JK Rowling’s Harry Potter books, Harry Potter and the Philosopher’s Stone, Harry Potter and the Chamber of Secrets, Harry Potter and the Prisoner of Azkaban, Harry Potter and the Goblet of Fire, and Harry Potter and the Order of the Phoenix (HP1-HP5), have attracted a considerable following.

But there is a mystery as to how many students attended Hogwarts school.

First, let us establish some dates. In HP2 we learn that Nearly Headless Nick was executed on October 31, 1492: the date is inscribed on his 500th deathday cake. (When he says in HP1 that he hasn’t eaten for almost 400 years, he seems to have mistaken the century.) This date is crucial: it tells us that the five books are concerned with the events of school years 1991-92, 1992-93 (with Nick’s 500th deathday in autumn term 1992), 1993-94, 1994-95 and 1995-96 respectively. From this we can deduce that Harry was born on July 31, 1980 (HP1 tells us that he was 11 on July 31, and Nick’s cake leads us to the year, 1991) and that his parents were killed and Lord Voldemort fell on October 31, 1981.

The most obvious indicator of the Hogwarts roll is the 200 students behind the Slytherin goal at the quidditch final in HP3. Slytherin is one of four houses, so assuming an equal number of pupils in each house, we have a first estimate of 800 students in the school, or an average of about 115 students in each of the seven school years. This ties in with the 650 extras employed in the first two films.

But we also have several indications that there were only around 40 students in Harry’s year. In HP1, there were 20 broomsticks for the joint Gryffindor-Slytherin class in flying - presumably half of the total in Harry’s year. Similarly, in HP2, there were 20 cauldrons for the same joint potions class, and in HP4, there were about 20 blast-ended skrewts for the same joint care of magical creatures class.

On the basis of the information in HP1 to HP4, I suggest that the school’s intake was 160 students in 1988-89 and earlier years; in 1989-90 the intake fell to 120, in 1990-91 it fell to 80, then in 1991-92 and 1992-93 it fell to 40, followed by a bounce back to some 200 students in 1993-94 before a return to its steady state level of 160 students in 1994-95. With these figures, there were a total of 160 + 160 + 120 + 80 + 40 + 40 + 200 = 800 students watching the quidditch final in 1993-94.

The most obvious explanation for such small classes in Harry’s year is a considerable decline in the wizard birthrate towards the end of Lord Voldemort’s reign, followed by a compensating increase some nine months after his fall.

However, in HP5, we find that 200 students from the 1989-90 and 1990-91 intakes were made prefects in 1995-96. The number of students in these years must, therefore, be increased above the proposed values of 120 and 80 to allow for those who were not made prefects in 1995-96. Further, it is not clear how these, or any similar set of figures, can be reconciled with the 30 students in Harry Potter’s defence against the dark arts class in HP5, or with the 100 tables, each seating 12, at the Yule ball in HP4, as 480 to 540 places should have been enough to seat the 400 students in the fourth through seventh years at Hogwarts, together with their teachers and guests.

In passing, I do not know whether it has been pointed out elsewhere, but the names of Dumbledore, Hagrid and Minerva occur in close proximity in Thomas Hardy’s The Mayor of Casterbridge when, shortly after his wife’s death, Michael Henchard reprimands his step-daughter, Elizabeth Jane, for her use of Wessex dialect words.

Bill Farebrother is a former honorary reader in econometrics at the School of Economic Studies, University of Manchester. As he has been blind for 11 years, his wife, Sheila, usually reads him the Harry Potter novels before the audiobooks appear. She read Harry Potter and the Order of the Phoenix, which Dr Farebrother estimates contains around a million words, within five days of publication in June 2003