[LEAPSECS] the inception of leap seconds

[Michael Deckers]

    On 2018-08-15 11:49, Zefram wrote:


> Time Service Announcement 14 #8 (1971-10-08) discusses the irregular
> leap (still called a "step") at the end of 1971, but weirdly gives a
> different size for that step from that which is implied by tai-utc.dat.
> The announcement states a step size of 107600 us, but the expressions in
> tai-utc.dat imply a step size of exactly 107758 us.  The announcement is
> .... The 107758 us computed from tai-utc.dat is in microseconds
> of TAI, and the leap is only a few nanoseconds shorter in UTC.


    I cannot explain the -107.6 ms jump of the Announcement; but
    the 1992 "Explanatory Supplement to the Astronomical Almanac"
    contains jumps of WWV on p 86..87 that are not in tai-utc.dat.
    Anyway, I also think that the jump of UTC(USNO) did not happen
    when TAI was 1972-01-01 + 10 s, as implied by the Announcement,
    but a bit earlier. See below.


> .................  The announcement is
> ambiguous as to whether this step size is specified in microseconds of UTC
> or of TAI, apparently ignoring the UTC frequency offset for this purpose,
> though the offset isn't anywhere near big enough to account for the
> discrepancy.


    While UTC is defined to be a piecewise linear function of TAI,
    the practice was (and still is) to specify TAI - UTC (and thus TAI) as
    a piecewise linear function of UTC. The "steps" specified in
    Bulletin C are steps in TAI - UTC, hence also of TAI, as a function
    of UTC -- which probably is what you mean by "microseconds of TAI".

    Time Service Announcement 14 #8 of 1971-10-08 is no exception: it gives
    TAI - 10 s - UTC(old) as maintained by the USNO as a function of 
UTC(old),
    where UTC(old) is the unique linear extension of UTC as defined directly
    before 1972-01-01. Thus, the member  2 592 (MJD - 41 317)
    has to be read as                    2 592·(UTC(old) - 
1972-01-01)/(1 d).

    The inverse relation to UTC as a function of TAI is not a function: UTC
    assumes some values twice, for different values of TAI (when UTC makes a
    jump down); and UTC did not assume some values (when UTC made a jump up,
    as it last did around 1968-02-01). So TAI is a sometimes two-valued
    (positive leaps) and sometimes undefined (negative leaps) "function"
    of UTC, and it is not always clear where it differs from the function
    TAI of UTC that is officially specified.

    The discontinuity of UTC near 1972-01-01 is an exception because the
    jump up of TAI - UTC from 9.892 242 s to 10 s was accompanied by a
    jump in the (piecewise constant) rate d(TAI)/d(UTC) from 1 + 2.592 ms/d
    down to 1 (the only case where both TAI - UTC and d(TAI - UTC) have been
    discontinuous). Here we do know that a jump of UTC from 1972-01-01
    to 1972-01-01 - 0.107 758 s must have happened when TAI was
    1972-01-01 + 9.892 242 s. At any other value of TAI between
    1972-01-01 + 9.892 242 s and 1972-01-01 + 10 s, the jump in phase
    would have been by a different amount, and not by an integral multiple
    of 1 µs.

    HTH

    Michael Deckers.