L. Wells, "Samuel Lewis Penfield, 1856–1906," in Biographical Memoirs (Washington, D.C.: National Academy of Sciences, 1909), vi:119–146; Shellie Snell, "Central Scientific Company: A Brief History," Robert A. Paselk Scientific Instrument Museum, Humboldt State University, http://www.humboldt.edu/scimus/Manufac/Cenco/Cenco.htm.
Location
Currently not on view
Credit Line
Gift of Kenyon College Department of Physics
1909-1950
patent date
1900
ID Number
1982.0147.02
accession number
1982.0147
catalog number
1982.0147.02
Object Name
protractor
Physical Description
metal (overall material)
plastic (overall material)
paper (overall material)
Measurements
overall: .3 cm x 16.2 cm x 8.5 cm; 1/8 in x 6 3/8 in x 3 11/32 in
place made
United States: Illinois, Chicago
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Protractors
National Museum of American History
Subject
Mathematics
Protractor
Mineralogy
Crystallography
Record ID
nmah_904387
Metadata Usage (text)
CC0
GUID (Link to Original Record)
https://n2t.net/ark:/65665/ng49ca746a7-4bbd-704b-e053-15f76fa0b4fa

Related Content

  • Protractors

    American History Museum
Protractor - Penfield Arm Protractor and Goniometer
There are restrictions for re-using this image. For more information, visit the Smithsonian's Terms of Use page .
International media Interoperability Framework
IIIF provides researchers rich metadata and media viewing options for comparison of works across cultural heritage collections. Visit the IIIF page to learn more.
View manifest View in Mirador Viewer

Footer logo

Link to homepage

Footer navigation

  • Contact Us
  • Job Opportunities
  • Get Involved
  • Inspector General
  • Records Requests
  • Accessibility
  • EEO & Small Business
  • Shop Online
  • Host Your Event
  • Press Room
  • Privacy
  • Terms of Use

Social media links

  • Facebook
  • Instagram
  • YouTube
  • LinkedIn

Get the latest news from the Smithsonian

Sign up for Smithsonian e-news

Get the latest news from the Smithsonian

Email powered by BlackBaud (Privacy Policy, Terms of Use)
CAPTCHA
This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.
Back to Top