THE BRITISH AND AMERICAN foreign secretaries put their heads together on the matter of Rhodesia the other day and came up with nothing. We say this not in derision but with a certain approval. For the several conflicts in Rhodesia -- between the multiracial regime in Salisbury and the guerrillas, and among each of these groupings -- have produced a degree of violence and fragmentation demonstrably beyond Anglo-American repair.

It is painful to recall that the Carter administration once saw in Rhodesia an exciting opportunity to make the United States both the champion of black majority rule in Africa and the manager of peaceable change. But the administration's diplomacy, as it developed, seemed to focus on the first of these roles -- though not openly enough to gain African credit for it -- and fulfillment of the second role was made that much more difficult. There is no doubt now that black majority rule is coming, but not peaceably, and not in a context ensuring white minority rights, and not under American patronage, and not in a way that promises to advance other American interests.

The transitional government of Ian Smith has just sponsored a poll in which whites approved a white-written majority-rule constitution due to take effect when general elections are held in April. At one point, those elections looked like they might help win international acceptance for the "internal" settlement. But the military deterioration since then has put them in a different light. The elections will be held under military-law conditions in the shrinking fraction of the country where the government's writ runs. Salisbury figures the vote will meet one of the two tests Congress set last year for lifting economic sanctions; it met the second by announcing its availability for negotiations with the guerrillas. But even if Salisbury meets Congress' technical requirements -- and it may -- what will that avail? Salisbury's talk of elections, the lifting of sanctions, and then somehow a miraculous Western bailout, sounds increasingly like whistling in the dark. The overwhelming fact is the war.

The guerrillas are winning, under the worst imaginable conditions for the future of Zimbabwe -- economic devastation, political radicalization, racial conflict, black civil war. Their military advance is sweeping away the whites and the assorted blacks of the transitional regime. There is blame enough all around; the leaders of Rhodesia/Zimbabwe deserve most of it. But what Americans cannot avoid asking is whether things are better or worse for the people of that brutalized country as a result of the administration's exertions in their behalf.