Historically Speaking: 2. The Oldest American Slide Rule

The second installation of the Historically Speaking reprint series is from November 1953. In it, editor Phillip Jones describes early versions of a slide rule, Palmer’s Computing Scale and Palmer’s Pocket Scale, from the 1840s:

Phillip S. Jones, “The Oldest American Slide Rule,” Mathematics Teacher, Vol. 46, No. 7 (November 1953), pp. 500–503. Reprinted with permission from Mathematics Teacher, ©1953 by the National Council of Teachers of Mathematics. All rights reserved.

Click on the title to download a pdf file of the article, “The Oldest American Slide Rule.”

The column opens with a suggested bibliography of the history of mathematics consisting of early articles from Scientific American, which our readers may also find interesting. The article about the Palmer slide rules begins on page 501. We additionally provide printable images of Palmer’s Pocket Scale for potential use in the classroom as described below.

Dr. Peggy Aldrich Kidwell, Curator in the Division of Medicine and Science at the National Museum of American History, Smithsonian Institution, offers a present-day response to the article. Dr. Kidwell’s research interests include the history of mathematics and computing, women in science, and the history of mathematical recreations in the United States. She is the author of several publications, including Tools of American Mathematics Teaching, 1800–2000, with Convergence co-editor Amy Ackerberg-Hastings and David Lindsay Roberts.

Phillip S. Jones’s fine article describes the “pocket scale” or “computing scale” copyrighted by Aaron Palmer in the early 1840s and sold until around 1870 by John E. Fuller. The piece illustrates several intriguing aspects of the history of the slide rule in the United States. The first is the transience of the slide rule itself. Jones proclaimed Palmer’s instrument to be “the oldest American slide rule.” It is unquestionably true that it is one of the first—if not the first—American circular slide rules to sell in the United States. One might note, however, that Solomon A. Jones, who was active in Hartford, Connecticut, from 1838 through 1841, sold a linear slide rule designed especially for carpenters—an example survives in the Smithsonian collections. It is perhaps more noteworthy that the slide rule, which became common in the country in the 1890s and was widely known to mathematics students when Jones wrote in 1953, is now primarily of interest to collectors. The handheld electronic calculator displaced it in the 1970s, though of course the underlying mathematics of logarithms are still widely taught and used.

Due to the efforts of diverse historically-minded people—and the ready availability of online sources—we now know a bit more about Palmer himself. According to Carol L. Hannan, writing on a website devoted to Historic Homes of Brockport, New York, he was a native of Canada who moved to western New York, settling in Brockport and then Rochester. Rochester city directories list him as a machinist in the 1860s and early 1870s, and then as an inventor until his death in 1884. His patented inventions focused more on improvements to farm machinery.^[1]

Palmer sold his computing scale with a book of instructions, which can now readily be consulted online. Thus, a curious teacher or student can easily print out a couple of copies of the illustration provided by Jones, cut the round disc out of one of them, hold everything together with a thumbtack or paper fastener, and have a working replica. Consulting the text can give a sense of the kind of arithmetic problems deemed of interest. Different editions of the booklet prepared by Palmer and then by Fuller tell historians more about the device’s sales and the reactions of those who saw it.

To call attention to his ideas, Palmer solicited recommendations from local authorities. The first he cites in his booklet, who wrote to him in 1842, were principals of academies (private secondary educational institutions) in and around Rochester. The following year, his reach extended to Boston, where he gained endorsements from Harvard professor Benjamin Peirce, textbook author Frederick Emerson, and educational reformer William B. Fowle. Palmer also garnered words of praise from businessmen and a lawyer. Curiously, the only recommendation to actually mention logarithms, describe the physical details of the object, and compare it to linear slide rules was one from George Clinton Whitlock, a Middlebury College graduate who was Professor of Mathematics and Natural Science in Genesee Wesleyan Seminary in Lima, New York. By the time of later editions of the instructions, Fuller could include references to exhibitions at world’s fairs and recommendations from such distinguished foreign mathematicians as Augustus De Morgan.^[2]

Finally, in case someone should like to look at an example of Palmer’s computing scale and its various revisions, readers should be forewarned that finding one is not an entirely easy process. The book and the instrument were often sold together, and hence may survive either in library collections or museums. To give only a few examples, Florian Cajori, who published fundamental 1909 articles on Aaron Palmer’s instrument and on its modification by Fuller, consulted examples from his contemporary Artemas Martin.^[3] It seems likely that these survive with other materials collected by Martin now in the library at American University. Jones described an example on display in 1953 at the Henry Ford Museum in Dearborn, Michigan. It seems probable that this is in the special collections of the University of Michigan. As Jones mentions, Harvard University had several examples of Palmer’s instrument. Waywiser, the database of the Harvard Collection of Scientific Instruments, now lists three examples of Palmer’s computing scale (all from 1843) as well as examples from 1845 and 1847 that combine Palmer’s scale with that introduced by Fuller. At the same time, the Harvard University Libraries boast five editions of Palmer’s various instruction manuals, as well as manuals that include Fuller’s changes. How many of these include examples of the actual slide rule is unclear. As these examples—as well as those in other locations—suggest, those seeking further examples of the scale have a daunting task ahead of them! Jones would undoubtedly be delighted.^[4]

Modern readers (and their students) may never have seen, much less used, a slide rule. Those who wish to learn more about them may wish to consult the WikiHow article, “How to Use a Slide Rule,” or the “Additional ISRM Galleries Slide Rule Resources” section of the website of the International Slide Rule Museum. Some thoughts to spur further thinking and discussion:

• The slide rules students were using when this article was published in 1953 were very different from Palmer's "oldest slide rule," just as today's calculators are very different from slide rules of the 1950s. (Images of slide rules typically used in high school and college classrooms can be viewed in the charming 1940 booklet by Don Herold, How to Choose a Slide Rule, or in Eric Marcotte’s gallery of Keuffel & Esser slide rules.) How have those advances in technology affected the way we think about and teach mathematics?
• The mathematical problems addressed by Palmer's slide rule are similar to those covered in arithmetic textbooks of the time period. How do our textbooks reflect current interests and technological capabilities?

Finally, we hope you will follow Dr. Kidwell's advice and experiment with your very own Palmer's Computing Scale. Print these two copies of the scale and attach them to each other as described above. You can find instructions on how to use the scale here. Let us know about your investigations!