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Students saw it slip out of his pocket during a public question-and-answer session earlier this week at Oxford University.
For nearly the entire speech, the unreleased device edged out more and more until it completely fell out of his pocket and onto the couch.
Watch for yourself:
You can see him quickly check his notifications - perhaps unlocking the phone with Face ID - before placing the phone upside down.
The iPhone X has a 5.8-inch screen, but in the hand, it should feel closer to the normal-sized iPhones, as opposed to the larger Plus models, so it's not humongous. It also sports a back casing made from glass, which should help it feel less slippery.
It's also possible - likely, even - that Cook simply wore a pair of pants with small pockets on Wednesday.