Well, not midsummer if you mean what we normally call midsummer on or about June 22 (hello, Helen).
If you do a count of the days from equinox to solstice you will find that the days normally associated with the Christian celebrations, Mayday and All Saints' Day* to be as much as a week off. The dating of the winter to spring cross quarter day is the closest, being sunset Feb 3rd to sunset Feb 4th this year. It has been my theory that this discrepancy is due to the fact that the Christian calendar was slowly losing synch with the solar year because of Julius Caesar's lack of precision in assigning leap years to every fourth year with no exceptions. The amount that the cross quarter days are off from reality would be a measure of the date that the Pagan holiday was pegged to the Christian calendar. Unfortunately I have not been able to get accurate information as to the dates that these connections were made and it is also confused by the fact that the quarter days were originally normalized, at least in the Roman calendar, to the 25th.
*The summer to fall cross quarter day is not celebrated by any "official" holiday. There are some harvest festival celebrated around that time, but, aside from a Scottish bank holiday, nothing as universal as the other cross quarter days.
