Variations in the Earth's Rotation
     Because of its rotation, the Earth has a certain angular momentum, which in the absence of any external interference, must remain constant (in physics this is referred to as the "conservation of angular momentum"). Its numerical value is the sum of the angular rate of motion of each part of the Earth multiplied by the mass of that part (times a constant which depends upon the units used), and if everything stayed where it is, not only would the angular momentum remain the same, but also the angular rate of motion, which can be expressed as some fraction of the sidereal period of rotation, or the rotation period of the Earth relative to the background of the stars (this is slightly different from the length of the day, as discussed in the page on Rotation Period and Day Length).
     However, everything does not remain exactly the same, for various reasons. For one thing, seasonal variations in the weather can change the distribution of air masses in the atmosphere, and currents in the ocean also have changes during the seasonal year, so sometimes there is a little more air and/or water nearer the Poles, and sometimes a little more near the Equator. Movement of mass toward the Poles means that it doesn't have to go eastward as fast to keep up with its surroundings, and frictional interactions with those surroundings transfer the excess motion of the mass that moves toward the Poles to the rest of the material in the atmosphere and oceans, causing the Earth as a whole to rotate slightly faster. Conversely, if more material moves toward the Equator, the transfer of motion (and momentum) from the rest of the Earth to that material causes the Earth as a whole to rotate slightly slower. The change in the rate is measured in tenths of thousandths of a second per day, but over the course of a season the effect can add up to a few thousandths of a second, which is easily detectible with modern technology. Similarly, if there is a large-scale eruption of material on the Sun that throws material at the Earth, the upper atmosphere of the Earth can be greatly heated and expand outward, toward outer space. The fact that it is now further from the axis of rotation of the Earth means that it has to go around the Earth faster to keep up with it, and its interaction with the lower atmosphere can produce changes in the overall rotation rate of a few ten thousandths of a second in periods as short as a few days.
     The changes discussed in the preceding paragraph are completely reversible, and do not produce long-term changes in the rotation of the Earth. As one season follows another, the effects of seasonal changes in one season are reversed by the effects of seasonal changes half a year later. As interaction with Solar gases ceases, gases in the upper atmosphere gradually cool, return to their normal locations, and the minor effects caused by their displacement disappear. But there are other changes that tend to be more permanent.
     One example, which is often in the news when a very large earthquake occurs, is the effect of a vertical displacement of material in the Earth. Every now and then you can read about a powerful earthquake changing the rotation of the Earth by a few millionths or billionths of a second, because of the upward or downward displacement of material as a result of the earthquake. Such news reports are interesting, but not really important, as the change in the rate of the Earth's rotation due to such causes is too small to measure in any way; so it is only mentioned here because sooner or later you are bound to hear something of the sort, and it doesn't hurt to know that it is not earth-shaking news.
     However, there are vertical displacements that do have noticeable effects. For instance, a little over ten thousand years ago much of the far Northern Hemisphere was buried under as much as three miles of ice, substantially depressing the surface of the Earth beneath the ice. Once the Ice Age ended, the ice melted and the previously buried landscape began to rebound. It is still doing so, and over the 2500 or so years for which the Earth's rate of rotation can be determined from historical accounts, that rebound has tended to slightly increase the rate of rotation of the Earth. But though this has been a one-way effect during recorded history, we live in an Ice Era in which Ice Ages and Interglacial Periods are expected to alternate at not entirely irregular intervals, and sooner or later the Earth will enter another Ice Age, and as the land beneath the new ice caps is once again depressed, the rotation of the Earth should gradually return to its "original" rate. (There are also similar effects due to vertical motions of not quite molten material in the mantle of the Earth, but they are not as easy to see or to measure.)

