It is worth noting that during the currency of the Parish Registers the form of recording dates changed - the year used to run from March to March, not January to December so an entry for, say, 21 January 1563 would in modern form refer to 21 January 1564. It is pre-1753 that the confusion could occur.
In 1751 the year started on 25 March and ended on 31 December. In 1752 the year started on 1 January and ended on 31 December, however it appears that as far as Great Harwood's Parish Records are concerned the year change did not happen until the following year with the last birth of 1752 being recorded on 8 March 1752 and the first of 1753 being three weeks later on 29 March 1753.
The pre-1752 calendar is known as the Julian, or Old Style and dates are sometimes shown in modern documents as OS to indicate what year is intended. The post-1752 calendar is the Gregorian calendar.
Old Style dates are sometimes shown as 21 Jan 1563/64, however spreadsheets and software which carry out calculations based on dates cannot handle this format.
I have tried to ensure that dates are shown in the modern form with the year running from January to December, mainly of this problem but also because otherwise it could look to modern eyes that someone died before they were born or that children were born uncomfortably soon after a marriage.
The following is based on a document I found on the Internet at the time of the Year 2000 scare regarding computer dates - much of the explanation related to Leap Years but does include a good explanation of the Julian and Gregorian calendars.
Julius Caesar (or more correctly, perhaps, Gaius Julius) who lived from 100-44 BC had a fascination with the calendar although he made some awful mathematical errors in his decrees regarding same. He named one of the summer months after himself.
Anyway, after meditation and consultation with his astronomers and others he realized that 365 days in a year was not quite accurate. Using the tools at his disposal he decided there had to be an extra quarter day tossed in each year to make things work out right. So the new calendar was devised according to his instructions. They went along that way for quite awhile, adding one day every four years to account for that left over bit each year. The error was not big enough to notice even over several hundred years.
Well, a few hudred years later the Pope called on one of his scholars and bright young men, a monk by the name of Dennis Aloysius and said "Dennis, figure out a new system of years to go by." Dennis thought about that for quite a while and after some serious calculations told the Pope that Jesus had been born in the 720th year of the Roman Era and that henceforth that would be known as year 1, and that therefore it was now the 520th year in the Christian era (520 AD).
Fast forward a thousand years or so, and Pope Gregory has been told by his advisors that the calendar is going to be adjusted again. As they explained it to Pope Gregory, Gaius Julius had it all wrong: instead of a year consisting of 365.25 days, it really only consisted of 365.2422 days, or 365 days, 5 hours, 48 minutes and 49 seconds. As a result of that 11 minute difference each year unaccounted for in Gaius Julius' calendar, it had gotten way out of whack, being some several days short of where it ought to be. By the time they can enforce this on all of Europe however, several more years have passed. In 1582 a general adjustment was made throughout Europe with the calendar; several days were just chopped out to make up the shortfall.
Just on general principles, England and her colonies in America did not go along with the adjusted calendar. By the middle 1700's though, this calendar dispute was getting awkward and embarrassing for the British. After all, they still did some trading with Continental Europe and it was getting a bit weary for folks here to say it was Tuesday, May 1 while people on the Continent were saying no, it is really Tuesday, May 12. Not only that, there was a movement afoot to change New Year's Day to January 1. Someone had thought, wisely, from long before that the perfect time to start the New Year was when spring started; a new year, new birth and all that ... so it has always been that March 24 was 'New Years Eve' and March 25 was New Years Day. For example, March 24, 1610 was followed by March 25, 1611 ... it was always done that way for however long. So 170 years after Catholic Europe the British gave in and agreed to adjust the calendars with the new year starting on January 1. September, 1752 saw the new Gregorian calendar take effect in America and England, and the calendar for that month looked like this:
We had to yank 11 days out while Europe only knocked about 8 days out since extra time passed before we finally did it. This, they assured us, plus following the new rules for leap years would keep everything in good shape for quite awhile. The people were a bit unhappy though and riots broke out demanding "Give us back our 11 days".
I no longer have the source of the original document, so cannot provide an attribution for it - If you are the original author please let me know so that I can provide an acknowledgment.
31 December 1750 was followed by 1 January 1750
24 March 1750 was followed by 25 March 1751
31 December 1751 was followed by 1 January 1752
2 September 1752 was followed by 14 September 1752
31 December 1752 was followed by 1 January 1753