TRUE TO VIRGINIA political tradition, Gov. John N. Dalton was careful in his brief inaugural speech not to make any "extravagant" promises and to talk instead about "the middle way - the way of moderation, of prudence, of reliance on time-tested principle." But couched in his carefully chosen words were some encouraging indications that the state's new chief executive is sensitive to some interests that have not found a particularly sensitive ear in the governor's office of late.

In forthright terms, Mr. Dalton reinforced a commitment to run an administration in which black as well as white Virginians, women as wellas men, would have a meaningful stake. "To the best of my ability," he said, "it will be a government free of discrimination based on race or sex, and a government providing moral, legal and political leadership in the struggle to eliminate such discrimination throughout society."

One could shrug this off as lip service, but Gov. Dalton had more to say: "This administration will not stop at nondiscrimination; it will actively seek to involve all our people in the government process." Moreover, the new governor already has begun to fulfill this promise. Among other things, he has broken new ground by naming the first black Virginian and first woman to hold top-level, policymaking positions in the state government.

The governor also gave heart to Northern Virginians by including mass transportation in his list of "tough problems" that the state government should be addressing. During his campaign and after the results were in, Mr. Dalton had indicated an appreciation of the political support to be courted in Northern Virginia. If the payoff turns out to be new understanding and help from Richmond for Metro and other concerns in this region, that is all well and good.

Still, just as it will take skillful executive leadership to win legislative support for some of Northern Virginia's concerns, Mr. Dalton will face some stiff tests involving minority interests. Right away, there is the task of deciding how to deal with federal efforts to bring about full desegregation of the state's colleges. So far, Mr. Dalton has avoided the tough-talk stance of his predecessor, Mills E. Godwin. The job now should be avoid litigation.

In the meantime, at least, John Dalton is saying that he won't be content with the status quo, that he envisages more than a simple extension of the last state administration. That in itself is good news.