Egyptian mummies, royal goblets from ancient Troy, a cast of the Code of Hammurabi, Greek vases, photos of Ice Age paintings 17,000 years old, a picture of the crumpled victims of Pompeii, the King of Judah's ring . . .

The kind of exhibit that you never finish looking at will open today in the Smithsonian's National Museum of Natural History. With a walth of materials, some of them stored away for decades in the Institution's cellars, the display ingeniously tracse key "Origins and Traditions" of Western civilization.

From Camp to Village, Village to City, City to State and State to Empire the progress of early peoples is deduced from the things they left behind, the scraps of business transactions on shards of pottery, the relics of ritual, the search for beauty that is evident from the most remote times in bead bracelets and paintings.

Like other recent Smithsonian exhibits, it dramatizes the 10,000 square feet of space allotted to it. There are lifesize dioramas with human figures depicting daily life in antique lands. There is a mockup of an ancient dock with ingots and amphora and ivory tusks piled on a wharf. There is a complete little bazaar straight out an Arabian Nights movie. There is an Italian peasant kitchen with Roman-style implements and a Roman cookbook.

. . . prehistoric hoes, clay tablets in clay envelopes, Roman glass, Diocletian's price control laws, ancient coins, Etruscan figurines, a mouse's jawbone, a 7-foot squars mosaic from Carthage, business letters on papyrus.

The show, the seventh in a series of new projects at the Institution, was put together by Robert K. Evans, an archeologist, and Brian Hesse, an anthropologist, and it bears the stamp of their serious approach to the subject. A huge amount of information is packed in among the spectacular visals, the filmstrips (an animated version of the Gilgamesh epic, for instance) and the dioramas.

The shift from hunting to farming is shown through artifacts and other evidence of the domestication of goats and barley. The birth of writing, apparently made necessary by the commerical and political demands of the ever-more-sophisticated city-state, is traced in fascinating detail.

There is a whole room on acient Troy, featuring many of the 100 objects that found their way to the Smithsonian after the death in 1890 of Heinrich Schliemann, the famed amateur archeologist who found what had always been believed to be merely a mythical city.

These relics are especially important to Trojan scholars now because the great bulk of the Troy discoveries, including the golden crowns and medallions, was lost during World War II in Berlin.

. . . a mummified crocodile, a mutilated bull, a mummified cat, a Fayum grave mask, a stone Etruscan spirit-boat, a chart of the wholesale trade in obsidian, an ancient Turkish saddle given to Teddy Roosevelt, a magnificent model of the Acropolis, a metal forge from King Solomon's time, Stone Age axes, wild barley grown by Smithsonian scientists, Celtic drawings . . .