So on my way to work yesterday and today, I was curious to know exactly when the middle of the year was. Of course, figuring out the day is pretty easy: 365 days/2 = 182.5 ~ 182 ==> July 2nd. However, I decided to push this a little further: what was the exact hour of the day that is the center? Well, seeing as how the number we got was actually rounded down by 0.5 (or half a day), then the exact middle of the day by hour is July 2nd at 12pm. However, a problem presents itself: this is all based on a 365-day calendar year, but what about with leap years?
According to the Julian calendar, the exact year is 365.25 days, which means that every 4th year we have an extra day, hence the reason February 29th exists only on years divisible by 4. This made me think a little, and so I came up with this: ((365.25*24)/2), which produces a result that puts the time on July 2nd at 3pm. Now, this seems to fit a little, since after 4 years we produce exactly midnight on the year after the leap year, but is this really correct? Even though computationally it seems correct, it just feels a little incorrect since there is a 3-hour difference. Oh well, I guess the exact middle hour of a Julian-calendar year is July 2nd at 3pm.
However, according to Wikipedia, a closer time may be calculated with resolution down to the second depending by what definition we use for the exact year. For example, using the value of a year based on the sidereal year, we can calculate the middle as ((365.256363051*24*60*60)/2 which is gives July 2nd at 3:04:34PM (it is rounded down since there is a small remainder).
I think that I like that result, so being the geek that I am I've set an alarm to go off on July 2nd at 3:04:34PM to remind me that I've hit the middle of the year to the second.