Washington ? Supreme Court Justice Ruth Bader Ginsburg is all business during the court’s public sessions. She zeroes in on lawyers who haven’t done their homework and her careful, reedy tone can quickly undercut some of her more flamboyant colleagues.

A few in the courtroom, however, briefly see a very different side of the Supreme Court’s second female justice, whose 10-year anniversary on the court is today. Female lawyers taking their oaths as members of the Supreme Court Bar often see a broad grin on Ginsburg’s thin face when they rise for an introduction to the court.

Ginsburg gained national prominence arguing, and winning, women’s rights cases before the Supreme Court and elsewhere. She was a long-serving federal judge when President Clinton picked her as his first Supreme Court appointment in 1993.

The first justice chosen by a Democratic president in decades, Ginsburg votes most often with the court’s more liberal wing. That means she frequently is on the losing side when the court splits 5-4 along ideological lines.

Ginsburg, 70, has emerged as a quiet peacemaker on the court, a liberal whom conservatives on and off the court can admire, said Douglas Kmiec, a conservative constitutional scholar at Pepperdine University’s law school.

Ginsburg usually sticks to the narrow meaning of laws and tries to keep the court’s nose out of problems that can be solved elsewhere, Kmiec and other law professors said. That cautious approach sometimes means she puts her own views aside.

“She always uses the phrase, ‘Get it right,”‘ said W. William Hodes, an Indianapolis lawyer and former Ginsburg law clerk. “Part of getting it right means not always voting for what you personally think is correct.”

Ginsburg had no such quandary in the case for which she is probably best-known. She wrote the 1996 ruling that forced the tax-supported Virginia Military Institute to open its doors to women.

Ginsburg might have used the opportunity to revel in what must have seemed a crowning moment in her own career as a women’s rights lawyer, but the ruling contains no gloating.

“Women seeking and fit for a VMI-quality education cannot be offered anything less, under the state’s obligation to afford them genuinely equal protection,” Ginsburg wrote.

Although less recognizable than the court’s first female justice, Sandra Day O’Connor, Ginsburg is one of the more visible members. She frequently gives speeches and turns up in unexpected places — a bit player in an opera and astride an elephant during a tour of India with Justice Antonin Scalia.