BEFORE IT'S FROZEN in the concrete of history, let's correct the common error of referring to Ronald Reagan as about to become "the 40th president of the United States." He will be the 39th, and there's both reason and precedent to say so.

This numerical dispute is an old one, as old, in fact, as the second administration of Grover Cleveland which began on March 4, 1893. And the dispute arises from the fact that Cleveland ran three times for president and won twice -- on the first and third attempts. In between, he lost to Benjamin Harrison, whom he defeated on the third try.

There is no disputing that Cleveland was the 22nd president; that is, he was the 22nd person to be president. It simply makes no sense to call him the 24th president as well because he was still the same man. His third try for the presidency surely produced a second Cleveland administration, but we don't number administrations. If we did, George Washington would have been our first and second president and John Adams our third.

That's the reason of it. Now, for the precedent, I cite the Congressional Directory, that compendium of useful and authoritative information about all three branches of government.

For as long as I know (and I have a 1918 edition), the Congressional Directory simply listed the presidents, without numbering them, until 1940. In a 1940 edition, during Franklin Roosevelt's second term, numbering was introduced, and Cleveland was number 22 only. FDR thus was listed as president number 31.

But during the Truman administration, in 1950, somebody switched the numbers; Cleveland was listed as both 22 and 24 and FDR became 32. A news item that year on the change iimplied that the feisty Truman himself had demanded two numbers for fellow Democrat Cleveland and number 33 for himself. I find no record of that, however.

Two years later, when Dwight Eisenhower entered the White House, the GOP inaugural committee decreed that Ike would be the 34th president. So the Directory continued to number Cleveland twice. However, in the 1957 Directory, issued during Ike's second term, all the numbers again were omitted. We returned to the status quo ante and we're there as of today.

Now I concede that the White House Historical Association, which publishes a book on the presidents, numbers Cleveland twice. And I concede that the Reagan inaugural committee calls him the 40th president in the programs it has printed. The committee reports it did so on advice from the National Archives. But does saying so make it so? Why abandon both reasons and precedent? Is that any way to get a new administration off to a good start?