The phrase is “on his watch”

A language nitpick:  Lately I’ve read phrases such as “this crisis in the Anglican Communion is happening under his [Rowan Williams’s] watch.”    Please, folks, humor an old Navy man:  The correct usage is “on his watch,” which basically means while he was on duty.   In Navy parlance, a “watch” is a specific period of time during which a watchstander is responsible for a particular watchstation, for example, the quartermaster of the watch (QMOW); the bosun’s mate of the watch (BMOW); the officer of the deck (OOD); etc.  At sea, most watches are between four and six hours long; if you’re standing four-and-twelve OOD watches, for example, then you and three other OODs stand watch on the bridge, on a rotating basis, for four hours each — e.g., 8 a.m. till 12 noon; 12 midnight till 4 a.m.; etc. — in between doing your respective regular “day” jobs.