On Jan 13, 2006, at 8:05 AM, Ed Davies wrote:

MJD 27123.5 means 12:00:00 on day 27123 if it's not a leap second
day, but what does it mean on a day with a positive leap second?

And we're back to the point in question.  The precise issue is the
definition of the concept of a "day".  A leap second itself is a
clearly defined moment in time.

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