President Carter completed the purge of his Cabinet yesterday by firing Transportation Secretary Brock Adams and accepting the resignation of Energy Secretary James R. Schlesinger Jr.

Announcing the final moves in the shakeup of the Carter Cabinet, White House press secretary Jody Powell said Deputy Defense Secretary Charles W. Duncan Jr. will be nominated to replace Schlesinger, who later told a news conference he will leave the government in October.

Powell also announced that Navy Secretary W. Graham Claytor Jr. will play a dual role in the Cabinet shuffle. He was named acting secretary of transportation yesterday, replacing Adams, who left his post immediately, and he later will be nominated as permanent successor to Duncan as deputy defense secretary.

When it was over, the grim-faced president appeared before reporters at the White House and, in a tersely worded prepared statement, pronounced himself well-pleased with the upheaved he and wrought.

"these changes are all constructive, and transition from one leader to another in each case will be orderly and properly conducted," he said.

Carter said he expected no further Cabinet changes, pledged to fill the vacancies created by the shakeup "without delay" and thanked those he had fired during the past 48 hours for their service.

"i need the full support of the American people in the future," the president said. "i am well-pleased with all the changes that have been made -- every single one. It has been a positive changes. There is absolutely no doubt in my mind that I and my administration will now be better able to serve this country and to resolve those problems and to meet those challenges that I described to the American people in my televison address Sunday evening."

With that statement, barely a minute long, Carter abruptly turned and left the room, refusing to answer questions.

By the end of the shakeup last night, it was clear that the extraordinary two-day purge really had only two intended victims -- Treasury Secretary W. Michael Blumenthal and Health, Education and Welfare Secretary Joseph A. Califano Jr., both considered disloyal by the White House staff and both fired from their jobs Thursday.

But to add to the impression of major changes in the administration, which Carter had promised in his nationally televised energy speech Sunday night, the White House threw into the mix the previously agreed-to resignations of Attorney General Griffin B. Bell, announced Thursday, and the departure of Schlesinger.

Energy Department sources said that before the president's trip to the Tokyo economic summit conference, Carter and Schlesinger had agreed that the abrasive energy secretary should leave the government this fall, because he would be a "political liability" in the 1980 presidential election campaign.

Like Blumenthal and Califano, Schlesinger had powerful enemies inside the White House. But to the end he retained 1carter's personal affection and loyalty. His letter from Carter, officially accepting his resignation as the president did the "resignations" of Blumenthal, Califano and Adams was the only one to contain the word "regret."

The one change on this prearranged shakeup was forced by Adams, whose public defiance of the White House led to his firing yesterday.

According to informed sources, White House chief of staff Hamilton Jordan told Adams Thursday he was to remain in the Cabinet but would have to get rid of at least two of his top assistants.

Later that same day, Adams issued a public statement saying his continued tenure in the Cabinet would depend on several factors, among them the administration's commitment to mass transit, his access to the president and the "responsiveness" of newly powerful presidential aids to Congress and the public.

Adams met with Carter for about 15 minutes yesterday morning at the White house, where the firing Adams had invited took place.

"it is not possible for any Cabinet member in any administration to place public conditions on the president and stay in his job," said one senior presidential aide.

Reaction to the firings continued to be generally negative yesterday. Sen. Ted Stevens of Alaska, assistant Republican leader, suggested that Carter may be "approaching some sort of mental problem."

"the pressures are so great we are worried about having some kind of breakdown," Stevens told reporters.

"he ought to go off and take a rest."

Stephens' comments were criticized by Senate Democrats. "Some people in Congress are losing their sense of proportion," said Senate Majority Whip Alan Cranston (D-Calif.). "He [Carter] is now taking charge."

By the end of the purge of the Cabinet the president repeatedly had described as "superb" and had vowed to keep intact, there were two major vacancies.

One was in the Department of Housing and Urban Development, whose secretary, Patricia Roberts Harris, will be nominated to succeed Califano at Hew.

The other was at the Department of Transportation, where Adams' sudden and unplanned departure left Claytor in an acting capacity while the White House begins the search for a successor.

Powell said yesterday that permanent apointees to both HUD and DOT are likey to come from outside the excutive branch of the government. He suggested last night they could come from Congress.

The White House also will have to find a successor to Claytor as secretary of the Navy, as Claytor will be assuming the deputy defense secretary post when a permanent Transportation secretary is installed.

While the high-visibility changes in the Cabinet apparently are cover, the Carter-ordered Shakeup will continue, seeping into lower levels of the government.

Yesterday was the deadline Jordan set for the return of "evalution forms" of hundreds of administration and White House aides. The forms have been ridiculed widely by administration officials and it was not clear how many would be returned to jordan.

In a television interview last night, Powell spoke of "weeding out" the White House staff.

The entire process marked a significant turning point in the Carter administration and clearly was designed to strengthen White House control over the government for the difficult reelection campaign facing the president.

The process has stretched over three weeks, including Carter's "domestic summit conference" at Camp David and his widely praised speeches on television last Sunday night and in Kansas City and Detroit last Monday.

Congressional critics of the Cabinet upheaved have contended that in purging his administration the president was undoing the political good he achieved from his speeches earlier in the week. But last night, a senior White House official predicted just the opposite will be true.

"the people who are saying that the events of the last two or three days have broken the momentum the president established will be proved wrong," he said. "it was a necessary interruption, but the success he had on Sunday and Monday will be repeated in the days and weeks ahead."

In the midst of the final tremor of the shakeup he had ordered, Carter went through another serene day yesterday, showing signs of strain only in his rigid and grim appearance to announce that the purge was at an end. His activities included an appearance in the White House Rose Garden at a cermony marking the 10th aniversary of the landing on the moon and in the Wite House East Room at a reception for participants in the White House Conference on Family.

White 1 House officials said yesterday that Carter would remain at the White House this weekend instead of going to Camp David, as he originally had planned to do.

As was the case Thursday, Powell delivered the word of the latest departures. The first to be announced was Adams,' not long after the transportation secretary had left the White House.

In his letter of resignation, released by the White House, Adams urged support for mass transportation and the development of a more fuel-efficient automobile, two of the items he had said Thursday would determine whether he wished to remain in the administration.

"i hope you find happiness in your job, and I join the whole nation in hoping that the remainder of your administration will be sucessful," he told the president.

Carter replied that he shared Adams' belief that the country's transportation system must be improved. "your continuing advice and support as we make this progress will be very valuable," he said.

In his resignation letter to the president, Schlesinger referred to their earlier agreement on Schlesinger's departure. "as we discussed prior to the Tokyo summit, it would be far better for you to have in place one who is less scarred by earlier battles," he said. He asserted the administration had made "impressive achievements" in terms of energy policy, but added, "i fear that the depth of out national problem has not as yet been accepted by the American people."

Carter replied: "under the most difficult circumstances, you have performed your duties superbly." CAPTION: Picture 1 ; Brock Adams at an afternoon press conference after his firing: "A Cabinet officer must work directly for the president - not the White House staff." By James A. Parcell - The Washington Post; Picture 2, Carter enters White House Press secretary Powell . . . By Frank Johnson -- The Washington Post; Picture 3, . . . to announce that his Cabinet shakeup is over, and vacancies will be filled "without delay." By Frank Johnston -- The Washington Post