It is impossible to read this now without horror. The politesse, the pointing up of sweetness, and the ascribing of “entire indifference” to the child evoke the classic stratagems of the pedophile, planning his campaign and convincing others (and, more important, himself) that he is doing no wrong—that there is no victim but merely a willing collaborator. After Carroll wrote his great poem “The Hunting of the Snark,” in 1876, the daughter of the illustrator became another friend. Her name was Winifred Holiday, and she recalled, “When he stayed with us he used to steal on the sly into my room after supper, and tell me strange impromptu stories as I sat on his knee in my nightie.”

Had Carroll lived today, and had such accounts been made public, he would have been either jailed or (a fate more infernal, for someone who treasured his privacy) hounded by an unforgiving press. The wish, we tell ourselves, is father of the deed; on the other hand, what was Carroll’s wish? If buried, it lay very deep beneath his outer crust. As Douglas-Fairhurst calmly states, “It is far easier to condemn Carroll than it is to decide exactly what he should be accused of.” There was no suggestion of physical abuse, and he himself thundered against any hint of impropriety, deeming even an expurgated Shakespeare to be unfit for junior readers. (He planned his own edition, just for girls: “I have a dream of Bowdlerising Bowdler.”) For us, the thunder is a giveaway, rumbling with guilt, but the fact remains that, in his time, Carroll both exemplified and enhanced what Douglas-Fairhurst calls “a more general trend towards seeing childhood as a separate realm.” If it was inconceivable, in genteel circles, that Carroll could present a carnal threat, that was not because he was a clergyman, or the writer of cherished books, but because children could never be objects of desire. Far from being adults in bud, they were fenced off, in a garden of unknowing, and that is why parents were content to let Carroll, himself an innocent, wander in and browse. Freud’s “Three Essays on the Theory of Sexuality,” including one on “Infantile Sexuality,” were published in 1905. Carroll, mercifully, had died seven years earlier.

There were periods, it is true, when gossip rustled around Oxford, and the Liddells briefly suspended relations with Carroll; but the source of the gossip is hard to trace. Segments of his diary were later excised by his family. Cohen believes that he may have proposed marriage, or mock marriage, to Alice, who was then aged eleven, but that is hard to prove. One thing we do know about, because Carroll reports it in his diary, is a rumor that he was using Alice and her sisters as a cover for wooing their governess, Miss Prickett, usually known as Pricks. The rumor tells you a great deal about the moral etiquette of the age: a warm affection for other people’s offspring was acceptable; underhanded courtship of a chaperone was not. We cannot know what it was to inhabit such an era, when a middle-aged man could take a picture of three small sisters and give it the title “Open Your Mouth and Shut Your Eyes.” Almost everything about Carroll now lies beyond the Freudian pale. All the more reason, then, to treasure the adventures of Alice on the page, which keep both their counsel and their cool—“strange impromptu stories,” by any reckoning, yet undying. The life of Carroll somehow fades away, leaving nothing but his books, just as a cat, on the branch of a tree, can slowly vanish, bequeathing only a smile.

To return to those books, as Douglas-Fairhurst admits, “can feel like such a relief.” His admirable method, in “The Story of Alice,” is to test the soil from which they arose, and to ask how long the scent of them has lingered in the air. He shows that Carroll, in swiftly sending Alice downward, was alert to a thriving fascination with netherworlds—whether in the London Underground, construction on which started in 1860, or, fifteen years earlier, in the English translation of a Norwegian novel, “which begins when the hero’s rope gives way and he falls into an abyss, although he still has enough time to take a cake out of his pocket and eat it.” Then, there was the aftermath: the Wonderland craze, which spawned feeble ripoffs and unsolicited sequels, as well as theatrical adaptations (which prompted Carroll to compose an overwrought essay on “ ‘Alice’ and the Stage”) and enamelled biscuit tins, to which, surprisingly, he gave his blessing. The cookies within dismayed him, though, and he requested that any tins sent to his friends were “to go out empty.” Three were delivered to “Mrs. and the Masters Hargreaves”—the grownup Alice Liddell and her sons.

Carroll kept in touch with her, while admitting that “it was not easy to link in one’s mind the new face with the olden memory.” After his death, Alice returned the compliment through her mere survival, which convinced readers that they were still in touch with him. The climax came in 1932, with a transatlantic trip, in the course of which two thousand guests filed into the gym at Columbia University to hear Mrs. Hargreaves speak. She also ingeniously claimed, in a radio broadcast, that “America and New York City are such exciting places they take me back to Wonderland.” (There is a stirring film, “Dreamchild,” from 1985, with a script by Dennis Potter, about her visit.) “That’ll be a comfort, one way—never to be an old woman,” Alice tells herself, near the start of her story, but the public was not in the least discomfited to learn that she had aged. The notion that this elderly dame and the seven-year-old of the books were one and the same person took root in received opinion, and there it has stuck: “Alice’s Adventures in Wonderland” is a roman à clef, we reassure ourselves, and the Liddell girl is the key.

So trustable is Douglas-Fairhurst as a key holder, and so heroic is his rummaging in the archives and toy boxes of Aliciana, that he leaves you wanting more. Carroll’s parodies of Wordsworth and Tennyson in the Alice books, for instance, are calculated and quite cruel; is there not more to say about a man who seemed reluctant to approach the writings of major poets except in the spirit of lampoon? Later writers, by contrast, were open in their allegiance to Carroll; it is satisfying to be told that Vladimir Nabokov, hired to translate “Alice’s Adventures in Wonderland” into Russian, in 1922, was paid with an advance of “a single US five-dollar bill,” and we should be grateful that Douglas-Fairhurst truffled around in “Finnegans Wake” to find some of Joyce’s lovely Carrollings (“Wonderlawn’s lost us for ever”), thus saving us the trouble. But why mention Carroll’s shy appearance on the sleeve of “Sgt. Pepper” and not probe further into his effect on John Lennon, whose lyrics for “I Am the Walrus” and other songs steal so cockily from the books? How about Monty Python; or the unhinged British passion for cryptic crosswords, sure to wreck a morning’s mental peace; or Mary Poppins, with her bottomless bag; or the demure girl who converses with monsters in Guillermo del Toro’s “Pan’s Labyrinth”; or the gray, moth-eaten hare devised by Jim Henson for “Dreamchild”; or the stop-motion “Alice,” directed by Jan Švankmajer, the most Carroll-mad animator of all? As for the anapest, the waltzing metre in which Carroll delighted (“I engage with the Snark—every night after dark— / In a dreamy delirious fight”), it lay dormant for decades, and then burst out in the keen exclamations of Dr. Seuss: “You have brains in your head. / You have feet in your shoes.”