President Reagan made a powerful case last night for his strike against Libya. The evidence of a Libyan hand in the West Berlin disco bombing on April 5 was, he said, "direct, precise and irrefutable." That bombing had been only the latest in a series of Libyan terrorist acts unfolding over the years; and other Libyan acts, the president said, were in the works. Ignoring Col. Qaddafi as many nations had done, the president fairly claimed, had not led to the abatement of his crimes. In recent days, quiet diplomacy, public condemnation, economic sanctions and demonstrations of American power had failed to convince the Libyan leader that the United States was serious about meaning to protect its citizens.

It is reasonable and necessary to ask whether the strike is more likely to slow Col. Qaddafi down or to incite him to raise the stakes. Any comprehensive judgment will have to take into account not only that the United States had reason and right to do what it did but whether the strike had the actual effect of reducing Libya's capacity or taste to conduct further depredations. For in Libya's eyes at least, the United States now is very close to being at war. This could have some dire consequences. Certainly extra vigilance will be required for some time. The unknown future costs of the American strike, however, have to be set against the known past costs of leaving Col. Qaddafi essentially free to carry out his outlaw policy, as his earlier victims had done.

It was sobering to find most of America's allies in Europe distancing themselves from the United States in the hours and days preceding the raid -- hours and days when they had grounds to suspect that Washington was planning retaliation. Only Britain, which let the American saircraft fly off from its bases, stood up to be counted. But it is not simply that the other Europeans wanted to dissociate themselves from a controversial military action; that much was perhaps understandable. It was that they did not enter earlier, in the spirit of alliance, into a range of sanctions short of military action -- actions that over time might perhaps have preempted a requirement for later military action.

A common view is that the Arab world will be in an uproar against the United States. That view, applied uncritically, demeans Arabs by suggesting they can have no compassion for the victims of terrorism, even when the perpetrator is a man such as Col. Qaddafi. The Libyan leader reaches for Arab leadership by making himself not merely the defier of the Western order but, specifically, the champion of the Palestinian cause. Yet moderate Arabs, for all their dismay that the United States does not act more resolutely on the Palestinian front, do not conclude that terrorism directed against Americans is therefore justifiable. It will be noticed by Arabs that Ronald Reagan waited six years to hit back, and then did so in a discriminating way -- in too discriminating a way, some of them may privately complain.

Terrorism will continue, but the war against terrorism will continue too, under a set of expectations significantly altered by Mr. Reagan's Libyan raid.