On the train, Harry sits with Neville and Luna until Slughorn invites him to tea. Then Harry endures hours of boring conversation with Slughorn and Hogwarts students with important connections (HBP7).
Timeline Notes
Even though the last chapter finished off on the Saturday immediately following Harry's birthday, this chapter implies that there is only a week between the trip to Diagon Alley and 1 September, even though there should be almost a month ("Harry spent a lot of the last week of the holidays...."). We do know that most of the chapter takes place on Saturday, 31 August and Sunday, 1 September, because this is the day the Hogwarts Express always leaves for Hogwarts; additionally, this aligns with the one hard fast date we are given in this book - Ron's birthday on Saturday, 1 March (HBP18).
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Tags: boring