Washington — Remember when small Westminster College in Fulton, Missouri, was immortalized by Winston Churchill's famous ''Iron Curtain'' speech there?
If the Reagan proposal for reductions in nuclear arms actually succeeds and leads to a permanent lessening of US-Soviet tensions, then small Eureka College in Illinois could similarly benefit.
Further, the President, as one White House staffer put it, was not ''unmindful'' that his college might gain a niche in the nation's history if the speech he gave there in the end is regarded as highly significant--even historic.
It is not unusual for presidents to choose a college campus as a site for a major foreign policy address. Chief executives see this as an appropriate theme for an audience expecting a thoughtful speech and some new, stimulating ideas.
Mr. Reagan, it is understood, did believe his address was most fitting for an academic community. But he also is said to have felt that what he had to say related particularly well to those coming in from adjoining farms to hear his words.
Farmers through the years have been keenly interested in war and peace issues. They have been acutely concerned over the possible loss of sons to the armed services, sons needed in tilling the land. Mr. Reagan was well aware of this.
Thus, the Reagan plan for deescalating the risk of war, at a time when many people are worried that the US and the Soviet Union may be moving toward a global nuclear confrontation, did, as the President anticipated, play especially well with the farmers.
They listened intently and applauded loudly on occasion, most noticeably at the Reagan assertion that ''I believe that the West can fashion a realistic, durable policy that will protect our interests and keep the peace, not just for this generation, but for your children and grandchildren.''
The academic-rural audience also showed its pleasure over these words: ''My duty as President is to ensure that the ultimate nightmare never occurs, that the prairies and the cities and the people who inhabit them remain free and untouched by nuclear conflict.''
There were children and grandchildren in attendance too. Crying babies accompanied the President for the last two-thirds of his address. If he noticed, he didn't show it. No one shushed the babies. It was clearly a gathering of those who shared the President's Eureka past. It was like a family reunion.
The President also had time for humor. He referred to an honorary degree the college had presented him a few years ago. While he was grateful for the honor, he said, ''it added to a feeling of guilt I've been nursing for twenty five years.''
''I always figured the first degree I was given was honorary,'' he quipped.
He again spoke of his lack of attention to his studies while at Eureka: ''I let football and other extracurricular activities eat into my study time, with the result that my grade average was closer to a C level required to maintain eligibility than it was to straight A's.'' He paused and continued: ''Even now I wonder what I might have accomplished if I'd studied harder.'' This brought long laughter from the audience.
On a serious note, Mr. Reagan remarked: ''I hope the commencement today will mark the commencement of a new era--a new start of a more peaceful, more secure world.''
As he left Eureka the President let it be known that his first objective was to have his speech accepted by leading thinkers in the US as a useful contribution to easing East-West tensions. He apparently has achieved this. Even critics who question the sincerity of his desire to reduce nuclear armaments grant that his conciliatory tone has been helpful.
The President, according to his aides, was also hopeful that the speech would blunt the so-called peace movement, here and abroad, which has been stimulated at least in part by a perception that the President's belligerency was heading the world toward a nuclear war.
Some observers say that Mr. Reagan may have accomplished this end. Some even venture the opinion that he may be on his way toward taking over the peace issue himself. This, the Reagan people say, is precisely what the President would like to have happan.