During the years of Peirce’s most intensive work for the Century Dictionary, his research on definitions would frequently carry over into other writings. As a result, it is sometimes difficult to determine whether some of the shorter, often fragmentary, manuscripts of this period are preparatory to a definition or are independent studies stimulated by his lexicographical research.27 “Note on Pythagorean Triangles” (sel. 13), is a good example. This short selection might be a variant form of Peirce’s definition of “Pythagorean triangle” for the dictionary or it might be only the beginning of a paper based on the research for that definition.
During the first half of the 1890s, Peirce undertook quite a number of textbooks, often simultaneously, but because of lost manuscripts and reorganizations on Peirce’s part, a precise recounting of his textbook projects may no longer be possible. Among the books mentioned by Peirce in his correspondence are a primary arithmetic, a practical arithmetic, a vulgar arithmetic, an arithmetic for young readers, a geometry, a projective geometry, a revision and expansion of his father’s 1873 Elementary Treatise on Plane and Solid Geometry, a trigonometry, and a topology—much of which would be reshaped into two books, the “New Elements of Geometry” (1894–95) and the “New Elements of Mathematics” (1895–96). Peirce also worked on several different logic books during the same period, including “The Light of Logic,” “The Short Logic,” and volume two of his proposed “Principles of Philosophy” on the “Theory of Demonstrative Reasoning.” And there were other book projects not aimed at the classroom. It is evident that Peirce turned to writing as one of his main hopes for increasing his annual income to a sufficient level and that textbooks fit centrally into his plans.
Several manuscripts listed in the Chronological Catalog for 1890, including two W8 selections, may belong to one of these book projects.28 In “Logical Studies of the Theory of Numbers” (sel. 15), a short document that continues earlier work on number theory,29 Peirce plans to investigate whether a proof procedure can be found for “higher arithmetic, so that we can see in advance precisely how a given proposition is to be demonstrated.” This is equivalent to asking whether there is an algorithm for finding solutions to equations in number theory, and in raising that question Peirce anticipates, in a more general way, David Hilbert’s “Tenth Problem,” posed in 1900 at the International Congress of Mathematicians in Paris, of determining whether there is an algorithm for solutions to Diophantine equations.30 Peirce probably aimed to translate such equations into Boolean algebra, but the paper stops a long way short of showing how he would have actually proceeded. In writing it, Peirce was perhaps stimulated by his recent work on the definition of “number” for the Century Dictionary, or he might have conceived it as preliminary work toward a foundational chapter for a mathematics textbook. “Promptuarium of Analytical Geometry” (sel. 16), on the other hand, seems clearly to have been intended to introduce students to analytical geometry and is very likely to have been written for a textbook on geometry.31 It was intended to demonstrate to the student how “the whole theory of lines is exactly like that of points.”
As the year came to an end, Peirce’s thoughts turned to personal matters— although not exclusively: he wrote a very long letter to Newcomb, apparently the day, perhaps the night, before Christmas, defending his views of infinitesimals and limits. Around this time, maybe on Christmas Day, Peirce drew up a list of all of the places where Juliette had spent her Christmases beginning in 1857—presumably the year of her birth. This is something they would have done together. And maybe in turning his attention to a record of events in Juliette’s life he was stimulated to jot down what he could recollect of his own beginnings, as we find in “My Life” (sel. 12). It is curious that he says he could remember nothing before he could talk and yet the earliest memories he recounts seem to be quite sensory, even imagistic.
1891 began auspiciously for Peirce with the publication of “The Architecture of Theories,” the lead article for the January issue of the Monist. The issue was announced in leading periodicals and free copies were widely distributed to advertise the journal. The Open Court, in noticing that issue, described Peirce as “one of the subtlest thinkers and logicians not only of America, but of the whole globe.”32 The January issue of Book Chat, published by Brentano’s, reported that:33
The January number of The Monist contains a most masterful philosophical paper on “The Architecture of Theories,” the first of a series from the pen of Prof. Charles S. Peirce, formerly lecturer on Logic at Johns Hopkins University, and well known as an original thinker. Prof. Peirce has heretofore written mostly upon the most recondite themes of Logic and Mathematics, but in this paper he undertakes, for the first time, to sketch out his general philosophical system, and he does so with a scope and competence that are truly singular. He breaks ground for his foundations in strata that far underlie any heretofore chosen for that purpose, and shows the outlines of a philosophy at once all-embracing and organic. The series, it is expected, will create considerable commotion in the philosophical world when its iconoclastic constructiveness shall be realized.
Writing to Carus on 12 January, Peirce told him that his views were “the fruit of long studies” and that he didn’t “expect or desire people to fall in” with his views at once. He welcomed Carus’s criticism of his conception of chance but explained that he regarded “chance, without any degree of conformity to law … as nonexistence, a mere germ of being in so far as it may acquire habits.”
As the new year began, it is doubtful that Peirce had much time to spare for anything except his enormous work on the Century Dictionary, and his concentration on his definitions would continue through the summer. The fourth volume of the Century had been published in November 1890, so as 1891 got underway, Peirce would have been working on proofs for the fifth volume, covering Q–Stro words, and even though the process was in the proof phase, Peirce was making a lot of revisions and additions that required considerable research. One consequence is that he could not have managed to make marked advances on the continuation of his report on gravity for Mendenhall. The manuscript under review Peirce had submitted more than a year earlier covered all of the technical, theoretical, and historical issues necessary for a comprehensive report on all of his unpublished gravity operations, but it only gave results for four stations: the Smithsonian, Ann Arbor, Madison, and Cornell. Peirce had promised to follow up with a second and concluding part giving the results for the Montreal, Albany, Hoboken, Fort Monroe, St. Augustine, and Key West stations. The reduction of the raw data, for which there were massive quantities, was slow and exceedingly demanding work and, though he had asked more than once for an assistant to be sent to Milford to help with the calculations, he was left to complete the work on his own. Mendenhall had written on 12 December 1890 to ask Peirce for a report on his progress, noting that “it would seem that all of the reductions ought to be finished by this time” and advising that some revisions were necessary before the report already in hand could be published. By that time, Mendenhall had heard back from two other reviewers, Hubert A. Newton, a mathematician from Yale, and mathematician and meteorologist William Ferrel, a Coast Survey Assistant famous for inventing the Survey’s tide predicting machine. Their reviews were mixed. Ferrel had found Peirce’s report to be “unnecessarily complicated” and thought that Peirce had made some mistakes, but he praised Peirce’s method and gave a positive assessment overall.34 Assuming that Peirce would rearrange his report in a more traditional way and add a final section of results from the remaining stations, Mendenhall had been given no grounds for rejecting the report.
On 4 February 1891, Peirce sent Mendenhall an accounting of both his progress and his projections. Indeed, he had completed the reductions and finished the work on the relative force of gravity for all of the stations. But a lot