There was, we thought, a certain rare dignity and beauty to the inaugural proceedings held in the Rotunda of the Capitol, rather than in the customary outdoor setting. Sorry about those people who, holding prime grandstand seats for the event, weren't able to be crammed into the Rotunda, but the indoor hall seemed to us a perfectly fitting backdrop for the president's swearing- in. Inside the Capitol, looking at the assemblage of people gathered there, as distinct from peering down the vista toward the White House, was where this particular president should have been yesterday. Much of what he was committing himself to will depend on good relationships within that Capitol building. And there was no more suitable background for his remarks about the necessity of healing bitter divisions and working together.

Clich,es? Well, of course there were a fair number. But we would say that by the standards set in the past for these speeches Mr. Reagan stayed pretty much on the scant and unflamboyant side. Some of the prose was resonant. It soared -- especially the part about the "American sound," as he called it. That sound "is hopeful," the president said, "big-hearted, idealistic, daring, decent and fair. That is our heritage. That is our song."

Those critics of Mr. Reagan who are not inclined to grant him an inaugural amnesty (or themselves a temporary rest) will point out that much which went on in the president's first term by no stretch of the imagination could be made to fit that description. Yet even the most committed sourpusses should be willing to concede that this president has given tens of millions of people in this country a feeling that safe, stable times are returned and that fundamental values they hold dear are back in vogue and unashamedly so. He has also given them a sense of possibility that seemed to have been entirely wrung out of our politics in the grim decades that preceded his first term. Mr. Reagan doesn't tell the people they are bad or neurotic or doomed each time a particular problem arises. For that they are duly grateful -- who wouldn't be?

Is there justification for this upbeat message? Can the optimism be even partially fulfilled? We will spare you (for today) yet another warning about what is waiting in the economic wings unless the president takes some steps he thus far seems disinclined to. We will even forbear to pursue our customary argument against the fatuous balanced-budget amendment -- at least for 24 hours. We will note instead that there were passages in Mr. Reagan's speech -- the part about how John Adams and Thomas Jefferson were ultimately able to compose horrendous political differences, the strong words on the necessity of racial justice in American life, the stress on emancpation of the individual spirit in our society -- that are full of promise if Mr. Reagan cares to follow their implications.

The president will have his share of opposition in both houses of Congress -- some of it will comprise resistance he should encounter. But by and large he has a freer hand and a freer field than any president has enjoyed since the late 1950s. The opposition party is in a shambles. His majority is huge. His personal popularity is even huger than that majority of voters. Mr. Reagan has tremendous opportunities just now to act on the more inspired parts of his inaugural pledge.