The Scarsdale Letter -- a raging, eloquent, often obscene letter that Jean Harris sent Dr. Herman Tarnower last March 10, the day she shot him dead -- was finally made public today, and its contents shocked a courtroom that by now would have seemed inured to shock.

There were charges that Lynne Tryforos, Harris's rival for Tarnower's affections, had not only destroyed $1,000 worth of Harris's clothing, but also had ruined a silk dress belonging to Harris by covering it with human excrement. There was the allegation that someone -- probably Tryforos -- had sent Harris a copy of Tarnower's will, with Harris' name "scratched out" and Tryforos' name written there instead.

There was, throughout, obscenity and loathing, both for herself and for the doctor. "Those tasteless diatribes at the dinner table that every man should have a wife half his age plus seven years. . . . made me feel like old, discarded garbage," she said.

Most of all there was rage directed at Tryforos, particularly at the news that the younger woman, not Jean Harris, was to be Tarnower's date for an upcoming testimonial dinner that spring.

"I am distraught," wrote Harris. "Your phone call to say that you prefer the company of a vicious, adulterous, psychotic whore has kept me awake almost 36 hours . . . this letter will ramble, but I had to do something besides shriek with pain . . . I will be there on the 19th of April, because it is my right to be there. . . . after 14 years of making love to you I have earned that right. . . . I don't care if the slut comes, even if she pops out of a cake naked . . . frosted with chocolate. . . ."

There was, as well, tremedous anger at the doctor, whose passion for Harris, according to George Bolen, the prosecutor in her murder trial, had been fading.

"I received a copy of your will with my name vigorously scratched out and Lynne's name in your handwriting written in three places," the letter said, ". . . you leaving her a quarter of a million dollars and her children $250,000 apiece and the boys and me nothing. . . . [it is] the culmination of 14 years of broken promises. . . ." n

The letter went on to describe those "broken promises": "'I want to buy you a whole new wardrobe, darling.' 'I want you to get your teeth fixed at my expense, darling.' 'My home is your home, darling.' 'Welcome home, darling.' 'The ring is yours forever, darling. If you leave it with me now, I will leave it to you in my will.' 'You have of course been well taken care of in my will, darling.' 'Let me buy an apartment with you in New York, darling.'"

Later, there were painful accusations about having watched the doctor "grow rich" in years when Harris was "destitute," of moments in which she had to borrow 50 cents from Tarnower's servent to pay the tolls on the highway. There was also a fierce attack on Tarnower for accusing her of taking books and stealing money. f

"Twice I have taken money from your wallet -- each time to pay for sick damage done to my property by your psychotic whore," she wrote. "I don't have the money to afford a sick playmate -- you do. She took a brand new nightgown that I paid $40.00 for and covered it with bright orange stains. . . . the second thing you paid for (I never replaced it) was a yellow silk dress . . . unfortunately, I forgot to pack it because it was new and still in a box in the downstairs closet. . . . when I returned it was still in the box, rolled up, not folded now, and smeared and vile with feces. I told you once it was something 'brown and sticky.' It was, quite simply, Herman Tarnower, human s---!"

Harris, former headmistress of Madeira School in McLean, Va., has been in court since October, charged with second-degree murder in the death of Tarnower, her lover, in the bedroom of his home. The prosecution, claiming that Tarnower had tired of Harris and had, the weekend before the shooting, told her he no longer wanted to see her, insists that Harris shot Tarnower intentionally in a jealous rage.

Harris, who has been on the witness stand for seven days, insists that she drove from her home in Virginia to the doctor's home in Westchester, N.Y., for a "few more moments of peace with Hi" before killing herself. She denies that Tarnower wanted to stop seeing her, or that a love triangle was a motive for the shooting. She also denies being angry at Tarnower. "I was upset," she says.

Developments of the past few days, however, indicate that Harris hated Lynne Tryforos, who was 20 years her junior. And the admission today into evidence of the Scarsdale Letter, which the defense team fought all the way up to New York Appellate Court, show clearly that Harris perceived Tryforos, who received $200,000 in Tarnower's will while Harris received $220,000, as a threat.

Harris had not wanted the letter read in court. "I think it would expose Hi in a way he doesn't need to be exposed," she had said, "and Lynne in a way that I don't care. . . . it is a very private letter. . . ."

