The time it takes the Earth to go round the Sun is not an integral multiple of the day (the time it takes the Earth to rotate once on its axis). A tropical year, defined as the interval from one spring equinox to the next, is very close to 365.2422 days.
The Julian calendar, instituted by the Roman Emperor Julius Caesar has a 365-day ordinary year with a 366-day leap year every fourth year. This gives a mean year length of 365.25 years, but the error from the correct 365.2422 was cummulative and by the sixteenth century, reform was considered desirable as the nominal equinoces (25 Mar/Sep) no longer corresponded with the actual equinoces . A new calendar was established in most Roman Catholic countries in 1582 under the authority of Pope Gregory XIII (hence the term Gregorian) ; in that year, the date October 4 was followed by October 15 - a correction of 10 days.
Associated with this correction plus a change in calculating leap years to avoid future corrections, came the adoption of January 1st as the start of a new calendar year, rather than March 25th.
England adopted this "Gregorian" calendar in 1752 (some what later than most other European countries though Greece held out until 1923 !) but by then the difference between Julian and Gregorian dates was 11 days - the 2nd of September 1752 was followed by 14th September 1752. These 'loss' of these 11 days required that all dates that were used for determining rent, wages etc be moved forward by 11 days - thus Tynwald day, originally midsummer's day, June 25th, was moved to 5th July.
The rule for leap years under the Gregorian calendar is that all years divisible by four are leap years EXCEPT century years NOT divisible by 400. Thus 1700, 1800, and 1900 were not leap years, while 2000 was. This rule gives 97 leap years in 400 years or a mean year length of exactly 365.2425 days. It will require a correction of a day in about 4100 !
The official Manx adoption of the new style calendar was in 1753 thus prior to this date all church records started the year from March 25. When looking at dates of the period between 1582 and 1753 great care is needed for the period 1 Jan through to 24 March as the year may be out by 1.
From 326 AD, Easter Sunday was determined as the ' Sunday following the Paschal Full Moon (PFM) date for the year based on the Julian Calendar. In the Julian Calendar there was a solar cycle of 28 years (when the days of the week and the days of the month coincide again) and a Metonic cycle of 19 years (because 19 solar years are roughly equal to 235 lunar months). In the Julian calendar PFM dates were made up of a simple cycle of 19 Julian calendar dates (Orthodox Christianity still uses this method and then converts the Julian date to the corresponding Gregorian date). However this had to be revised with the adoption of the Gregorian calendar