Why did not Phileas Fogg notice that his pocket watch ( set to London Time ) was behind the local time as he traveled eastwards?
Fogg's watch was not set to London Time (he kept on changing it as he traveled). Passepartout’s watch was. However, it did not show the date in addition to the time.
This was described in chapter 37 (the last chapter). Fogg's error was an accident.
How was it that a man so exact and fastidious could have made this error of a day? How came he to think that he had arrived in London on Saturday, the twenty-first day of December, when it was really Friday, the twentieth, the seventy- ninth day only from his departure? The cause of the error is very simple. Phileas Fogg had, without suspecting it, gained one day on his journey, and this merely because he had travelled constantly eastward; he would, on the contrary, have lost a day had he gone in the opposite direction, that is, westward. In journeying eastward he had gone towards the sun, and the days therefore diminished for him as many times four minutes as he crossed degrees in this direction. There are three hundred and sixty degrees on the circumference of the earth; and these three hundred and sixty degrees, multiplied by four minutes, gives precisely twenty-four hours—that is, the day unconsciously gained. In other words, while Phileas Fogg, going eastward, saw the sun pass the meridian eighty times, his friends in London only saw it pass the meridian seventy-nine times. This is why they awaited him at the Reform Club on Saturday, and not Sunday, as Mr. Fogg thought. And Passepartout’s famous family watch, which had always kept London time, would have betrayed this fact, if it had marked the days as well as the hours and the minutes!