THE FEDERAL Reserve Board is now walking a desperately narrow path. It decided last week to continue the past summer's cautious relaxation and to keep trying to ease interest rates somewhat lower. The country would find it deeply comforting to think that this path might lead directly and quickly to a burst of growth and rapid reduction of unemployment. But don't count on it. The board's primary concern is to keep things from getting worse and, beyond that, to avoid choking off even a weak and sluggish recovery. Its ability to go further is constrained by inflation that is still at a disquieting level.

Any hint of a return to the inflationary tonics of the 1970s risks another paroxysm in the financial markets, shooting interest rates upward again. That happened in the near-panic of March 1980, and twice since then. The economy can't afford a repetition. That's why the Federal Reserve has to move with caution.

The dramatically high unemployment rate is, unfortunately, only the most visible of the signs of weakness and distress in the economy. It would be gratifying to be able simply to turn on the valves full and let cheap credit flow out to business. Until a few years ago, that was the standard remedy. But it won't work this time. People who lend, and most particularly the banks, remember what happened after the recession of 1975. They lost a lot of money in those years by underestimating inflation, and they are determined not to make that mistake again.

The truth is that monetary policy -- meaning the money supply and interest rates -- is a poor instrument for steering the economy. Its uses are narrow in the best of circumstances, and the Reagan administration has all but paralyzed it by putting too much pressure on it. The original Reagan prescription was to use tax cuts to make the economy grow, and tight money to end inflation. That, of course, has proved an enormous fiasco. The tax cuts have produced large inflationary deficits which, colliding with the tight money policy, generate extraordinarily high interest rates and unemployment. Because the administration has no weapon against inflation except monetary policy, the Federal Reserve is left with very little room for maneuver.

The real turning point in the Federal Reserve's policy was at the beginning of July. Since then, it has rather rapidly increased the money supply, inducing a significant fall in interest. The prime rate is down 31/2 percentage points since then, and certificates of deposit by five or more.

The recession having gone on far longer than it expected, the Federal Reserve is now letting the money supply go somewhat higher than it thought prudent in July. It argues, correctly, that the traditional money supply statistics are poor guides to what's happening now. So far, the markets have accepted that view. But as long as the Reagan deficits continue, it would be unrealistic to expect the Federal Reserve to move much faster on interest rates. It is already pressing the limits of the possible.