Convent on Styx

by Gladys Mitchell

From fantasticfiction.com: "The nuns of the Order of Companions of the Poor summon eminent psychiatrist and sleuth Dame Beatrice Lestrange Bradley to investigate a series of anonymous letters, but when she arrives the prime suspect has just been found drowned in the convent school pond, with, appropriately enough, her own massive Family Bible. Dame Beatrice leads a fine cast of eccentric characters as she gradually unravels the truth from the sniping gossip of the convent's paying guests and the rumours of ghosts among the school children."