I recently received a mail from a site visitor, who had discovered from Boswell's original birth certificate that he was actually born on October 18, 1740, and not on October 29, 1740, as is generally thought. There is, however, a perfectly good explanation for this apparent discrepancy.
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The actual change-over in the U.K. took place on the day following September 2, 1752 - which was September 14 instead of September 3. The year 1753 was the first to fully follow the Gregorian calendar.
For Boswell, this meant that while his birthday was on October 18, 1740, according to the Julian calendar, it was 11 days later - on October 29, 1740 - according to the Gregorian calendar. This is sometimes marked as October 18 (O.S.), October 29 (N.S.) for Old Style (Julian) and New Style (Gregorian) respectively.
It is therefore entirely correct when the original birth certificate states the birth of James Boswell as being October 18, 1740, which it was according to the Julian calendar then in use. And it is equally correct when modern sources state it as being October 29, 1740, which it is in accordance with the Gregorian calendar now in use.
It should also be noted, that the question of calendars has no major relevance to Boswell's personal papers and journals, as these were of course, with the possible exception of a few letters, entirely written after 1752.
There are a few references to the matter in The Life of Johnson where it is written for the year 1752 that "on the 17th of March, O.S., [Johnson's] wife died." Slightly further on Boswell quotes from the first entry of Johnson's diary for the year 1753: "Jan. 1, 1753, N.S. which I shall use for the future."