The National Museum of American History has never figured out whether its mission is to chronicle our civic arrangements or to serve as a trash can of popular culture. With "On Time," its quirky new millennial eve exhibit about clocks, calendars and how we measure and apportion time, it manages to do both.

But as engaging as the exhibit is, it demonstrates precisely the sort of bizarre choices that, year in and year out, make American History the most exasperating museum in the Smithsonian family.

Why, for example, would any museum with a pretense of seriousness devote vast display space to the impact of the Mickey Mouse watch and barely mention that of the marine chronometer, which made possible the calculation of longitude and the accurate navigation and mapping of the globe?

How could the exhibit never mention the excruciating Cold War role of time in the inertial guidance systems for nuclear missiles? After all, in a weapons system in which time equals distance, if your watch is off, your missiles fall on the wrong people, among other difficulties.

These are not small considerations, either in the development of timekeeping or in that of American history, and one is tempted to infer dark motives on the part of Timex Corp., which underwrote virtually the whole 4,000-square-foot exhibit. But clearly that would be senseless. In fact, Timex so understates its role that we don't even get a film clip of John Cameron Swayze torturing a timepiece that "takes a licking and keeps on ticking." If that isn't part of American history, what is?

What's best about "On Time" is the way it makes us think in new ways about aspects and objects of daily life. Few may remember, for example, that the word "clock" comes from the German word for bell. The first clockwork mechanisms were built in the 13th century, not to show the hour but to toll bells at regular intervals to better regulate the rhythms of urban life and "symbolize community wealth, civic order and modernity."

It would take another century before the big hand and the little hand made their appearance. Meantime, the exhibit asks us to consider why we began measuring time at all. For thousands of years, mankind was content to regulate time by appetite or the need for sleep or by the changing length of days or the cycle of seasons. The Babylonians and the Egyptians adopted the convention of dividing the day into 24 hours with two 12-hour segments, but it was a fairly approximate process, depending as it did on sundials and other instruments of inexactitude.

Clocks came with town life, and they took a big leap forward in the 18th century with Sir Isaac Newton and the concept of the clockwork universe.

One of the more dazzling artifacts in "On Time" is a four-face mahogany-case clock built in 1769 by one Joseph Ellicott, a millwright, sheriff and state assemblyman from Bucks County, Pa., who later moved to Maryland, where he gave his family name to Ellicott City.

The clock, which remains in excellent order, not only tells time and shows the phases of the moon and planets, but also plays 24 music box ditties, one each hour, ranging from "The Hounds Are All Out" (1 p.m.) and "God Save the King" (4 p.m.) to "Dear Cloe Give Me Sweet Kisses" (9 p.m.) and "A Plague on Those Wenches" (11 p.m.).

One would think such an instrument would be the timepiece of the ages. The French, however, can never leave anything alone, and so we have displayed an even more intricate Berthoud Freres timepiece from the 1790s. In the same spirit of overthrowing the old that gave the guillotine so much employment, the French attempted to make time metric. They divided the day into 10 100-minute hours and the year into 12 30-day months (each divided into three 10-day "decades"), with the arbitrary addition of five extra days at the end of each year, plus an additional day each leap year.

For some reason, this system never caught on.

In those days, as in ours, timepieces were a sign of wealth and status. Watches wouldn't be widely mass-produced until the 1880s. As long as the United States was an agricultural country, most people didn't need clocks and watches. Each farm moved to its own rhythm.

After 1820, however, the Industrial Revolution depended on getting crowds of workers to the same place at the same time. Time became not only a convention but a discipline, particularly crucial to "civilizing" children and pre-industrial immigrants.

Not for nothing the weighty importance of "making the trains run on time"--a realization that was underlined on Aug. 12, 1853, when two trains attempting to use the same stretch of track near Pawtucket, R.I., ran head-on into the shortcomings of inaccurate timekeeping. And each other.

From 1920 to 1960, the exhibit informs us, Americans were obsessed with using time efficiently. Since then we've been trying to expand time, splitting it into billionths of a second, perhaps to give us the illusion we have more of it.

Well, maybe and maybe not.

The truth is that a computer-driven digital age depends on timekeeping exactitude to such an extent that since 1967 the length of a second has been defined as how long it takes an atom of cesium 133 to vibrate 9,192,631,770 times when subjected to electromagnetic waves.

Atomic clocks help us do that. We even add leap seconds to the national atomic clock every few years. What precision!

So how is it we missed the need to tell our computers next month what century it is?

"On Time," alas, doesn't tell us.