Somehow you can't believe you're really seeing it.

How can anything so famous and important look like that? The Enigma, the great Nazi cipher machine that won the war -- for the other side -- why, it's nothing but an old Remington typewriter and some wires in a wooden box.

It is part of a tiny gem of an exhibit on cipher machines of the two world wars, to be displayed all year at the National Museum of American History. The show goes back to Jefferson's "wheel cypher" and the 1918 Potomac Code, a thin book with 1,800 code words and the quaint warning "Secret -- Must Not Fall Into Hands of Enemy" on its cover.

There is also good old M-94, used by the army from 1922 clear up to Pearl Harbor, and the Sigaba, a never-broken cipher machine that Roosevelt and Churchill used to correspond on. This, like the revolutionary Hebern electric machine, works with an electrically driven rotor on whose rim is engraved an alphabet, allowing vastly more complex letter changes.

But the Enigma is the star exhibit, along with the British Ultra device that conquered it. All through World War II the Germans used various forms of the Enigma, invincibly confident that it could never be broken. And all through the war, or at least the crucial last years, the British were reading their messages. A Polish machine called Bombe, a computer seven feet high and 12 feet wide (pictured in the exhibit), led the British to the solution.

The problem was this: Push a key on the Enigma typewriter, and it flashes through three or four or five different rotors, each of which changes it to a different letter. Push another key, and the rotors all move, making in effect a whole new code. It's like having a separate cipher for each letter in the message. A five-rotor machine can produce almost 12 million different alphabets.

No wonder the Nazis thought it unbreakable.

The British solution was basically to build a machine just like it, a machine whose mind worked the same way as Enigma's.

In the Atlantic, the Germans were destroying convoys at will, sinking 21 ships in four days in 1943. That changed dramatically with Ultra, which revealed the enemy submarine rendezous to the Allies. In the war with Japan, the Americans broke the enemy Purple cipher in time to turn the battle to Midway into an ambush, changing the course of history. And when Admiral Yamamoto flew to the Solomons on an inspection tour, the Americans got word of it and shot him down, depriving the Japanese of their most intelligent leader.

Two things about war ciphers are sometimes overlooked. First, the messages, even when decoded, are usually maddeningly fragmentary. No one says, "We are attacking Midway." What you get are ship positions and courses and orders for extra trench-digging tools (not logical on shipboard) and maybe a " good hunting!" and a "banzai!" or two. They need expert interpretation, a lot of imagination and more than a little luck Second, the knowledge must be used in a way that keeps the enemy from realizing his cipher is broken.

After the war, bitter survivors charged that lives often were lost, doomed operations were allowed to go ahead, rather than reveal the secret that we knew what we knew.

In any case, here are the machines themselves, safe and harmless under glass in the Smithsonian, declassified at last. There is even a sample message: a wire from Martin Bohrmann and Admiral Doenitz making Seyss-Inquart the successor the Hitler, replacing Goering. How eerie it must have been to read over the shoulders of the enemy even in the last agonies of the Third Reich. Quite unBritish.