Today, as prosecutor Bolen read her letter to the jury, her expression was fixed, impassive. The chin was defiantly upturned, the head turned slightly away from the jury, the eyes looking up and across the room, almost into space, as if she were putting distance between herself and the scene. The jury, which has heard many days of tedious testimony in this case, listened breathless, rapt.

The letter was long -- 10 pages -- and handwritten. And the most striking things about it, aside from the repeated references to Tryforos as a "whore" and to Harris' own feelings of being "old and pathetice," were the stories of the infighting between the two women in Tarnower's life, an ugly, immature, exchange that Tarower apparently did little to ease. (When Harris found her clothes slashed in Tarnower's home, she said, she mentioned it to Tryforos and was told, "You cut them up yourself and blamed it on me.")

It was also clear from the letter, although Harris had denied it on the stand, that Tarnower had threatened to stop seeing her if she did not stop harassing Tryforos -- that Tryforos was the doctor's preferred woman. "You keep me in control by threatening me with banishment," Harris wrote, "an easy threat which you know I couldn't live with and so I stay home alone while you make love to someone who who has almost totally destroyed me."

There were plaintive cries from Harris about her fears of being unattractive. "To be jeered at, and called 'old and pathetic' made me seriously consider borrowing $5,000 just before I left New York and telling a doctor to make me young again -- to do anything but make me not feel like discarded trash -- I lost my nerve because there was always the chance I'd end up feeling uglier than before."

There was anger that Tarnower had sold the engagement ring that she had returned to him during a time her income "before taxes was $12,000 a year" and "I had two children in private school"; anger that her son had lost a scholarship because Harris had told her son's college that she would be marrying Tarnower and not need the funds. "I desperately needed money all these years. I couldn't have sold the ring. It was tangible proof of your love and it meant more than life itself. That you sold it the summer your adulterous slut finally got her divorce and needed money is a kind of sick, cynical act, that left me old and bitter and sick."

And there was indication -- as the prosecutor had said -- that not being invited by Tarnower to be with him the night he was honored had had a devastating effect on Harris.

"I have been publicly humiliated again and again but not on the 19th of April [the day of the testimonial dinner]," she wrote. "It is the apex of your career and I believe I have earned the right to watch it if only from a dark corner near the kitchen. . . . she has you every single moment in March -- for Christ's sake, give me April."

Following the reading of the letter, the prosecutor pushed Harris as hard as she's been pushed in this trial. There was suggestions that she could have killed herself the night she shot the doctor if she had really intended to. "Why did you take the gun away from your head to shot it [after it didn't go off]," thundered the prosecutor. "Why didn't you keep it there and shoot it again and again and again."

There was suggestion that Harris was not leaving the house to call for help after the shooting, that she was merely fleeing.

And finally, at the end of the day, there were the accusations that Harris, in her testimony of wanting to "die a private death," was being dishonest.

"You said you wanted death to be a private thing, but you knew Dr. Tarnower was an internationally known figure . . .," said Bolen, fairly shouting.

"That's interesting," said Harris, calmly, with a little smile, "I never thought of Hi as famous, simply as an old friend, though obviously that's the reason for this whole performance, because he was well known?"

"Would you be aware of the consequences of having your body with a bullet in your head found on the pond near his estate. . . . do you think that would in any way have enhanced his reputation . . .?" asked the prosecutor.

". . . . Hi was very strong, he would have been sorry, but he would survive very well . . .," said Harris.

The prosecutor changed his line of questioning.

Hadn't it been a fact that the day Harris shot Tarnower he told her he had proposed to Tryforos; hadn't the doctor told Harris she had lied and cheated?

He yelled at her across the stand."Isn't it a fact that the doctor, the morning, of March 10, told you you were going to inherit $240,000 . . .?"

The defense attorney was on his feet, screaming for a mistrial; the judge overruled him.

The prosecutor made his last attack then, an attack out of the movies and the tabloids.

"Isn't it a fact that on March 10, 1980, you intended to kill Herman Tarnower and yourself because if you couldn't have him no one would?" he shouted.

"No, Mr. Bolen, it is not," snapped back Harris, composed and calm.

"No more questions," said the prosecutor, ending his cross-examination.

The trial adjourned, and, as the theater, from the back of the room, came scattered applause.