It has been more than 300 years since the first William Byrd arrived in Virginia, and more than 50 years since one of his great-great-grandsons founded the state's long-dominant political machine. For decades, the Byrd name has been a symbol of entrenched tradition, fiscal conservatism and racial tension in the Old Dominion.

Over the years, the end of the Byrd era has been repeatedly declared: with the downfall of racial segregation, which had been espoused by the Byrd family; with the Senate retirement and death of Harry Flood Byrd Sr.; with key defeats for Byrd candidates around the state, and with the switch by Byrd's son, Harry Jr., from Democrat to Independent.

Yesterday, when Harry Byrd Jr. announced his plans to retire from the Senate seat he has held since 1965, an epoch of the state's history appeared to be ending. Soon, for the first time in half a century, there will be no Byrds in public office in Virginia, and political analysts again were quick to proclaim the end of the Byrds' influence.

"His retirement will mark the end of an era in Virginia," said Linwood Holton, a former Virginia Governor. "It was a personal era. The name Harry Flood Byrd runs through two generations now."

"The Byrd name outlasted the Byrd machine," said J. Harvie Wilkinson, a University of Virginia law professor and Byrd biographer. "It is still resonant of the values that Virginians held dear: tradition, conservatism and integrity."

Even with yesterday's announcement, there were hints of an attempt to revive the family's power. Winchester Star publisher Thomas T. Byrd, stood with his father at yesterday's Richmond news conference, and the 66-year-old senator expressed hope that one of his sons would carry on the family political tradition.

To many Virginians, Sen. Byrd was indistinguishable from his father, a farmer who parlayed an apple farm into a million-dollar business. Both men espoused limited government, and were tight-fisted advocates of balanced budgeting.

Nevertheless, Harry Byrd Jr., a millionaire newspaper owner and apple farmer, is widely regarded as lacking much of his father's personal dynamism and political clout. As a Virginia state senator, he served chiefly as one of his father's lieutenants. In the U.S. Senate, he has been viewed as a low-profile loner with no Senate power base. Unlike his father, he made no attempt to dominate the workings of Virginia's state politics.

Even some of his admirers question Byrd's recent political influence. Since his reelection in 1975, says conservative analyst Paul M. Weyrich, "he really hasn't done much . . . He has offered very little by way of amendments. He has participated very little by way of floor action. He has offered very few bills."

Byrd's long-time senate aide, Jack Brooks, put it this way: "He visualized himself as being a somewhat lonely warrior in reducing government spending and centralization of power in Washington."

Eight generations of Byrds preceded Harry Jr. in Virginia. William Byrd I came to the New World in 1670. William Byrd II founded Richmond. William Byrd III reputedly wasted the family fortune. Sen. Byrd's grandfather served as speaker of the state's House of Delegates. His father was governor, then senator; and an uncle, Admiral Richard E. Byrd, explored Antarctica.

It was Harry Byrd Sr. who built the foundation of the family's financial and political stature in modern Virginia.

For much of his life, his son, known as "Little Harry," stood in the shadow of his more flamboyant father. During the 18 years he spent in Virginia's state Senate, Byrd had a reputation as a quiet, hard-working senator who took care never to upstage the senior Byrd.

During the years that the elder Byrd was making headlines rallying Virginians to the "massive resistance" against court-ordered desegregation, Harry Jr. was one of his father's most trusted lieutenants in the state senate. "He and former governor Mills E. Godwin were the ringleaders in shutting the schools down," said Armistead L. Boothe, a long-time Byrd battler who came close to defeating the younger Byrd in a senatorial primary in 1966.

Byrd's role in opposing school desegregation cast a shadow over his political career, particularly among black voters. "He had a very negative impact in the area of bettering race relations," said state Sen. L. Douglas Wilder, the Virginia senate's only black member, said yesterday. "The greatest thing Byrd's resignation would bring would be hope in the minds of black citizens that things will improve."

When his father retired in the middle of his senate term in 1965, Harry Jr. was named to fill the vacant seat -- but he did not make any direct overtures toward taking over the political machine that his father had so carefully built through years of alliances with the state's courthouse leaders.

At the time, some said the younger Byrd had little interest in the kind of nitty-gritty, backroom politicking that had so fascinated his father. Others theorized that he did not have his father's political savvy, or that he realized that a broadening state electorate rapidly was making the Byrd machine obsolete.

It was hardly surprising, then, when Byrd in 1970 broke with the Democratic party of his father and announced that he would run for reelection as an independent. His ostensible reason was a philosophical one -- he said at the time that he opposed the Democratic party's loyalty oath -- but observers pegged it as more of a pragmatic political move.

"What Harry Byrd Jr. was able to do . . . was to move from a limited electorate to winning on conservative issues with a broader electorate," said Larry Sabato, a Virginia political science professor. "What he realized, and what saved him, was that he could no longer run a machine."

In the U.S. Senate, Byrd practiced a code of limited government. He introduced little legislation, rarely sought the political spotlight, and devoted much time to offering amendments from the floor in repeated attempts to curtail government spending, especially for foreign aid.

"There are just too many laws," Byrd explained some years ago. "I've always felt that every time we pass one bill we should repeal another."

During his 16 Senate years, Byrd has only sponsored 39 bills and resolutions, according to a tally by his staff. By contrast, aides say, he offered 90 floor amendments, 60 of which were approved.

Perhaps his most noted legislative measure -- the 1971 "Byrd Amendment" modifying a U.S. embargo to permit importation of Rhodesian chrome -- was a misnomer because it was not an amendment. Widely hailed by conservative strategists, it was inserted in an authorization bill being drafted by the Senate Armed Services Committee.

Byrd clashed with President Carter over the appointment of U.S. judges in Virginia. Holding out for his list of 10 white male candidates, Byrd blocked the administration from naming a black judge, James E. Sheffield. The nomination was withdrawn amid bitter controversy.