I can’t quite accept that Julius Caesar or Pope Gregory figured out these adjustments themselves. What forgotten chronologists did?

The Sky This Week, 2012 February 28 – March 6 — Naval Oceanography Portal

As you undoubtedly know, February 29th makes its (almost) once-every-four-year appearance this week, prompting many people to ponder "Why?" The answer lies in our attempt to carve up the year into an integral number of days. The system of leap years as we know it was first instituted by Julius Caesar c. 46BCE. In the Julian Calendar a leap year occurred every four years, giving a mean duration of a calendar year of 365.25 days over a four-year cycle. The Earth’s so-called "Tropical Year" (the time it takes between two successive occurrences of the Vernal Equinox) is 365.2422 years, thus the mean Julian Calendar year exceeded the Tropical Year in length by some 11 minutes. This had the effect of displacing the calendar date of the Equinox by one day every 128 years. By 1582 the cumulative difference between the Julian Calendar and the Equinox was some 10 days (which bollixed up the computation of the date of Easter), prompting Pope Gregory XIII to promote a reform to the calendar which still bears his name. In the Gregorian Calendar leap years occur every four years except in years ending in "00" (e.g. 1700, 1800, 1900, 2100, etc.) However, years ending in "00" that are evenly divisible by 400 (e.g. 1600, 2000, 2400) *are* leap years, which yields 97 leap years in a 400-year cycle. Dividing 97/400 = 0.2425, thus the mean duration of a Gregorian year is 365.2425 days, which is only 26 seconds longer than the Tropical Year. This is the system which has been more or less "universally" adopted.

The Sky This Week, 2012 February 28 – March 6 — Naval Oceanography Portal

Incredible accuracy for adjustments made 430 years ago.

I can’t quite reconcile the preceding with a different observation:

With no other correction, the vernal equinox would occur, on average, about 5 minutes earlier each year. — Kevin McKeown