Overseas observers of the American scene should feed into their calculations the fact that Ronald Reagan has revived his lagging presidential authority in Washington by winning a cliff-hanger test in the Senate over selling modern American arms to Saudi Arabia.
He had been doing poorly of late over his economic program. He was unable to push through the Congress his idea of further cuts in the federal budget.
Doubts about his political skill, and authority, were dawning. Members of his own party and some conservative Democrats who had been supporting him were beginning to talk about the desirability of ''distancing themselves'' from Mr. Reagan before next year's midterm elections.
Well, put all that away - for the moment at least. The political battle over the sale of the modern weapons to the Saudis was a rough one. The opposition, spearheaded by the powerful Israel lobby, did its utmost. The President won. The margin was narrow (52 votes against 48 votes), but the important thing was not the margin but the fact of Mr. Reagan winning or losing. He won.
This means that the American President is now free to pursue a Mideast policy that recognizes Arab rights and interests and looks toward collaboration with the Arab countries in military as well as political and economic matters.
Israel's views will, of course, continue to be treated with respect and sympathy in Washington. But Israel will no longer exercise a de facto veto over Mr. Reagan's Middle East policies. Nor is Israel likely to become the centerpiece in Washington thinking about a stronger American military presence in the area. Egypt and Saudi Arabia could become more important features in future military planning.
The political battle over American guns to the Saudis also has important domestic implications. After a bad start, the White House showed considerable political skill in managing the later stages of the affair. The strategy was to appear to be a possible loser until the last two days, then to come forward with enough converts to make victory conceivable. It was well thought out and executed. The tactics used in winning individual senators to the President's side were forceful. Mr. Reagan can play politics effectively.
In other words, other governments should continue to view and deal with President Reagan on the assumption that he is still an effective occupant of the White House who can accept and win a tough contest in the Senate.
There may be clouds gathering around his economic policies. His foreign policies have yet to be discernible in detail. But he is still effective as a fighter for his economic policies, and he still has the opportunity to become effective in foreign policy.
The AWACS fight between President and Senate was bound to be expensive for the President, whichever way it went. In order to contest the issue he had to spend political capital, win or lose. Because of the struggle he has fewer favors in reserve to spend on other issues with Congress that lie ahead.
In retrospect, either he should never have made the AWACS offer to the Saudis , or he should have bargained for clearance of the project with Israeli Prime Minister Menachem Begin when Mr. Begin was last in Washington. There was no advance bargaining.
The fight was a drain on Washington's energies. But the drain could have been only a mild consolation for the men in the Kremlin. For still another week they continued to sit on the sidelines and watch as Poland, the biggest and most populous of all their East European clients and official allies, continued to grope for a new form of government that could feed the Polish people without taking them out of the Moscow alliance.
What a humiliation it must be both in the Kremlin and in Warsaw for communists to have to recognize that the government they set up in Poland has become bankrupt both literally and figuratively. It cannot pay its debts to the West. It cannot feed its own people. And how does it change into a more effective instrument of government?
Matters had reached a crisis condition in Poland by the past week. Rioting and disorder were beginning to develop in many places. It was no longer just a case of the government vs. the unions. Segments of the general public were getting unruly. The police were not always in effective control of the streets.
With matters so far gone the Polish government probably did what it had to do: turn to the Army. Foreign observers watch with fascination. The Army in Poland is the safer instrument. The police are generally regarded by the people as agents of the communist party. But the Army has managed to keep something of its distance from the party. It still has the reputation of being a Polish rather than a communist Army. The people trust it to be fair to them.
And it was sent in primarily not to police the streets, but to see to it that whatever food is available in any area be distributed fairly and efficiently. The first acts of the Army teams sent out into the provinces were to check on the efficiency and honesty of food distribution. They started out to serve the people rather than the party.
The use of the Army may work. As far back as May private opinion polls in Poland seemed to indicate that a majority of the population was ready to accept more austerity and higher prices for food rather than follow the more extreme union leaders into more protests in the streets. A splinter left wing had developed in the union movement. The public had not followed it. The Army could hope to impose restraint without finding the mass of the population against it.
Meanwhile President Reagan had come home from meeting some of the less affluent of the world at Cancun. Members of his staff claimed that he had listened and learned: about poverty in Africa and Asia, about India's distrust of Pakistan, about China's distrust of Taiwan.
It was the President's first meeting with high officials of the Chinese government. He talked with the Chinese delegation led by Foreign Minister Zhao Ziyang. He is said to have discussed his own plans for sending new weapons to Taiwan. He heard the Chinese objections - at first hand. They are strong.
The education of Ronald Reagan continues.