Not many Americans still repose in the United Nations great hopes for peace and harmony. But many do see it as a principal place of engagement with the Third World. In the Carter period, there was a keen readiness to find common ground with these nations. By the Reagan period, however, the common feeling was that many members were trying to take advantage of the United States and that this country had gone too far in seeking to accommodate them.

These were the circumstances in which President Reagan sent Jeane Kirkpatrick, a highly articulate and intellectual Democrat who cares deeply about ideas in politics, to the United Nations. In other foreign policy posts, a certain amount of mumbling is unavoidable, even useful. At the U.N., however, there is a requirement for plain speaking. Ambassador Kirkpatrick did more than present and defend administration policies there. As she put it the other day, she "spoke for freedom." She did it clearly and persistently. In all the argument about her views and her general role within the administration and her part in its various internal bloodlettings, this matter tends to get lost. You do not have to be on Mrs. Kirkpatrick's side in those policy disputes to believe that, in relation to the U.N., the job needed to be done -- and she did it.

There is an argument for being patient and forbearing at the U.N. when, as so often happens, American interests, friends and values come under gratuitous political assault. It is that Third Worlders are sensitive and frustrated and it does no particular harm to let them sound off at American expense. But this is a specious argument. Self-respect and self-interest demand that the United States take the U.N. seriously. Those who want to use it as a political playpen demean the organization -- and then wonder why its processes do not serve them better. Ambassador Kirkpatrick had it exactly right when she said, many times, that words matter, ideas matter, fairness matters.

And she got results. "Last night," she said in the General Assembly Dec. 14, addressing one special American concern, "this body took note of an abusive practice which the United Nations has been guilty of for some time; it took note of the practice of singling out particular countries for special criticism. More importantly, last night we all took a step in the direction of correcting this abuse. As this body is aware, such selective name-calling is almost entirely reserved for the United States and Israel. It is very selective indeed. The Soviet Union goes unnamed in the resolution on Afghanistan; Vietnam goes unnamed in the resolution on Kampuchea -- in both of which cases, aggressive, expansionist invasions and occupations took place. Yet no names are named. . . ."

Mrs. Kirkpatrick's political future is a matter of much speculation these days. But whatever comes, her contribution at the U.N. remains. The battle is far from over, but she made it a place worthier of cultivation and respect.