For the past 18 of his 59 years, Dr. Ian Stevenson has been coolly and meticulously studying what he scientifically refers to as "cases suggestive of reincarnation." A map on the wall of his Charlottesville office is ticked with variously colored pins that represent cases of different types; dark green metal file cabinets are crammed with reports of varying detail on 1,700 subjects: an outgoing mail basket is stuffed with correspondence destined for every corner of the orb, the incoming mail is less noluminout, but often riveting in its detail.

"My 9-year-old son talks frequently of another life in which he he died at the age of 27 in an auto accident," a woman writes from upstate New York. "His description of death and rebirth is matter-of-fact and without dramatics. Until now, I have not encouraged a full discussion of the subject, as I do not know how to handle it. Of his supposed former life, he knows his line, his parents' names and occupations, where he lived and how he died. His story does not vary except for small details. He insists he was 'told' to choose his father and me as his parents . . ."

This comes, from the files, indexed away in a plain manila folder. Stevenson's office - an old, yellow, Gothic-looking building that houses what's designated The Division of Parapsychology, Department of Psychiatry, University of Virginia School of Medicine - has none of the macabre or outrageous touches one might associate with so unusual an endeavor: no crystal balls or witches' uniforms, talismans or ancient books of secret writings. The place is plainly the residence of a scholar, with two Physicians' Desk References the only clue that the man in charge is a doctor.

While reincarnation conjures up images of quackery to many, the topic does have a history of serious intellectual consideration. Greek philosophers pondered it, Nobel Prize winners studied it, and Darwin pushed the issue into western thought. In the east, reincarnations is as acceptable as the American Express card.

And even in this great land of cynics, Stevenson is being approached more seriously - both by his colleagues and, more immediately by the individuals who write him.

"Twenty years ago," he says, there never would have been an office like this on a campus, and I'm fascinated by the letters of support I get that say: I wish I had known about your research years ago.When Billy was 3, he used to prattle on about being a pilot and shot down and now he's 10 and doesn't remember anything."

Stevenson himself, dressed in a tweed three-piece suit and brown Oxfords, seems more like an English professor than a man on the edges of the parapsychological frontier. Canadian by birth, his perfectly intonated English is steeped in the Cadences of Chaucer and James. He chooses his words with utmost care, frequently pushing thoughts into the impersonal realm of "one would think" to avoid any type of bias, fastidiously protecting the unusual status of his medical school division - the only parapsychologcal unit Stevenson knows to exist on any university campus.

"I became interested in parapsychology as a child," Stevenson says. "My mother had a library on the subject, and I used to read a lot of her books when I was younger. But it was actually much later that I became scientifically interested in what is now called parapsychology, after medical school (McGill in Montreal) and practice as a psychiatrist (chairman of U.Va.'s department).

"There are so many features of human behavior that aren't adequately explained by current psychological theories. Childhood fears: the fear of airplane motors in one infant, who would be lying out in the sun and become excited and cries when a plane passed overhead; or fear of water, in a baby that would scream and yell when being bathed before it could even speak."

So, one might surmise, one baby had been killed in a plane crash in a previous life, and the other drowned?

"Not that simple," Stevenson replies", but we can make fascinating correlations. A case I'm studying in Alabama. A young boy 10 or 12 was playing in a house with a friend. The friend pointed a loaded gun at him and shot him accidentally. Another boy born shortly after that named the boy who had shot the other one, described the boy's house and gave an account quite rich in detail of his previous personality.

"The key to this kind of work is careful interviewing of the subjects involved, verifying the facts of each case and ascertaining how possible it would have been for the child to have found out the information himself" - a process some critics question. 'Incredible' Methodology

"What he's saying is very upsetting to the way we think," says Dr. Albert Stunkard, a professor of psychiatry at the University of Pennsylvania Medical School. "The trouble is that he's dealing with something that can't be handled empirically. I know there are lots of people who disagree with him, but most of their criticism is done without reviewing his work. He's an incredible mathodologist, hard to fault. He's very convincing, but I'm not convinced. Which is not to say that his research isn't valid."

Last year, after the prestigious Journal of Nervous and Mental Disease published several of Stevenson's papers, readers reponded in an unprecedented way.

"I must have had three or four hundred requests for reprints from scientists in every discipline," says Dr. Eugene Brody, a psychiatrist at the University of Maryland Medical School who edits the journal "It's pretty clear to me that there's a lot of interest in this topic. I don't agree with Stevenson's conclusions, but he's defintely not just some crazy guy."

Stevenson is mostly interested in cases involving young children who claim to have had a previous life, especially when the child spontaneously offers evidence of this previous personality in his conversation "I'm suspect of cases in which the subject is an adult" he says, "because you can't really control the subconscious infulences derived from information to which the adult has been exposed."

