use of the articles

You can say either "the next day" or "next day". Your question "why?" is meaningless.

Not very clear, Centrox, unfortunately. Next day means tomorrow and the next day means the day after. The sentence was taken from Longman Practical English Grammar, where they seem to do everything by the book. In this case, their own book, which says that tomorrow in indirect speech in the past is "the next day". This makes all this even more confusing. I would understand if the sentence began with "Next day...", because in most cases you can omit the definite article at the beginning. Could it be a typo then?

It does not. "Next week", "next month" or "next year", without the definite article, are used in the present to refer to the week, month or year (in the future) immediately following the present one, but this usage does not extend to the day after today, which is only called "tomorrow".


"The next day", "the next week", "the next month" or "the next year" refer to a day, week, month or year, in the past or future or at an unspecified time, which immediately follows another day, week, month or year. The article can be omitted in casual speech when referring to days.

Examples:

I saw my father on Tuesday. The next day I bought a car.
I saw my father on Tuesday. Next day I bought a car.
I spent July in London. The next month I went to Spain.
I was divorced in 1984. The next year I married again.


I having my hair cut today. Tomorrow I am going fishing.

In the future, when I talk about these events I might say "Last Monday I had my hair cut. The next day (or next day) I went fishing."


Not a typo.

Thanks a lot. Was really very helpful.

Well, they can't be wrong then, if they're using their own book as an authority.