The use of a 365-day calendar year with occasional leap years was introduced in 46 B.C.E. with the Julian calendar. The Julian calendar was formed by Julius Caesar, who had commissioned the Alexandrian astronomer Sosigenes to revise the calendar system. Sosigenes used a tropical solar year, which calculates to 365.25 days per year. This was slightly off, because the actual tropical solar year is 365.242199 days. This discrepancy caused there to be 10 days missing by the year 1582. That year, Pope Gregory XIII issued a papal bull (decree) to fix the Julian calendar. The Jesuit astronomer Christoph Clavius undertook the Pope’s decree and designed what is now known as the Gregorian calendar. In order to correct for the loss of one day every 130 years, the Gregorian calendar drops 3 leap years every 400 years. According to this system, years are leap years only if divisible by 400—thus, 1600 and 2000 are leap years; 1700, 1800, and 1900 are not. Because the solar year is shortening, today a one-second adjustment—called a leap second—is made (usually on December 31 at midnight) when necessary to compensate.