A remarkable feature of the presentation is the inversion of the logical order throughout the whole paper. The system of the author seems to be to give first concluded results, then the method by which these results were obtained, then the formulae and principles on which these methods rest, then the derivation of these formulae, then the data on which the derivation rests, and so on until the original observations are reached. The human mind cannot follow a course of reasoning in this way, and the first thing to be done with the paper is to reconstruct it in logical order.
Newcomb also objected to Peirce’s reliance on logarithmic seconds, which he believed accomplished nothing except to confuse the reader. “On the whole the paper does not seem to me one which would prove useful scientifically or would redound to the credit of the Survey if published in its present form.” Ultimately, Mendenhall would decline to publish Peirce’s laboriously ground-out report and would justify his decision with words that echoed Newcomb. On 21 September the following year, having decided that Peirce’s report as submitted was not publishable, and still waiting for the report for the north-south stations, Mendenhall would inform Peirce that his services would be discontinued at the end of 1891. That would bring to an end Peirce’s thirty-one years of federal service and, without a pension, Peirce would have no regular income. As for Peirce’s 1889 report, it would be bundled up in brown wrapping and sent to the archives where it would disappear, mislaid, for more than seventy-five years.
At the end of the period covered by the writings in this volume, Peirce’s report was still under review, and nearly a year and a half would pass before Mendenhall would write the letter informing Peirce that his services were no longer desired. But given how much time Peirce spent preparing the 1889 report, and how crucial a role it played in determining his fate, it seems appropriate to consider a little further some of the circumstances pertaining to the report’s composition and quality. A number of delaying factors have already been noted, including Peirce’s commitment to other writings and projects, his attending to family matters, and also his discouragement, perhaps even depression, over his treatment by the Washington office. But Victor Lenzen, in the best study to date of this report,43 emphasized two additional factors that must be taken into account.
Since 1883, Peirce had waited in vain for new pendulums from Paris, with which he hoped to improve upon the results obtained with the set of Peirce pendulums. The latter had been manufactured in the U.S. in 1881, and data obtained from their use required many corrections that could be avoided with better constructed pendulums. While in Paris in 1883, Peirce had arranged with P. F. Gautier, instrument maker for the French Bureau of Longitude, for new pendulums to be constructed according to his own improved design, and it was a constant source of frustration that he had not been allowed to stay in France until the pendulums were finished. He kept hoping until his final days with the Survey that they would be sent for.
A related but more general reason for Peirce’s slow progress was his insistence, for his own reputation and that of the Survey, that his pendulum work met the highest standards of scientific performance. He could not accept the view that had become entrenched in all levels of U.S. Government that only fast practical results were wanted. Peirce was working to advance science, and it was thanks to the precision of his research that he had earned the respect of his peers. He could not surrender to what he believed to be anti-science.
Another important factor in that contributed to the demise of Peirce’s report was Mendenhall’s disagreement on how gravity results should be represented. Peirce was adamant in his view that gravity is best understood as an acceleration, not a force,44 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