THE JASON VOYAGE; The Quest for the Golden Fleece. By Tim Severin. Simon and Schuster. 263 pp. $18.95.

THE QUEST for the golden fleece, the Argonauts' voyage from Greece to the far eastern shores of the Black Sea, was already an old story for Homer's audience; when Circe, in The Odyssey, charts Odysseus' course for home, she mentions the Argo as "known to all." The version of the story Homer and his audience knew has not come down to us; the earliest connected account we have was written much later, by the Alexandrian poet Apollonius of Rhodes, some time in the 3rd century B.C. His epic poem, The Argonautica, describes the voyage out in great detail, rises to an emotional climax with Medea's love for Jason and her decisive role in his success, and then brings the Argo, pursued y Colchian fleets, safely home to Greece by a different route. Some of the adventures of the Argonauts are purely mythical (the two- winged members of the crew who chase the Harpies, for example), but a good many of the geographical details of the voyage out (though not of the return) do seem to correspond to the realities of the terrain.

Most scholars are inclined to believe that Apollonius, who had the resources of the great library at Alexandria at his disposal, was drawing on earlier accounts which, in the distorting mirror of epic imagination, reflected some of the particulars of the Greek colonization of the Black Sea coasts from the 8th to the 6th centuries B.C. -- in much the same way as Shakespeare's Tempest puts to poetic use tales brought back from the waters of the New World by Elizabethan seamen.

The possibility that Apollonius might also have had access to still earlier versions of the saga, to the version known to Homer, for example, and that this version might have been a poetic echo of a real voyage or voyages made in the Bronze Age, before the first millenium, seemed to be ruled out because Bronze Age ships, as far as we can tell from their representations in art, were galleys with no more than 10 oars to a side, and it seemed certain that no such vessel, even with the help of a primitive sail, could make its way through the narrows of the Dardanelles, not to mention the more formidable Bosporus, against the flow of the "Pontick sea, whose icy current and compulsive course ne'er feels retiring ebb but keeps due on to the Propontis and the Hellespont."

Tim Severin, however, who had already followed in the wake of Sinbad the Sailor on a reconstructed 8th- century Arab trader and sailed from Ireland to America in a leather boat like Saint Brendan, decided to build a Bronze Age 20-oared galley, recruit a crew of modern Argonauts and follow Jason's route from Volos in northern Greece to Colchis on the River Phasis, which is now the Rhioni River in the Soviet Republic of Georgia. This enthralling book, written with verve and humor and equipped with maps, plans of the boat and over 70 color photographs, is his record of the voyage.

The modern Argonauts were volunteers who came for the sport; four of them had sailed with Severin on the Sinbad voyage -- 8,000 miles from Muscat to Canton. All of them, to judge from their names, were British or Irish, except for a Norwegian artist, whose evocative sketches are reproduced in the book. Only eight of the original crew went all the way to Georgia; those who had to leave at various points were replaced first by Greek and then by Turkish volunteers. The boat was designed by the naval architect who had furnished the blueprints for the Arab trader and Saint Brendan's ox-hide boat; it was built by a Greek shipwright on the island of Spetses.

Though the modern Argo was equipped with a sail (decorated with images of three Mycenean warriors), it was the back-breaking and blistering labor of pulling on 14-foot oars that propelled her over most of the 1,500 sea miles she had to go; just off Eregli on the Turkish coast, with 46 days behind them and 33 still to go, the Argonauts heard the rowing-master announce the count of 200,000 strokes so far. Yet it was the wind and sail that saved them more than once. As the Argo made her way into the Dardanelles, with only 15 oarsmen aboard and an adverse current that might run up to three or four knots, "we were saved," Severin writes "by the most extraordinary wind, a changing wind that might have been whistled up specially for us." They were equally lucky a few days later; a southerly wind, abnormal for that time of year, gave them the best day's sailing of the entire voyage to bring them out of the straits into the sea of Marmora.

IT WAS NOT all plain sailing, however. They once wallowed for 36 hours, helpless in a Black Sea gale; on another occasion they bare escaped being smashed on the rocks when one of the two steering oars broke. Whenever the wind died or blew against them, they spent hour after hour at the oars, sometimes 11 hours in one day; it was work that Severin himself calls "mindless, repetitive and boring," something "everyone loathed." For compensation they had the enthusiastic welcome they received whenever they came ashore -- in Greece, in Turkey, and most spectacular and overwhelming of all, in Soviet Georgia, where a relief crew of Soviet athletes took over the oars, while the Argonauts were feted, feasted and entertained by dancers and magnificent male choruses.

All through his account of the voyage east, Severin is at pains to try to ground the details of Apollonius' narrative in solid geographical fact, and some of the correspondences between the ancient and the modern ventures, especially those relating to wind and weather conditions, are indeed striking. Other connections however, especially attempts to find modern equivalents for some of the more obstinately mythical components of the ancient poem, are not entirely convincing, and the belief that Bronze Age vessels actually made such voyages has to be maintained in the face of the fact that the archaeological record shows no sign of Mycenean penetration so far east. The heroic endeavor of the modern Argonauts does not prove that a Bronze Age Jason sailed to Colchis but it has certainly proved one important thing -- that he could have. So it was entirely fitting that the Georgians, when they gave their party for the 20th-century Argonauts, provided their captain with a companion for the evening: Princess Medea, "a stunningly beautiful Georgian actress . . . dressed in a pure white Greek costume."