AT FIRST GLANCE, the continuing and severe decline of the dollar is inexplicable. But on a hard second look, slide is only the world's response to President Carter's plan to control inflation. The outlines of the inflation plan were well known long in advance, and the final version last week was, if anything, stronger than the previous hints and leaks had suggested. The Treasury keeps saying, plaintively, that the "fundamentals" of American economic strength are sound.But there is one fundamental indicator that has consistently pointed to trouble, and that is the rate at which the U.S. money supply has been expanding.

The money supply is controlled by the Federal Reserve Board, and in recent months the numbers of new dollars have been rising much faster than the targets set for them by the Fed itself. Those numbers are followed with the most unblinking attention by the currency brokers, both here and abroad. Rapid growth of the money supply is taken to be the signal of high inflation of the dollar in months and years to come. To be more explicit, a lot of the traders suspect the White House of leaning on the Fed to keep money easy during the election campaign. That, after all, is what governments commonly do. The traders have been responding by selling dollars and buying other currencies that, they believe, have beeter prospects for stability of value.

The Federal Reserve Board faces an ugly dilemma. If it holds the money supply down, it could cause a shortage - which means very high interest rates and bankruptcies, perhaps pitching the country into a severe recession. But if the Fed accommondates the demand for money, it increases the pressures for inflation. What ought the Fed to do?

Theoretically, the exchange system is supposed to stabilize itself. A cheaper dollar makes American goods more competitive abroad, increasing American exports and eliminating the very large American trade deficit. That process is now beginning to work - but not very rapidly or, in the judgment of the currency traders, very convincingly. There's nothing wrong with the theory. But the values of currencies are moving much faster than the trade patterns can adjust. The theory also says, unfortunately, that a declining dollar means a small but perceptible reduction of the American standard of living. It's not a free ride.

But there's a much more immediate penalty in the fall of the dollar. It's inflationary, because it makes imported goods more expensive. The dollar has already sunk low enough to pose a real threat to the Carter anti-inflation plan. As a rough rule of thumb, a 10 percent decline in the international value of the dollar means an increase of 1.5 percent in consumer prices. Over the past year, the dollar has fallen a shocking 18 percent, in relation to the currencies of all other industrial countries, averaged in proportion to U.S. trade with each of them. Within the past month alone, the drop has been 7 percent. As the effects filter through the American economy, they will exert a steady force upward on prices for months to come. It is a bad beginning for wage and price guidelines.

Under these circumstances, the right decision for the Federal Reserve Board is to restrain the money supply more forcefully than it has been doing. In the balancing of risks, it is now clearly more dangerous to err on the side of too great a monetary expansion. If the effects of high interest begin to hobble the domestic economy - as they have not yet significantly begun to do, in a striking departure from past experience - the Fed can relax its constraints later. But if it generates too much money now, that mistake cannot be reversed. It would send the dollar driving down again - carrying with it, possibly, any chance of success for the new wage and price guidelines.