Writings of Charles S. Peirce: A Chronological Edition, Volume 6. Charles S. Peirce

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СКАЧАТЬ and that relative determinations of gravity—where gravity at a location is measured relative to gravity at another location—provide greater accuracy than absolute determinations and are all that is needed for determining the figure of the earth. In his report on gravity at Fort Conger (sel. 30), Peirce had introduced a new relative measure that he called “logarithmic seconds.” These new units, reintroduced in the 1889 report (sel. 36, pp. 289–90), were meant to facilitate the calculation and use of gravity results. Lenzen explains that when gravity is expressed in logarithmic seconds, “a difference of values of gravity at two stations in log. secs, is numerically equal to the difference in the corresponding numbers of oscillations per day at the stations of a pendulum that beats seconds at the mean equatorial station.”⁴⁵ Mendenhall, for his part, was equally adamant that gravity should always be expressed in units of force called “dynes” and, besides, he thought that Peirce’s logarithmic seconds were obscure and confusing. He was not moved by Peirce’s defense that they were not obscure to mathematical geodesists, “men who have to deal with the most intricate parts of the calculus,” and that they had the very useful effect of “making all the operations of reduction and comparison additions & subtractions in place of multiplications and divisions” (22 July 1890). Mendenhall told Peirce that of course it was his own business how he wanted to restrict the meaning of “g” for his personal use, but that “when acting for the public … one must be guided by the general consensus of opinion of those generally admitted to be the highest authorities; personal preferences and especially any weakness towards ‘eccentricity’ must often give way” (24 July 1890). Mendenhall was unwilling to recognize that at that time there was no one in the United States who was a higher authority in these matters than Peirce.

      A more important disagreement between Peirce and Mendenhall concerned the method for conducting gravity operations and the precision to be aimed for. Mendenhall had become persuaded that it was acceptable to give up absolute determinations altogether and, in general, to sacrifice precision for economy as long as results were satisfactory for ordinary practical purposes. Accordingly, Mendenhall, following the lead of Robert von Sterneck of Austria-Hungary, had adopted a new style short “half-seconds” invariable pendulum that could be carried from station to station and put into operation at a fraction of the cost associated with Peirce’s use of the yard and meter pendulums, especially their use in the complex operations required to determine absolute values.⁴⁶ In his first gravity report, published in 1892, Mendenhall explained that the Coast Survey would no longer follow the traditional European-style gravity studies that Peirce had instituted in the U.S. because they were too expensive, cumbersome, slow, and inefficient. The half-second pendulum, by contrast, solved all of these difficulties: “One of the principal advantages of this apparatus is the ease with which it may be used, and the few and inexpensive preparations necessary for its installation.”⁴⁷

      In June 1894, two and a half years after Peirce’s forced resignation, Mendenhall testified before the Congressional Committee on Naval Affairs where he was questioned about Peirce.⁴⁸ He told the Committee that much of Peirce’s work “was of the highest character, and it has received praise from the European geodesists and others, physicists, etc., but it lacked the practical quality which I believed to be essential.” He explained that after the successful introduction of his half-second pendulums, he “became convinced that Professor Peirce’s services to the Survey were no longer necessary.” Mendenhall added that the results Peirce had been working on in his final years had not been published because Newcomb and other experts had judged that they were “not valuable.”

      Was that a fair assessment of the results Peirce worked so hard to obtain during his last years at the Survey? It is difficult to evaluate scientific work that never became part of the public record, but Lenzen concluded that Peirce’s unpublished monograph was much more important than Mendenhall supposed. Some of Peirce’s accomplishments, according to Lenzen, are the following:⁴⁹ 1. Peirce’s calculation of “provisional maximum values of the departure of the geoid from the mean spheroid” (pp. 289ff.) is one of the earliest applications, if not the first, of Stokes’s theory of the form of the geoid. 2. Several of the corrections used in the report were original with Peirce. These include the correction for flexure of the pendulum support (pp. 295–99), which Peirce had introduced in his 1876 “Report on Gravity at Initial Stations” (W4:131–33); the correction for the unequal expansion of the upper and lower parts of the pendulum, introduced by Peirce in 1885 (W5: sel. 53) but first applied in the 1889 report (p. 341); the correction for the inclination of the knife-edge (pp. 340–41); and the correction for the second atmospheric effect. 3. Peirce’s calculation of the absolute value of gravity for the Smithsonian station, appropriately converted, appears to match a result obtained seventeen years later by the Geodetic Institute at Potsdam, which became the reference value throughout the world.⁵⁰

      In considering the importance of the 1889 paper, Lenzen emphasized the significance of Peirce’s “second atmospheric effect,” the effect of the viscosity of air on the motion of a pendulum. Peirce had introduced this correction in his report for 1876 (W4:104–106) but only as an a posteriori correction. In the 1889 paper he applied and compared both a priori and a posteriori corrections, for he had designed the Peirce pendulums to facilitate just such a comparison for the viscosity correction. The theory Peirce applied was that of G. G. Stokes, but the formula Peirce used for his calculations took account of more factors than did Stokes’s formula. Lenzen concluded that it was unfortunate that Peirce’s “highly original discussion of the second atmospheric effect” had not been published, for it would certainly have been of interest to “Professor Stokes, Lucasian Professor of Mathematics, and in charge of the British Gravity Survey.” Lenzen closed his study with the following assessment: “In the light of a review that I have made of the development of pendulums for the determination of gravity, it is my firm judgment that the experimental and theoretical work represented in Peirce’s Report on Gravity at the Smithsonian, Ann Arbor; Madison, and Cornell was the best work of its kind in the nineteenth century.”⁵¹ However, as was pointed out above, Peirce’s report was far from finished, and had it been published without improvements, his innovations might well have gone unheeded.

      Life for the Peirce’s in their new house, during its renovation in the summer of 1889 could not have been idyllic. Overseeing construction and running the estate would have been pressure enough, but Peirce was expected to give full days of attention to his work for the Coast Survey, and somehow find time to write his definitions. Besides, many other lines of thought were constantly working themselves out under his pen. In August, Peirce published in the Nation a review of St. George Stock’s Deductive Logic (sel. 35). It was Peirce’s first review for the Nation since reviewing Abbot’s Scientific Theism (W5: sel. 46) in 1886. Peirce’s review of Stock was the kind of review an author dreads; the best Peirce could say was that “it would be impossible for a man who has been studying and teaching logic at Oxford for seventeen years to write a thoroughly bad book on the subject,” but he added immediately that any teacher who decided to use Stock instead of Bain “would be doing his pupils an injury.” Peirce was not one to mince words. He declared that “the best expositions of the subject” force students step by step to see the close connection between “formal rules and the trains of thought which actually go on in their own mind” and that every logic text should have at least a brief treatment of symbolic logic. Stocks book failed on both counts. Peirce announced that “there is no subject in which there is more urgent need of a new book,” probably knowing he would soon resume his own effort to fill that need (see W5, sels. 54–56). By the end of 1890, he was working to transform his correspondence course lessons into a text book entitled “Light of Logic.” The fragment that the present editors have entitled “Reasoning” (sel. 37) probably dates from early 1890 and may have been written with such a book in mind.

      By the end of September the first phase of construction at Quicktown was complete. Peirce wrote to Jem with some satisfaction that “our house” is “very comfortable, very pretty” and “not in the least in the Queen Anne nor any other style. It is our own original style” (30 September 1889). He continued with a description of his estate and plans for its development and added: СКАЧАТЬ