President Reagan and King Hussein of Jordan have given the traditional friendship between the US and Jordan a new start. But where the new warmth will lead - at least in terms of Middle East peace - nobody yet knows.
What is certain for the moment is that Reagan and Hussein liked each other during their two days of talks. How much behind-the-scenes pressure was exerted one way or the other during those Nov. 2-3 talks is not yet apparent, but according to diplomats who watch such things, ''the chemistry'' between the two leaders was right.
It also now seems virtually certain that King Hussein will receive American rather than Soviet assistance in building up his country's air defense system.
During the Carter administration, King Hussein postponed visits to Washington because of US ''arm-twisting'' in a bid to sell him on the Egyptian-Israeli peace treaty.
His visit in June, 1980, restored a semblance of good relations, but President Carter, or at least some of his aides, continued to give the impression that the White House could not quite forgive Hussein for not supporting the US-sponsored Camp David agreements between Egypt and Israel.
On Nov. 3, as King Hussein and President Reagan said farewell at the White House, it was almost as if the Carter administration snubs and the King's refusal to endorse Camp David had been forgotten.
''The atmosphere has been extremely friendly,'' a Jordanian diplomat said near the end of the talks.
''Our differences are well known, but we've been able to discuss those differences,'' the diplomat said. ''The differences did not mean that there aren't many areas of possible cooperation between our two countries.''
In their departure statements, the two leaders indicated that cooperation was possible on US military aid and the sale of air defense systems to Jordan. Such air defense would be intended in part to counter any possible Syrian moves against Jordan.
During his visit to Moscow earlier this year, Hussein had discussed the possibility of accepting a Soviet offer of air defense weapons. As he has done in the past, the King now seems to have succeeded in using the threat of going to the Soviets for weapons as a lever to obtain American military aid.
''The security and well being of the Hashemite Kingdom of Jordan is a matter of historic and enduring concern for the United States,'' said President Reagan in his farewell statement to the King just outside the White House. ''We agreed that reinforcing this friendship is a primary goal, and discussed how our relations can be strengthened.''
King Hussein responded that his talks with Reagan left him ''more reassured'' and ''more confident'' than he had ever been following talks with Reagan's predecessors in the White House.
But the gap between the two sides was also still apparent.
President Reagan said that both leaders agreed on the necessity for ''making progress toward a just, lasting, and comprehensive Middle East peace, on the profound dangers which threaten the security of the region, and on the necessity to work in complementary ways to address these serious issues.''
But in answer to a question, the President also seemed to indicate that he was unwilling to endorse the Saudi Arabian peace plan, which King Hussein has said he finds acceptable.