What is the purpose of the prefatory essays at the beginning of each chapter in Tom Jones?
If by prefatory "essays" you mean (1) his dedication to Lyttleton, "To the Honourable GEORGE LYTTLETON, ESQ; One of the Lords Commissioners of the Treasury" and (2) "Chapter i. — The introduction to the work, or bill of fare to the feast" and (3) "Chapter ii. — A short description of squire Allworthy, and a fuller account of Miss Bridget Allworthy, his sister," then it must be said that each serve very different purposes and only the dedication to Lyttleton can rightly be said to a prefatory item as the other two, though prefatory in nature, are actual chapters in the narrative and cannot conceivably be omitted or skipped over, as a true preface (usually) can, because omission would sabotage the comprehensibility of what comes after, which is Mr Allworthy's encounter with the babe in his bed.
he was preparing to step into bed, when, upon opening the cloathes, to his great surprize he beheld an infant, wrapt up in some coarse linen, in a sweet and profound sleep, between his sheets. He stood some time lost in astonishment at this sight;
Yet, if you must think of these two chapters as prefatory, then we can discern their purposes. The purpose of the dedication to Lyttleton is to thank his benefactor ("I partly owe to you my existence") and to beg his protection over the manuscript ("desire your protection of this work"). It is also to recognize Lyttleton's inspiration for the truly good Mr Allworthy, whose goodness is symbolized by his name ("picture of a truly benevolent mind") and to finally offer the manuscript to the good recommendation of readers based upon the good reputation of Lyttleton ("From the name of my patron, indeed, I hope my reader will be convinced").
The purpose of Chapter i is to establish the author as the narrator and as an "intrusive" narrator with a "close proximity" to a view of events. Fielding is openly establishing himself as the narrator, a practice not frequently seen in contemporary fiction. Fielding is also establishing himself as a active commentator on the events and personalities and motives of the narrative. He does this through a comparison to a feast and by referring to Pope as an authority on the expression of wit:
But the whole, to continue the same metaphor, consists in the cookery of the author; for, as Mr Pope tells us—
"True wit is nature to advantage drest;
What oft was thought, but ne'er so well exprest."
The purpose of Chapter ii is to describe the inner character, qualities and nature Mr Allworthy, upon whom so much depends, and his unmarried sister, Miss Bridget Allworthy, who is critical in many regards. This distinct focus on the natures of these two characters establishes the motives and mentality behind their actions. Fielding's aim is that they be understood, not misunderstood.
[Allworthy had] an agreeable person, a sound constitution, a solid understanding, and a benevolent heart; ... He now lived, for the most part, retired in the country, with one sister, for whom he had a very tender affection. ... [she was a] good a sort of woman, [but] was so far from regretting [her lack] of beauty, that she never mentioned that perfection [in others], ... without contempt;....