The December meeting of the Business Council here this week provides one of those convenient political North Stars by which to track Jimmy Carter's travels with the business community.

Interviews with council members, who are the board chairment of more than 100 of the nation's biggest corporations, suggest that the president and big business are sailing together much more comfortably these days.

Two years ago, then president-elect Carter chose not to attend the council meeting. It was taken as a bad sign and served at the time only to heighten anxieties that the new president would be no particular friend to commerical interests.

Last year Carter did attend. He shook a few hands but appeared uncomfortable in the midst of it all. He still lacked rapport with many of the leaders present and his speech gave little assurance to executives worried then about creeping inflation and an obstinate trade deficit.

Wednesday night, Carter showed up again, only this time the mood on both sides of the podium was markedly more relaxed. The president spoke confidently of his economic program and the progress achieved so far-7 million new jobs, record exports, a 37 percent increase in corporate profits, a $40 billion tax redution.

More importantly, Carter identified with his corporate audience, acknowledging political debts owed them for support in victories on the Panama Canal, the energy bill and civil service reform act. He also promised to do his most to allay business' chief concerns-runaway inflation, deficit federal spending, lack of investment incentives and expensive regulations.

"It was an interesting contrast with two years ago," Irving Shapiro, chairman of DuPont and a leading spokesman for the business community, said afterward. 'He didn't know us very well then and was uncertain. He knows us better now, and the council knows him."

This accommodation with business has been key to the political education of Jimmy Carter, as critical in strengthening his presidency as his new, more respectful approach to Congress or his more prudent remarks on foreign affairs. Having to lean on business for political favors, Carter in the process has become more sensitive to its concerns. The business leaders, in turn, now more readily support the president's economic program or, at least, have been less eager to criticize.

Their attitude toward Carter is still far from enthusiastic. The board chairmen were slow to rise to their feet at the end of Carter's remarks Wednesday, their applause was measured-polite but hardly excited. Carter is a man many of them continue to believe lacks the experience and the sense of command to be president.

Asked to assess Carter's two years in office, Thomas Murphy, chairman of General Motors, offered simply this lukewarm endorsement: "He's the only President we've got and we are going to continue working with him."

Now more than ever, Carter needs the cooperation of the business community. His atni-inflation campaign ranks as his administration's number one domestic priority, and much of his future political standing rides on the outcome of the new wage-price programs.

Parts of his purpose Wednesday night was to plead for support for the new anti-inflation program, now revised in what White House officials say will be the las major tinkering for awhile. Carter made repeated appeals to the business leaders to "give me your pledge of compliance."

"There is no excuse now for you to delay," he said, "and it would add a great deal to me and my influence in controlling inflation if you would do so."

Business and labor alike remain skeptical that a voluntary guidelines program will do much to slow inflation, but business has been quicker to embrace the president's program than have the unions. No sooner had Carter finished speaking the other night than John DeButts who soom will retire as chairman of AT&T and of the Business Council, stood up to boost the president.

"There are some questions about the possible success of the program," he allowed but promptly added, "I happen to believe that the program will work. He told his colleagues, too, that he trusted Carter to keep his part of the bargain by reducing federal spending and relaxing regulatory pressures. "I happen to believe the president is sincere," he said.

During much of his time in office, Carter has been chided by the business community for having no economic program - at least not one the business leaders could fathom or accept. The rest of the world felt the same way and showed its lack of confidence by running down the value of the American dollar. In view of Carter's background as a small business-man-farmer and his seeming inability to fashion an effective economic policy, he was regarded in many financial circles as an economic neophyte.

It is a measure of how far Carter has come on this score that he could boast Wednesday about having finally shaped "a good team" of economic advisers and "a much more consistent administration (economic) policy."

But the transformation from ineffectual performer to master conductor of the economy has been rather sudden and only ver recent. It is marked by two major speeches this fall-the first on October 24 which introduced the tougher wage-price program, and the second on Nov. 1 which stunned the world with a series of monetary actions designed to recuse the dollar.

"He's on the right track," remarked David Rockefeller, chairman of Chase Manhattan Bank. "The October 24 speech coupled with the November 1 speech put together a package that the world was looking for.

"I've been to Europe and Asia since those speeches," Rockefeller noted, "and there is a feeling there that what Carter did was the right thing. I think we should have confidence."

Part of the reason for the greater faith in Carter exhibited by the business community derives from a greater faith the business leaders have in themselves. They are feeling politically bolder following a year of major legislative victories-including the defeat of the common situs picketing bill and labor law reform and enactment of more liberal capital gains and investment tax credits. They can afford to be a little more magnanimous.

They recognize their goals now as being in concert with the president's. Their chief worry is whether Carter's economic program can achieve those goals in time.

If Carter sticks to his program of shrinking the federal budget and squeezing the money supply. pressures on the White House are sure to build-from growing ranks of the unemployed, from borrowers who can't afford high interest rates, from special interest groups seeking to save their piece of the federal pie.

What the business leaders still wonder is whether Carter can stand firm. In his remarks to the Business Council yesterday, Shapiro put it this way:

"We can live with slower economic growth in 1979 and 1980-even a mild recession-but we cannot afford the consequences of a reversal of the policies now in place. One much hope that the resolve of the administration will be a match for the pressures that are certain to appear next year." CAPTION: Picture 1, President Carter fields a question from the audience at the Mayflower Hotel, Wednesday night after warning the Business Council that Americans may be talking themselves into a recession. By Joe Heiberger-The Washington Post; Pictures 2 and 3, Du Pont Co. Chairman Irving Shapiro (left) and Chase Manhattan Chairman David Rockefeller here Wednesday. Photos by Joe Heiberger-The Washington Post