Mrs. Ronald Reagan. The White House. Washington, D. C.

Dear Mrs. Reagan:

Washington is always awash in rumors, and one of the most persisent and mysterious of them is that you are our one hope for arms control. They seriously believe that you have in mind posterity and want the word "Peacemaker" to be forever identified with your husband.

Why they think so is not clear to all of us. You have not spoken on the subject. Nothing that has transpired in the five years since your husband took office would suggest that you have persuaded him that he should go down in history as a hero of the ages, as a world leader who reduced, or even ended, the threat of nuclear war.

But hard-headed politicians, among them Republican senators who have the most aching concern to believe what is so far myth, argue that you are the White House dove. They concede there is not a shred of evidence on the point. They start with the unarguable proposition of your devotion to your husband and reason like this:

"He can't say he's reduced the size of government -- it's bigger than when he took over."

He can't say he's balanced the budget. He's got the biggest deficit in history. So what's left?"

Are they right?

Where some of us have the most trouble believing that you are nudging him towards glory as the man who made the world a safer place is, frankly, his record. One summit meeting with Gorbachev, where no progress was made on arms control and one summit meeting to come. It's not much.

Put up against his insistence on "Star Wars," as he hates it to be called, it is, in fact, nothing. The strategic defense initiative may not be foolhardy, as some scientists say it is, but your husband admits it won't be an umbrella for the world's children and their parents. But it would cost a trillion dollars and take 20 years. Where's the money coming from in the Gramm-Rudman era? And any successor to your husband could cancel it with a stroke. If he persists with Star Wars, he goes down as a spendthrift visionary. It's better than the "warmonger" charge you fought so long, but not much.

Mikhail Gorbachev has now given you your big chance. If you say, "Take it, Ronnie," it could happen. If you don't, we will settle back in the dreary round of threats and escalations. You can tell him that Star Wars is not worth a chance for immortality as a man of peace.

We don't know what you thought of Gorbachev when you met him in Geneva. You have a shrewd instinct for sensing men who can help or hurt your husband. Maybe you thought he was like all the rest of the Soviets, out to con Europe and take over the world.

But maybe you found out from him, or his wife, that he has his eye on history, too, and wants to go down as the first Soviet leader to make the system work. If he really wants to show communism as something other than repressive and incompetent, he has to cut back on the military spending. Which did you think?

Maybe his offer is a "slick propaganda trick," as some of your husband's helpers dubbed it for the evening news shows the day it arrived.

But the fact is that Gorbachev has called your husband's bluff. You remember that when he began talking about Star Wars, he said his real goal was "the elimination of nuclear weapons."

Gorbachev says that's what he wants, too. And he has delivered a blueprint. It's not good enough to respond, as several have, that the president said it first.

This is a chance to go about it, or at least as good as we are likely to get in our time.

You can be sure nobody else will push for it. The men around your husband are distinctly miffed that Gorbachev came out of the blue at them, with a dramatic offer to continue the test-ban and reduce nuclear weapons. They had thought he was too busy getting ready for his party congress to drop something this big on them.

Secretary of State George Shultz said the Soviets should have made the offer at Geneva. Secretary of Defense Caspar Weinberger says there's "not much new in them" and that they are a "restatement of other proposals."

You can be sure that Richard Perle, the Defense Department watchdog against arms treaties, is busy right now tearing it apart, word by word.

Shultz couldn't be enthusiastic. Arms control talk inflames the right, which is after him anyway. Weinberger is rational on any subject but the Soviets. He's convinced the only thing you can trust them to do is to cheat on treaties. Your husband's new national security adviser, John Poindexter, doesn't sound like a champion in the field.

Congress would ratify a treaty your husband made. But if Congress leans on him to take this chance, he may get his back up. He doesn't like public advice.

So there's only you. At least that's the rumor. A lot of us hope you'll confirm it. Sincerely, Hoping.