DIANA TRILLING has written a long, occasionally in-

sightful and frequently soporific book about Jean Harris, the schoolmarm who killed Herman Tarnower, the diet doctor. The book is loaded with admirably serious notions, but it fails to establish its central premise: that Jean Harris and "Hi" Tarnower are sufficiently interesting people to warrant such laborious scrutiny. Trilling struggles mightily to give weight to them and their strange case, but ends up proving mainly that you can't make a silk purse out of a sow's ear.

She was drawn to the case, Trilling writes, because "I'm fascinated by the kind of world that Dr. Tarnower and Mrs. Harris inhabited together and what happened between them for their relationship to ensue in such tragedy." She perceived in that relationship a variety of sweeping themes: "Love and sexual passion, honor, money, envy, jealousy, greed, death, greatness and meanness of spirit, the anguishing anatomy of class differences. . . ." In the end, she came to see Jean Harris as a character in a novel--"She belongs to the novel in the way that Emma Bovary does, or Anna Karenina. They too were characters in contradiction"--and she offers this volume as, in effect, a substitute for that novel.

It is a noble and honorable effort, but it does not succeed. In part that is because Trilling insists on recapitulating the trial of Jean Harris at exhaustive and interminable length; had she trimmed her arguments down to 15,000 or 20,000 words, Mrs. Harris would have been a provocative magazine article, but as a book it's mostly padding. But the greatest problem is simply that Trilling is dealing with two very dull people.

The basic facts of the case must now be as familiar as those of the Lindbergh or Hearst kidnappings--two similarly sensational cases involving people of wealth and position. On the night of March 10, 1980, Dr. Herman Tarnower, author of a hugely successful book promoting his "Scarsdale diet," was killed in his bedroom in the wealthy community of Purchase, New York. His killer was Jean Harris, headmistress of the Madeira School for girls in Northern Virginia and his lover for a decade and a half. She claimed that the killing was accidental, that she had intended to commit suicide; but a year later she was found guilty on three different counts, one of them being second-degree murder, and she is now serving the first year of a 15-year sentence.

Certainly the case has the ingredients of high drama: a wealthy Jewish doctor killed by the headmistress of a finishing school for WASPish girls; the triangular element added by the doctor's increasing interest in a younger woman, Lynne Tryforos; the ambiance in Purchase of money, exclusivity and quiet glamour; the rich supply of undertones and overtones, among them feminism and class rivalry. Yet there was less to the case than initially met the eye. Once the sensation of the killing had faded, there was little left to hold our interest; Jean Harris revealed herself to be uncommunicative and withdrawn, and Hi Tarnower turned out to have been so thoroughly dislikable that sympathy for him was out of the question.

These two people pose insurmountable problems for Trilling. Because one is so distant and the other so contemptible, there is nothing to engage us in a book as long as this one. Presumably what is to interest us in lieu of sympathetic characters is Trilling's view of their situation, but in that case the clanking of the machinery is just too evident. What does it mean, for example, when she writes as follows:

"Tarnower with his dry striving and worldly salvations, his best seller and his reputation which has traveled as far as China, his angry suffering mistress and his senseless violent death, was perhaps as representative of his moment as Gatsby, with his impossible dream named Daisy, she of the thrilling voice that was 'full of money,' had been representative of the American twenties. . . . Fitzgerald was unafraid of the word 'vulgar.' I wanted his courage to speak in such clean terms of Tarnower's house and the kind of life it stood for. Could he or Mrs. Harris have known, could they have endured to know, how inglorious were the social heights to which they'd attained?"

What this means, so far as I can discern, is that Trilling is struggling to find significance and, in its absence, inventing it. She does demonstrate, amply, the tastelessness, vulgarity and ostentation of Tarnower's life, and her comments on the weird fascination it held for Jean Harris are devastating. But the Gatsby comparison is utterly strained, a transparent example of reaching for a theme that isn't there; Trilling allows herself to do far too much of this.

She is best when she is employing her powers of observation and commentary. Especially when she is writing about money and/or class, she is perceptive and interesting. Her comments on the social situation of the Jews of Westchester County are thoughtful; her description of the students and parents of Madeira is clinical and unsparing. Her most useful remarks about Jean Harris have to do with that woman's position "on the outside looking in"--a person employed by the wealthy in order to oversee the education of their daughters, but not allowed full admission into their world. Here, if anywhere, is where one finds echoes of Gatsby.

But when Trilling moves from social commentary to a narrative of the trial, she is on unfamiliar ground and does not know quite what to do; her answer is to tell us everything and then, just for good measure, to tell us more. She employs the first-person singular to wild excess, almost to the point of self-parody. Her prose style has a casualness that is so forced it practically screams to be noticed; even Pauline Kael might blush if caught employing so many contractions. And of Trilling's attempts at amateur psychoanalysis, the less said the better.

What the Harris case comes down to is that one shallow person was killed by another shallow person. All the glitter and notoriety with which the case is surrounded cannot disguise the emptiness at its center. It is this which defeats Diana Trilling; Mrs. Harris is much ado about nothing.