• Three pictures with a short explanation of what leap seconds are about and why they cannot have a schedule.
• The legal number of elapsed seconds since 1972
• In 1955 the duration of one second was redefined to be unrelated to the duration of one day
• One person who suggested the idea of leap seconds also pointed out that leap seconds would cause problems for automated systems. Before the first leap second happened he explained that USNO time systems would not use leap seconds.
• a calendar of the ITU-R process of attempting to abandon leap seconds in UTC
• A history of precision time scales
• Plots and tables of length of day and ruminations thereon
• Plots of differences between time scales over long history
• Correct precision handling of leap seconds using code already on POSIX systems
• Plots of differences between time scales at year 2100
• time scales have a choice of goals -- pick any two of three
  But which two? A look at where the decision processes went wrong.

The reduction of Heures définitives to a uniform system and to the mean pole of the epoch

Bulletin Horaire series H number 2 page 43

Other web pages about Bulletin Horaire

Bulletin Horaire was the regular publication of the Bureau International de l'Heure (BIH, International Time Bureau). Nicolas Stoyko served at and ran BIH for four decades, and his wife Anna Stoyko also served there. Before they retired in 1965 they summarized 42 years of data published by BIH. See here for more views of their summary data.

From inception the BIH was tasked with the difficult problem to make sense of observations of time from around the world and try to combine those into an improved estimate of what time it had been. The data were monstrously heterogeneous.

• Each observatory had limited opportunities to make observations due to its own weather.
• Each observatory had its own unique clocks for recording observations, and the number and quality of those clocks changed over the passage of the decades.
• Some observatories had only one clock of poor quality while others had arrays of the best quality clocks.
• Some observatories had direct electrical connections to control radio broadcasts of time signals while other observatories had a single radio for receiving radio broadcast time signals from other sites.
• Some observatories had various pen and smoke recorders to make reviewable records for comparing arrival times of radio signals while other observatories only had a human straining at faintly audible tones from far away broadcasts.
• Short wave and long wave radio signals propagated at different speeds and over different paths.
• Each observatory used different methods for combining the time values of their clocks and interpolating across intervals when the clocks were not working.
• Each observatory used different equipment with different systematic errors and different humans with different "personal equations".
• From one year to another different observatories participated, stopped participating, and changed their observers and equipment.
• Over the decades observatories changed their algorithms for reducing observations and changed systematic corrections to their time values, sometimes without informing BIH.

Nicolas Stoyko joined the BIH in 1926 and by 1931 he had created an algorithm for combining the heterogeneous data into a "mean observatory". Starting with 1931 the BIH published Heure définitive of the mean observatory as the best estimate of what time it had been and how much each of the contributing observatories had deviated from that mean. The calculation of the mean observatory was performed using all of the data for a calendar year. As observatories, equipment, people, and worldwide events changed, the mean observatory varied from one year to the next. This means that the final tabulated values of Heure définitive for each year could be in a different reference system than any other year.

At various points in the history of the BIH the Bulletin Horaire published tables of the estimated systematic offsets between the tabulations of Heure définitive in different years. In 1964 Anna Stoyko reviewed the tabulations of Heure définitive for each year from 1931 through 1963 and published tables required to calculate the systematic offsets.

The BIH 1962 system for Heure définitive

Note that even after the advent of atomic chronometers there were still shifts over a range of 5 ms between the time systems of one year and another.