• The legal number of elapsed seconds since 1972
• My effort to track the process of attempting to abandon leap seconds
• A history of precision time scales
• Plots and tables of length of day and ruminations thereon
• Plots of differences between time scales
• How to keep your POSIX kernel from having to leap

Plots of the time dilemma

What nature does, and what time providers must handle

The plot below shows the variability of the rotation of the earth and the challenge that it poses to time keepers who are tasked with keeping clocks set to agree with the ongoing count of days in a calendar. Note that the earth sometimes spins slower, and sometimes spins faster. The variations are basically due to weather in the atmosphere, oceans, and core of the earth. This is why there cannot be a leap second schedule, for issuing a schedule of leap seconds would be like making a schedule of the weather.

The insertion of leap seconds is required by international agreements.
The number of leap seconds which must be inserted into UTC is proportional to the shaded area under the curve.

What humans do, and what time consumers must accept

People like to agree on the answer to the question

What time is it?

In order to set all clocks to the same time at a nanosecond level there must be some agency in charge of deciding what time it is, and there must be mechanisms for distributing that time from the time producers to the time consumers. Radio broadcasts of time signals have long been the most common mechanism, and consumers do not have much choice about how they get their time.

The plot below shows the kinds of time which have been used internally by physicists and astronomers along with the kinds of time which have been available to the general public.

• The descending line is time according to clocks that are set to agree with the rotation of the earth. It is the kind of time which results from subdividing calendar days into hours, minutes, and seconds.
• Horizontal lines are from chronometers ticking atomic seconds that have no relation to the rotation of the earth, no connection to the count of calendar days.
• The blue line is the kind of time which has been broadcast as the basis for legal and civil time. In 1972 that was changed to have leap seconds.
• A little known fact is that computing devices, phones, tablets using the Android software internally use GPS time, not UTC.

What humans used to do, and why reconstructing the past is a mess

Prior to the era of coordination every agency responsible for broadcasts of time signals reset its clock as needed in order to keep the broadcasts in agreement with earth rotation. From the beginning it had been inconceivable that the radio broadcasts could be allowed to differ significantly from earth rotation. The following plot shows the behavior of time signals broadcast by the US NBS which made 29 leaps during 3 years. In constrast with the plot above where flat means uniform, the following plot shows UT2 as flat, and atomic time as slanted curves with leaps.

The US and UK agreed to coordinate their broadcasts of time signals in 1959 August, and coordination began on 1960-01-01. Prior to that date these sorts of steps or leaps were inserted regularly into all time scales, and each national agency responsible for broadcasts of time signals added steps of different sizes at different times. Prior to atomic chronometers there was no easy way to make a record of the steps or a plot like this because there was no chronometer more stable than the earth.