For the same reason, Stevenson is skeptical of hypnotic regression of adults into previous personalities although he considers a few cases "good" - Bridey Murphy the American house wife. Jensen, who spoke Swedish in her tiause, and recently, a Virginia woman, Dolores Jay, who says she was murdered a century ago in Germany when her name was Gretchen Gottlieb. Detailing the Obscure

"One thing you look for in a good case is richness of obscure detail," says Stevenson. "For example, Bridey, who had never been to Ireland nor knew anyone from there, spoke of a place in Cork called The Meadows. It's hard to explain where that bit of information could have come from."

Stevenson is also wary of previous lives revealed in dreams, although he says that some cases are worthy of more attention than others.

"We have the case of an elderly American woman. She has recurrent vivid dreams of being chased by an American Indian, who grabes her hair and begins to bring his hatchet down on her and then she wakes up. In the dream she has blond curly hair; in real life, straight and brown. Now this might be an inherited memory: Historically there is evidence that the last Indian raid in Virginia occurred on her ancestral property and the family cabin was burnt down in it."

Of course, ther is a possibility - which might have been proposed by Freud - that the dream is more realistically some subconscious expression of the woman's fears or hopes or even the transformation of some childhood experience.

"Surely a Freudian would argue that way," says Stevenson. "But I thik he'd be wrong. That's exactly the type of rigid attitude that turned me away from Freudian psychology and from many of the other rigid approaches to human behavior.

"I have to admit that the results in parapsychology aren't that good. There have been no great breakthroughs. But there aren't any real breakthroughs in orthodox psychology, either. I don't think there is any real proof in science except in mathematics. You only have probabilities." Plato, Kant . . .

Still, whatever the probabilities, reincarnation has tended to fascinate men throughout history. Plato discussed it in "the Republic," and in the western world no less a thinker than Immanuel Kant himself seriously considered the paranormal.

It was really Darwin's indirect questioning of the existence of the soul that focused much of the western interest in reincarnation. In 1882, the prestigious Society for Psychical Research was founded in London (members included Henri Bergson and William James) to apply scientific method to paraphyschological phenomena. By 1930, research shifted away from theoretical survival after physical death to studies of extrasensory perception.

In 1960, prompted perhaps by several research grants in the area and by the countercultural interest in mysticism and drug experiences, scientific studies were again begun on reincarnation.

Meanwhile, in the East the concept of reincarnation has long been accepted, which may explain why a large majority of Stevenson's cases are from the East.

Actually," says Stevensons, "we don't really know how common these cases are anywhere. I've got 1,700 files. I haven't the faintest idea of how often this happens. It may be much more common in the West than we think.

"It is striking, though, to compare attitudes of American parents, and, say, Indian parents. In the West, life begins at conception: nine months in the certainly the product of the collision of ovum and sperm and the social environment. Personality is assemblyed like a Ford on the line: It has no antecedents prior to conception.

"This concept generates a tremendous amount of guilt on the part of Western parents. If the child is physcally or pshychically malformed, guilt is ascribed, just as society judges Ford guilty for defective brakes and 100,000 cars are recalled.

"Whereas in India, children are just people who spend a certain amount of time with the parents. This permits the parents to enjoy the children more, and the children can't blame the parents and vice versa, and things are much more open and less judgemental, that if a child brings up conservation dents in the West where children began to speak of a past life and the parents threatened the child with being made a fool of or going crazy. What to Do

"My advice to parents," he says, is that if a child brings up conversation about a previous personality, it's all right to listen. If he says things, it's okay to ask questions. If the child says, "My mommy didn't dress like that,' it's fine to ask how she did dress. "But don't pump the child."

Stevenson is currently completing a book on cases suggestive of reincarnation in Burma and Lebanon, and also working on a volume discussing the place in reincarnation studies of deformities and birthmarks. He's also completed half of a book aimed at the general reader, but laments that he tends "to write footnotes and heavy language."

There is not a lack of material. Stevenson is inundated with correspondence and phone calls (which he refuses to take unless the person has previously written), and is forever trekking about the globe to question subjects and witnesses.

"Some of it's terribly fascinating," he says, "One child in India claims to have once lived in Kansas. And of course there is the rubbish. We dismiss any cases of Venusian fantasies. Unsolved Problems

"Obviously one hope is to obtain further evidence bearing on the existence of life after death. But as a psychiatrist, I'm interested in how these studies can throw light on half a dozen principally unsolved problems: childhood phobias, childhood interests and nightmares, parent child relationships, sexual gender problems.

"There is an extraordinary case of a woman in Burma who says she was once a Japanese pilot shot down during the war. She refuses to wear women's clothing and actually refers to herself as a man trapped in the body of a woman. I haven't heard from many homosexuals, but this is a fascinating concept."

After all this, however, Ian Stevenson is not willing to take the final step, at least not in public.

Does he believe in reincarnation?

"I decline to answer," he says. "It's important for me to keep my stance in the background. People have to make up their own minds on the basis of available evidence."