Tidal Slowing
     As noted in the previous section, the effects discussed there are more or less cyclic, and cannot be expected to produce long-term permanent changes in the distribution of mass on or in the Earth, or in its angular motion. However, there is a very significant interaction between the Earth, Sun and Moon that causes a more or less continual slowing of the rate of the Earth's rotation, referred to as tidal slowing because it is the result of the gravitational force of the Moon (and to a lesser extent the Sun) on the tidal bulge raised in the oceans and body of the Earth by the Sun and Moon. How this works is beyond the scope of the relatively simple discussion meant for this page, and will be covered in a future page on Tidal Slowing, but to summarize, (1) as the Earth rotates to the east the Sun and Moon seem to move around the sky to the west, more or less the same as everything else in the sky. (2) Since the tides in the oceans and body of the Earth are more or less aligned with the direction of the Moon (since it is twice as important as the Sun in raising tides), as the Moon moves westward in the sky the tides in the oceans and body of the Earth move westward around the surface of the Earth, or in the opposite direction as the rest of the Earth. (3) Because of this, frictional forces between the tides and the rest of the Earth (about half of which takes place in the body of the Earth, about half in the deep oceans, and the rest in regions where we see tides at the surface) are gradually pushing the Earth westward, thereby slowing its eastward rotation. The amount of this slowing is very small, amounting to about one or two thousandths of a second change in the length of the day over periods of a century of so. Still, over very long periods of time this can add up, so that (for example) about five thousand years ago, when the first pyramids were being built, the Earth was rotating about 1/20th of a second or so faster than now. There is no way that ancient timekeepers could have measured the length of the day or the rotation of the sky accurately enough for us to find direct evidence of this in ancient records, but there are records of ancient solar eclipses which tell us that the cumulative effect of the slowing during the 2500 or so years for which we have reasonably accurate historical records has reduced the amount that the Earth rotates to the east by about a fifth of a rotation. In other words, if the Earth were still rotating at the same rate as it did 2500 years ago, it would have rotated an extra fifth of the way around (or about 5000 extra miles) in addition to all the rotations it accumulated during that period. We can tell this by looking at records of where eclipses took place in the past. In the 1600's there was an eclipse of the Sun in which the shadow of the Moon passed right through London. A survey of the houses and blocks where a total eclipse was visible was carried out at the time, so we know exactly how the surface of the Earth was aligned at the time of the eclipse, and if we compare where the eclipse was visible to where it would have been visible if the Earth had been rotating at its current rate throughout the several hundred years since that time, we find that the shadow was many tens of miles away from its "proper" location. Similarly, eclipses that we calculate should have been visible at some particular place 2500+ years ago were actually observed at places thousands of miles away. Such comparisons show that the rate of slowing has been roughly the same as the current rate throughout recorded history, and geological data indicate that similar slowing has been going on throughout the entire history of the Earth.
     Of course, if the Earth's eastward rotation has been slowing throughout its history its angular momentum must have been decreasing, and at the start of this discussion I said that angular momentum must be "conserved". But there is no problem with that, as it turns out that the "lost" momentum is transferred to the orbit of the Moon, and as a result the Moon is gradually increasing its distance from us at a rate of a couple of centimeters or so per year, and in a few tens of millions of years will be so far from us that it will always look smaller than the Sun, and total eclipses of the Sun will be impossible. Going in the other direction in time, the Moon must have once been much closer to us than now, and in fact it is thought that when the Earth and Moon were formed they were at least three times closer than now, and probably considerably closer than that. However, again, that is a topic for another page.

Why We Need Leap Seconds, And How They Are Used
     But if the Earth is and has been slowing throughout its history, then the length of the day is gradually getting longer, and the 86,400 seconds in an average day must be gradually increasing. This means that over time we will need more seconds in each day, or at least some small fraction of an extra second (based on the previous section, about an extra couple of thousandths of a second more each day about a century from now). However, adding some extra fraction of a second to the length of each day feels ridiculous, and would certainly be inconvenient and impractical. So astronomers have settled on the concept of "leap seconds" for reconciling the gradually lengthening period of one day with a fixed number (86,400) of fixed-length seconds (the second being defined as an exact, specific amount of time in modern physics). Namely, as the Earth gradually changes its rate of rotation, and its eastward motion gradually gets "out of sync" with the fixed number of seconds in a day, when the difference between the two becomes larger than half a second we add a second to our clocks before going on to the next day. This is always done at midnight on the evening of June 30/July 1, or at midnight on the evening of December 31/January 1. On such occasions, a clock reading UTC (Coordinated Universal Time) 23:59:59 would be followed by 23:59:60, before going on to 00:00:00 of the next day. This method of adding seconds was instituted in 1972, and by early 2015, twenty five "leap seconds" had been added to clocks in this way (and another addition was scheduled for June 30, 2015 at the time of this writing). It is also conceivable that due to the more changeable variations in the Earth's rate of rotation we might need to delete a second, in which case UTC 23:59:58 would be followed by 00:00:00, thereby excising the second in between; but this has not occured in the 43 years so far.
     Most people have no need to know the time between events years or tens of years apart to accuracies of a second or better, but some people (primarily astronomers) do, and for their sake a running count is kept of the discrepancy between time as defined by a constant rate (namely, the rate of rotation of the Earth in 1900) and time as defined by the current orientation of the Earth's surface in space. At the moment, the difference between the two is a little over a minute (since it is only based on about a century of gradually slowing rotation), but over very long periods of time the discrepancy will continue to grow, at a gradually accelerating rate (since the size of the error in the 86,400 seconds used to define a day and the actual length of a day is gradually increasing); and the fact that eclipses that took place thousands of years ago took place a third of the way round the globe compared to where we would have expected them to be seen means that during that time, the fraction of a 1/20th of a second error per day, multiplied by the huge number of days involved, amounts to about 8 hours (a third of a day).

(The above was written in about an hour as the result of the discovery that a page I thought already contained a discussion of this topic didn't actually address it at all. As a result, though hopefully reasonably clear and complete, I doubt it would remain exactly the same if I had the time to carefully edit it for accuracy and readability. A cursory reading revealed no obvious errors, but I will return to this page, carefully edit it and add some diagrams and tables at a hopefully not much later date. In the meantime, if you have any questions about or difficulties with the material as presented, please feel free to contact me.)