Recalling Yesterday - Futility Closet

From P.M.H. Kendall and G.M. Thomas, Mathematical Puzzles for the Connoisseur, 1962:

I’ve just been reading Jules Verne’s Around the World in Eighty Days — you know, where Phileas Fogg lost a day on the way round. Our science master says that ships put it right nowadays by having a thing called a Universal Date Line in the Pacific. When you cross the line from East to West you put the calendar on a day; and when you cross it the other way you put the calendar back. What I want to know is, when Puck put a girdle round the Earth in forty minutes and presumably did the right thing on crossing the Date Line, why didn’t he get back on the day before he started — or the day after, according to which way round he went?

I asked the English master this and he got quite cross about it and said it was nothing to do with Shakespeare. But if you flew round the earth as quickly as Puck it would matter, wouldn’t it?

Wouldn’t it? Why doesn’t Puck lose a day?

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“It is quite true that anyone traveling across the Date Line would have to gain or lose a day. However, Puck travelled sufficiently fast to overtake the Sun and the time. When he passed the twelve o’clock midnight time he would also have to pass from one day to another. This latter change will always opposes the change made at the Date Line, causing Puck to arrive back the day he set out.”