Another reason I need to revisit the original Bishops Transcripts of the Llangar parish registers, is to clarify the meaning of dates such as "1750=51".
I have been advised by a knowledgeable friend that the answer lies in the history of the British calendar, as described (for example) in "Ancestral Trails - The Complete Guide to British Genealogy and Family History" by Mark D. Herber (in association with the Society of Genealogists).

Dates recorded before 1752 can be confusing. From about 1190 until 1 January 1752 the Julian calendar was used in England and each new year began officially on 25 March, Lady Day, rather than on 1 January. Therefore, the year 1750 began on 25 March but ended on 24 March of the year that we would now call 1751. Consequently, dates that are noted in old records in January, February and up to 24 March 1750, were actually recorded in 1751, months after 25 March 1750 or 1 April 1750, for example.
Lord Chesterfield's Act of Parliament in 1751 replaced this calendar with the Gregorian calendar which was already used in Scotland and most of Europe. The year 1751 commenced, as in previous years, on 25 March 1751, but ended on 31 December 1751 so that 1752 and subsequent new years then started on 1 January. On this basis, any date in January, February, or 1-24 March in any year up to and including 1751 needs to have its year increased by one.

1. The new year in Saxon and Norman records began on 25 December rather than 25 March or 1 January.

2. Books or documents written after 1752 often apply the new style of calendar with the year going from January to December, when referring to dates before 1752 but then some do not. So a reference to 20 March 1700 might be in the old-style, that is in the last month of the year that began on 25 March 1700 but would nowadays be in the year 1701. Or, alternatively, 20 March 1700 might be a revised new-style reference to 20 March 1169 on the old style calendar but with a 1 added to the original written year. Thus if old-style or new-style is not clearly stated on the record, you can never be sure what the year was.

3. Even before 1752 some people already considered that the year began on 1 January, rather that on 25 March, and they often noted dates in records prior to 1752, in the form 1 January 1730/1 or 1730-1 or 1730=31, as in the Llangar transcripts. One should always indicate in one's notes whether a pre-1752 date is old style (OS) or new style (NS), or perhaps record the date in both styles to avoid future uncertainty. For example, a date could be recorded as February 1749/50 to show that the date was in February 1749 (old style) but in February 1750 (new style).

The Julian calendar was also eleven days out of step with the Gregorian calendar, due, I believe, to accumulated inaccuracies such as the missing leap years. When it was 28 June in Scotland it was only 17 June in England. In order to bring England into line with Europe and Scotland, eleven dates (3-13 September) were omitted from September 1751 in England and Wales, so that 14 September followed 2 September.

But even that is not the end of the problem with the Llangar bishop's transcripts: on some pages the year is not specified, so one has to go by the page sequence - but as some pages are out of sequence, one can't be sure.

Source:
"Ancestral Trails - The Complete Guide to British Genealogy and Family History" by Mark Herber, second edition published 2004 in association with the Society of Genealogists by Sutton Publishing Ltd., Stroud, Gloucestershire; ISBN 0-8063-1541-5 (hardback)
obtainable through the UK Society of Genealogists website at http://www.sog.org.uk/.

- 1st December 2000

[Source citation updated 21st September 2004 by John Ball]