WASHINGTON — Nothing says serious business in Washington like the term special counsel.

It resonates solemnly through the capital and inspires grave talk, including the possibility of significant wrongdoing at the highest levels with the potential of historic consequences.

The implied gravity of the term, freighted with history, was a chief reason Democrats were so eager for a special prosecutor to investigate any connection between Russia and the Trump campaign, and a chief reason Republicans were so leery of an appointment. Both sides knew the naming of a special counsel would elevate questions about Russian meddling in the election and related matters to an entirely different level, from both a political and an investigatory standpoint.

Now Robert S. Mueller III, the former prosecutor and F.B.I. director, takes his place in the pantheon of specially appointed investigators tasked with getting to the bottom of Washington scandals, beginning with the Whiskey Ring during the Grant administration through Teapot Dome, Watergate, Iran-contra and Whitewater. Just four months into President Trump’s tenure, he faces the prospect that an aggressive, high-powered and well-resourced inquiry into any connections with Russia could become a near permanent fixture of his presidency.