Two different calendar systems are used, Gregorian and Julian.
These are nearly identical systems with Gregorian making a small
adjustment to the frequency of leap years; this facilitates
improved synchronization with solar events like the equinoxes.
The Gregorian calendar reform was introduced in 1582, but its
adoption continued up to 1923. By default cal uses the adoption
date of 3 Sept 1752. From that date forward the Gregorian
calendar is displayed; previous dates use the Julian calendar
system. 11 days were removed at the time of adoption to bring the
calendar in sync with solar events. So Sept 1752 has a mix of
Julian and Gregorian dates by which the 2nd is followed by the
14th (the 3rd through the 13th are absent).