Vanderbilt officials say they have no record that Mrs. King was ever exposed to radioactive iron, a situation that highlights a problem in Vanderbilt's public relations strategy and the mothers' quest for answers: most of the original documents from the experiment have been lost or inadvertently destroyed, Vanderbilt says. A document mentions that 819 of 2,300 women in the test received radioactive iron, but only partial records on about 200 who were given the radioactive iron have been found.

The university contends, though, that even if she had been exposed, Mrs. King, like the other mothers, would have been given only trace quantities of radioactivity and was properly informed about it twice. The first time was when the radioactive iron was administered in the late 1940's, when nuclear materials were widely and more casually used in laboratories. The second time was in the follow-up in the mid-1960's, when the risks of overexposure were well known. In that study, Vanderbilt researchers found the three cancer deaths in children, deaths the university says were an act of nature.

Vanderbilt has recruited members of its faculty to make its case. One of the most important figures is Dr. William J. Darby, a nutritionist who helped arrange the original study in the 1940's. Dr. Darby, who is 80, says he vividly recalls important aspects of the study, including informing the women about the iron. 'We Always Told the Women'

"We wanted to know the nutritional problems and the nutritional status of women coming into our clinic," Dr. Darby said. "We always told the women what we were up to. I couldn't tell you exactly what we told them, but I am certain we told them it was radioactively labeled iron."

Vanderbilt has also dispatched Dr. Charles F. Federspiel, its top medical statistician, to critique the follow-up, published in 1969 in The American Journal of Epidemiology. While finding three cancer deaths among 634 children born to women fed the radioactive iron, the study also said that none of 655 children born to women who did not take the iron had developed cancer.

Childhood cancer is relatively rare, according to the National Cancer Institute. In the 1960's, 1 in 1,000 children under 15 developed any type of cancer. But leukemia, sarcoma and bone cancer, the types developed by the three children in the trial, were even rarer; about 1 child in 100,000 developed bone cancer.

The study's authors called the increase in cancer mortality in the group of children exposed to radioactive iron "small, but statistically significant." But Dr. Federspiel concluded in an unpublished critique that the authors incorrectly tabulated their results. In doing so, he said in an interview, the study found an excess of cancer that really did not exist. Researcher Sees No Proof