First, the horror-the shaking of the earth, the rain of burning ash, the choking fumes, the screams.

Now, the wonder-the centuries suspended, the Roman past made present, the town, at last, untombed.

Add the poignant details-the watchdog's studded collar, the wine jugs and earrings, the gladiator's dagger, the street signs and toys.

"Pompeii AD 79," the traveling exhibition now visiting Manhattan's American Museum of Natural History, ought to be-but isn't-an eerie, awesome show.

Something dulls its magic. Its objects disappoint even when they glint with gold. They are too crude and commonplace. The daily life that they suggest is as unexalted as our own.

If Sleeping Beauty's sleep is more moving than Rip Van Winkle's, it is, at least in part, because she is a beauty. Shakespeare gives his best lines to valiant warriors, kings, and melodious young lovers; his carpenters and tradesmen are there to provoke laughter. When it comes to being moved by art, most viewers are snobs.

Both the King Tut and Pompeii shows offer a glimpse into the tomb, but only one begins to satisfy our snobbery. The roughly painted pictures produced in Pompeii 1,900 years ago have not improved with age. A rusted iron hammer, even one preserved by the ashes of Vesuvius, remains a rusted hammer. The man who used that hammer was much like you or me. Pompeii was a provincial mercantile port much like any other. The Pompeii exhibition, compared, say to King Tut's is a vulgar, grass-roots show.

The pharoah thought himeself a god, he was rich beyond belief. His jewelers, sculptors, goldsmiths, all accomplished masters, call to mind his cooks. Just imagine what he ate.

The man who dropped that hammer when Vesuvius erupted probably ate sausages in one of Pompeii's wine shops. And if the crude graffiti found there are any indication, he suspected the proprietor of watering the wine.

He might have heard that watchdog growl. He probably liked games, and screamed with raw excitement when the gladiator he'd bet on plunged his trident or his sword into an opponent. He might have played at dice. Perhaps he used the gaming pieces that are in this show.

An erect phallus made of clay or bronze was probably displayed at the doorway of his house to insure good luck. He might have worshipped Isis, Dionysus, Aphrodite, Jupiter, or Pan, or all of the above; he had scores of gods to chose from.

Perhaps he frequented the baths of Marcus Crassus Frugi-a carved marble ad promoting that establishment, put up by one Januarius, the freedom there in charge, is included in this show.

The more we learn about his life the more it seems like ours, and the more is seems like ours, the less we seem to care. So what if he ate sausages while cheeseburges are today's preference, so what if he drank heated wine (we know that from the samovars discovered at Pompeii), while cold beer is a modern-day choice.

Architectural historians, who care about the carved capitals of columns, have learned much from Pompeii. So have archeologists who have sifted throughs its rubbish pits and analyzed its gardens. But the rest of us have more to learn from the surviving books and plays of the Roman dramatists. Our imaginations soar at the story of Pompeii, but this show brings them down. What it lacks is first-rate art.

Suppose that volcano erupted, say, in Maryland, and in two days buried Rockville. If-2,000 years from now-the city was unearthed, would its Coke bottles, its ashtrays, its baseball cards and its rusted iron hammers be displayed as art?

"Pompeii AD 79" first opened in London in 1976. More than a million viewers saw the show in Boston, Chicago and Dallas before it opened in New York. The National Gallery of Art in Washington had a chance to show it, but turned the offer down. It is not hard to see why.

The figurines and statues, oil lamps, toys tools, gaming pieces, cymbals, pots-pans, and glasses, wall paintings and mosaics included in the exhibition are often curious, often touching, but only rarely beautiful.

The hallows left by corpses buried in the ashes have been cast in plaster, and their postures tell sad tales, butwhy go to museums to consider death? All of us will die, our possessions will be scattered, our technologies superseded, our houses will decay. Everybody knows that. The specialists who study the history of Italy have learned much, and will learn yet more, from the ruins of Pompeii, but the 350 objects clunkily installed at the American Museum of Natural History, those saddening souvenirs, together tell us something we already know.

There is a "discretionary admission fee" of $1.50 for adults and 75 cents for children at the New York museum. "Pompeii AD 79" is scheduled to close on July 31. CAPTION: Picture 1, Theater mask of marble from Pompeii; Picture 2, Pompeii hammer from one piece of iron