“If you could even guess the nature of this castle’s secret,” said Claude Bowes-Lyon, 13th Earl of Strathmore, “you would get down on your knees and thank God it was not yours.” That awful secret was once the talk of Europe. From perhaps the 1840s until 1905, the Earl’s ancestral seat at Glamis Castle, in the Scottish lowlands, was home to a “mystery of mysteries”—an enigma that involved a hidden room, a secret passage, solemn initiations, scandal, and shadowy figures glimpsed by night on castle battlements. The conundrum engaged two generations of high society until, soon after 1900, the secret...