This evening, just about the time you're thinking about heading out for the New Year's celebration, when nobody's paying too much attention to the time, they're going to slip another second into the day: a leap second.

Normally, clocks would go from 6:59:59 p.m. to 7:00:00. But this year, time will go from 6:59:59 to 6:59:60 to 7:00:00. (Midnight, actually, in Greenwich Mean Time.) A leap second will have been inserted just to get time back into line.

It turns out that the earth is not quite as predictable as folks would have you think. For one thing, the earth has been slowing down slightly "for some centuries now," according to Alan Fiala, an astronomer at the U.S. Naval Observatory off Massachusetts Avenue.

The earth is not, as they say in the astronomy business, "a constant rotator." Tides and a little atmospheric drag keep things from coming off like . . . clockwork.

Over at the observatory they have atomic clocks that use cesium atoms to measure time. Cesium atoms are used, according to another astronomer - Donald Percival - because they emit a known frequency under certain conditions.

But our crowded little planet here, going on its unending voyage around the sun, doesn't always show up on time (as measured by atomic clocks) for reasons already mentioned. So, when things get more than half a second out of whack, the people who watch the clock all over the world get together and agree on inserting a second to get things back on schedule. Thus, tonight they'll be slipping in a leap second.

Some relevant statistics: In 1976, a leap second was also inserted on Dec. 31. The same thing happened the year before. In 1972, two leap seconds were inserted - one on June 30 and the other on Dec. 31.Before 1972 they inserted tenths of seconds. The last year to come off with the right number of days, hours and seconds was 1965, then there were no leap seconds.

Tenths of seconds are nothing in the big scheme of things. Those who specialize in the measurement of such things have identified micro-seconds (that's a millionth), nano-seconds (which is a billionth) and now femto-seconds (that's a millionth of a billionth of a second). This may all seem a little unncessary to someone boiling an egg, but it's useful information anyway.

One hesitates to bring up the next point, which is off the point but on the same general subject. It's about sunrises and sunsets.

The Naval Observatory publishes a table of sunrises and sunsets, giving the times for every day of the year. The table is of interest primarily, one supposes, to personal injury lawyers involved in litigation over auto accidents, fishermen (and fisherwomen), Orthodox and Conservative Jews wanting to know when holiday observances begin, pilots, etc.

The table has a little caveat on the back:

"This table . . . may be used in any year of the 20th century and within the geographical boundary of the stated place with an error not exceeding 2 minutes and generally less than 1 minute. It may also be used anywhere in the vicinity of the stated place with an additional error of less than 1 minute for each nine miles, reckoned from the station of the U.S. Weather Bureau for the stated place . . ."

The tables are figured out mathematically. They are figured down only to the minute, but that isn't the point. In you really want seconds, you can get them. The point is - they don't check the tables!

"Not that I know of," Fiala said, when asked if the tables had ever been checked. "I don't know that anyone's gone out with the table" to check it. "The time of sunrise and sunset in any particular time and in any particular location does not vary more than a minute or two in any century."

Fiala acknowledged, however, that terms like "sunrise" and "sunset" were pretty imprecise.

"The instant of sunrise and sunset said. "You can only measure it within two or three minutes because it depends on things like local terrain, atmospheric conditions, vegetation.

"To compute a sunrise," Fiala said, "you have to define what a horizon is." A perfect sunrise would take a flat horizon, unobstructed and a clear sky. "In real life, you just never meet these conditions." And that's the kind of problems they run up against in trying to be more precise.