Most people remember Williams as the illustrator of the "Little House" series and of E.B. White's "Stuart Little" before the film industry ruined Stuart. Why, I wanted to know, is Williams the illustrator of the first Frances title but from then on another Hoban, Lillian, draws the badgers? Was there some sort of rupture? Didn't Williams like Frances? Or did the Hobans want to keep her in the family? Therapists will tell you that they avoid giving out personal information to their clients because it sometimes leads to troublesome fantasies on the part of those clients. Even tiny nuggets of information -- an appointment canceled because of an illness in the therapist's family, say, or a client seeing his shrink in the deli aisle at Safeway -- can get blown way out of proportion. I thought about this idea after I began dissecting the dedication pages in the Frances books. Who are Brom and Esme? Who is Julia? And why do they rate dedications? Why not me, of course, is the obsessive's true question.

It took me some effort to find a copy of the last Frances book, "Egg Thoughts and Other Frances Songs," the only one of the series that's now out of print. Along the way I stumbled across a Web site devoted to the much-published and highly original Russell Hoban, who, it turns out, has written far more books on more far-reaching subjects than I ever imagined. (Think "Turtle Diary," "The Medusa Frequency" and "The Mouse and His Child" among dozens of other titles.) I also discovered, via the Web site, more than I really wanted to know about the real-life history of Frances. It seems that Hoban and his wife, illustrator Lillian, had four children -- that would be Brom, Esme, Julia and also Phoebe. In 1969, the year "A Birthday" and "Best Friends" were published, the Hobans moved to England. There was a divorce. Lillian took the kids back to the States, and Russell stayed behind. I'm not sure if my reading of "Egg Thoughts" would have felt more or less elegiac had I not found the Hoban Web site, but elegiac -- as well as funny and shrewd -- is how it feels.

Which is not to say that it's any sadder a book than the other Frances titles: It's mostly sad because it's the last one. Frances' personality -- her wistfulness, her unmasked desires and her wonder -- is distilled in this context, separated from the developed narrative dilemmas that drive the other stories. With "Egg Thoughts," Hoban seems to be offering fans of Frances a chance to expand her story on their own, since he had closed that door for himself.

It's hard not to love some of Frances' koanlike epiphanies, such as the first line of "Homework": "Homework sits on top of Sunday, squashing Sunday flat." But the song that really gets to me, the one that sums up the whole of childhood, is "Lorna Doone, Last Cookie Song (I Shared It With Gloria)." Who else but Russell Hoban, through the pensive Frances, has thought to immortalize the humble resignation of eating the final, plain cookie, the one left behind after all the good ones have been taken? Set against this nearly ineffable backdrop, Frances makes me wonder if obsession, really, is not much more than our play against time, our struggle against losing something that left, however fleetingly, such a sweet taste in our mouths.

All the sandwich cookies sweet
In their frilly paper neat
They are gone this afternoon,
They have left you, Lorna Doone ...
You are plain and you are square
And your flavor's only fair.
Soon there'll be an empty place
Where we saw your smiling face.
Lorna Doone, Lorna Doone,
You were last but you weren't wasted.
Lorna Doone, Lorna Doone,
We'll remember how you tasted.

Every child knows that you hang on to what makes you feel good. I know that Frances is out there somewhere, and she has graduate degrees and an amiable relationship with her first husband. She and Gloria chat on the phone nearly every week. Her dad still smokes that pipe, his chin, as always, thoughtfully tucked. Frances has a garden like her mother's, abundant with tall waving snapdragons, and she subscribes to Utne Reader. I just know there's always plenty of cake at her house. Mine, too.

Order "Mothers Who Think: Tales of Real-Life Parenthood" from the editors of Mothers Who Think.