NONFICTION : THE BOOKMAKER’S DAUGHTER: A Memory Unbound <i> by Shirley Abbott (Ticknor & Fields: $19.95; 290 pp.).</i>

Until the late 1940s, Hot Springs, Ark., was known in certain urban, Northern circles as much for its tolerance of illegal betting as for the curative powers of its mineral waters. Author Abbott’s recollection of that town and its collection of bookies and politicians on the take (Damon Runyon meets William Faulkner) makes for wonderful reading. Her memory of her family is darker. Her father was a cashier at a bookmaking parlor, and encouraged her to be something other girls her age in Hot Springs weren’t--well-read. But their relationship broke down, first over integration, and then over her father’s objection to her moving north. She apparently never forgave him before his death. To the reader, the fact that she has become a writer suggests that his lessons took hold, and that perhaps he deserves more overt warmth than Abbott chooses (or is able) to display.