With the third millennium upon us, some information has appeared on the web to help educate us on the issue.
Pope Gregory XIII made three changes. He
But Protestant England and America didn't change to the New Style dating until 1752. By this time the gap was 11 days (due to a Julian leap year in 1700) so the correction was to have 2 September 1752 followed by 14 September.
Under the Old Style (Julian Calendar) the range of months in the same year
was
Mar(25-31), Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec, Jan,
Feb, Mar(1-24).
This leads to the seeming error of having 23 April 1736 occuring before
19 February 1736 or the day after 24 Mar 1743 begin 25 Mar 1744.
To handle this dating confusion, unless there are other dates to
confirm which system was being used, double years are recorded, such as
23 Feb 1736/7, whenever a date for the years 1583 to 1752 falls between 1 Jan
and 24 Mar. If it is clear which dating system was used, some people use
the abbreviations O.S. (Old Style Julian) and N.S. (New Style Gregorian) after
dates.
Here's a Unix command to try out:
> cal 9 1752
September 1752
S M Tu W Th F S
1 2 14 15 16
17 18 19 20 21 22 23
24 25 26 27 28 29 30
Which is documented in the man pages for that utility.