When Joyce was completing Ulysses in 1920 and 1921 he produced two elaborate tables, now sometimes called the Linati schema and the Gilbert schema, to help friends understand the design behind "my damned monster-novel." Each schema starts with a column of Homeric titles for the eighteen chapters, which appeared without titles both in The Little Review and in the 1922 printing of the novel. Subsequent columns supply various other kinds of identifying information about each chapter. The schemas are strange beasts. Some thoughtful people have regarded them as chimeras, unhelpful for reading the novel. But they are interesting documents that possess some hermeneutic value.
Joyce had always planned for Ulysses to echo events in Homer's poem, and as he wrote early chapters he described them to friends using names drawn from characters and places in the epic. When he began receiving galley proofs from Maurice Darantière in June 1921, and filling the unfortunate printer's margins with elaborate additions to the set text, he revised and extended the Homeric correspondences of earlier chapters to make them consistent with what was evidently becoming a more serious engagement with Homer in later chapters. This compositional process, detailed in Michael Groden's textual study Ulysses in Progress (Princeton UP, 1977), suggests that a reader may be well advised to look for precise narrative correspondences between the novel's 18 chapters and certain parts of Homer's epic tale.
Nine months earlier, on 21 September 1920, Joyce had sent to his Italian translator Carlo Linati a "summary-key-skeleton-schema (for home use only)" that indicated the importance of certain Homeric correspondences, as well as numerous other compositional principles. He listed in hand-written Italian the Title of each chapter (drawn from an episode in the narrative of the Odyssey), the Hour at which its action takes place on June 16, a representative Color (or, in a couple of instances, two colors), some Persons from the Odyssey (presumably meant to correspond to people in the chapter, but not so identified), a narrative Technique (or, often, more than one), a corresponding Science or Art in other fields of intellectual endeavor, a general Significance, a bodily Organ, and a Symbol (several for each chapter).
Some of the entries on the Linati chart suggest interesting lines of reading, while others, including many of the Homeric persons, seem gratuitous, impenetrably obscure, even bizarre. The schema is long and sprawling, and it multiplies orders of categorization to the point of becoming disorderly. Chapters are numbered in two ways, with a straightforward 1-18 and a confusing 1-3, 1-12, 1-3 emphasizing the novel's division into three parts. Time superscriptures ("Dawn," "Morning," "Mid-Day," "Day," "Midnight") detract from the elegant, though oversimplified, assignment of each chapter to a numerical "hour."
The sprawling and cryptic document does, however, twinkle with glimpses of Joyce's thought processes. One notable example: to explain the absence of "organs" for the book's first three chapters, Joyce wrote vertically across those three lines, "Telemaco non soffre ancora il corpo," Telemachus does not yet suffer (endure, bear) a body.
In November 1921 Joyce produced a revised schema for the writer Valery Larbaud, who was preparing to deliver a lecture on the forthcoming novel in Paris. He also sent a copy to his biographer Herbert Gorman, and it seems that several other people saw versions of this chart during the 1920s, always with the caveat that it was for private use and not to be published, until Joyce finally authorized Stuart Gilbert to publish a copy in his critical study James Joyce's Ulysses (1930).
The new schema had a slightly varied line of headings: Title, Scene, Hour, Organ, Art, Colour, Symbol, Technic, and Correspondences. Scene was a new category. Significance was omitted. Correspondences went beyond Persons, by noting precise parallels between characters in Ulysses and the Odyssey. The Hour entries do not always agree with those in the Linati schema. Both documents show the day starting at 8:00 (the Linati shows Telemachus and Calypso occurring at "8-9," while the Gilbert assigns both to "8 AM"), but they differ on Nestor and Lotus Eaters (Linati says "9-10" while Gilbert says "10"[-11]), and on Proteus and Calypso (Linati 10-11 and Gilbert 11[-12]). The two documents agree on the six chapters from Aeolus to Cyclops, assigning each to a successive hour (12-1, 1-2, 2-3, 3-4, 4-5, 5-6), and on Nausicaa (8-9) and Oxen of the Sun (10-11). Disagreements enter again, however, with the final four chapters: the first schema has Circe, Eumaeus, and Ithaca occupying the hours immediately after Oxen (11-12, 12-1, 1-2), while the revised one postpones each by an hour (12 AM, 1 AM, 2 AM). The Linati schema lists an infinity symbol for Penelope, while the Gilbert simply records a dash.
The new schema was somewhat tidier, and since Joyce composed it after finishing all eighteen chapters and making revisions to earlier chapters, it may better reflect his knowledge of his own book, at least in some instances. But the tidiness comes at the expense of capaciousness. To take one of many examples, the Linati schema identifies the Significance of Aeolus as "The Mockery of Victory," and the Symbols as "Machines: Wind: Fame: Kite: Failed Destinies: Press: mutability." The Larbaud schema simply identifies a single, not very evocative Symbol: "Editor."
Joyce came to regret his decision to go public, and quite possibly rued having composed the schemas in the first place. Based on a conversation in 1937, in which Joyce told him that the collaboration with Gilbert was "A terrible mistake, an advertisement for the book. I regret it very much," the novelist Vladimir Nabokov decided that the whole symbolic superstructure was a kind of perverse game, not to be taken seriously. In his Lectures on Literature (delivered over the course of two decades at Wellesley and Cornell), Nabokov acknowledges "That there is a very vague and very general Homeric echo of the theme of wanderings in Bloom’s case," but he argues that searching for detailed correspondences would reduce the novel to "a pedant’s stale allegory."
Similarly, Ezra Pound reckoned that Joyce's rickety structures were a kind of scaffolding that had helped him to conceptualize his project as he worked but could be discarded upon completion. He called the schemas an affaire de cuisine, more interesting to the chef in the kitchen than to the diner consuming the meal. Although I too feel considerable skepticism toward the schemas, this website mentions them in the headnotes to each chapter, and occasionally in other notes when they promise to enrich the reading of a passage.