Hello Goodbye Hello: A Circle of 101 Remarkable Meetings by Craig Brown. The book tracks chance encounters between rich and famous people throughout history and how one meeting leads to the next, etc.
Two short chapters describe Houdini's meeting with the Tsar of Russia during his tour in 1903, and then his encounter with Teddy Roosevelt aboard the Imperator in 1914.
According to our friend Leo Hevia, who tipped me off to this book, the author gets a few things wrong about Houdini's escapes. Apparently he believes that the Big Secret was Bess slipping Houdini the keys with a kiss.
Purchase Hello Goodbye Hello: A Circle of 101 Remarkable Meetings on Amazon.