THE TEDDY bear is a fine example - the American eagle is another - in which the symbols of politics and statecraft have infused into the nation's cultural life.

And yet the eagle has not proved satisfactory in bed, by and large, while the bear has slept with all.

The Smithsonian Institution, in its long task of diffusing knowledge, has round to the teddy bear and now displays, in the Museum of History and Technology, a case of ursine lore attached to President Theodore Roosevelt.

Roosevelt was in Mississippi in the November of 1902 when he declined to shoot a bear cub. There was at this time some commotion about boundary lines between Mississippi and Louisiana, and the cartoonist for The Washington Post seized on the theme. "Drawing the Line," to incorporate both the boundary question and the president's refusal to shoot the small bear. As a hunter, Roosevelt drew the line.

Some cartoons take a while to figure out.

Clifford K. Berryman, the cartoonist, went from The Post to The Washington Star where he remained with great distinction for roughly a century, and where several generations of copy boys held him in affectionate awe. It is said to be very hard to fool copy boys about the basic character of Journalists. They know dark things. Berryman was a prince.

The teddy bear, as a symbol for Roosevelt, caught on famously, and the Ideal Toy Co. began manufacturing them in 1903. The Theodore Bear Co. entered the competition with additional bears in 1905.

There are men now living who well remember the ultimate version of the bear, fitted with brass wheels and a back suitable for infant riding, and complete with an iron ring in the head which, when pulled, caused a growl to come forth, at least in the first several days of hard use, and a grating sound thereafter.

But as Herbert Collins says - he is the curator of political history - the desideratum was a cuddy bear. Children deprived of teddy bears cuddled pillows Collins said, but bears were thought ideal. Others say their Poody, a pillow, was as good as any bear. In 1972, Collins went on. Champ Clark sought the nomination and gave Woodrow Wilson a certain scare, though Clark lost.

Clark was from Missouri and a song about a bound dog was attached to him. Efforts were made to manufacture hound dogs to replace teddy bears in the nation's mind and cribs but a hound dog is not as good for cuddling as a bear.

And why the hell not? one might ask Collins.

"They just aren't," he said.

When hounds marched in a parade for Champ Clark in Baltimore. Collins said, the Clark opponents threw mud at them.

The nation has had her shameful moments but then not a great deal is expected of Maryland politics and voters, some say.

The teddy bear has remained a power in the nursery for 75 years now, although hounds never caught on except among the most mature and discriminating, it is thought.

Collins has been working for some months arranging the show (the display is designed by Jim Piper) and last June motored to St. Louis to consult with collectors of political items.

There he found treasure for the current show. A game called Feed the Teddy Bear is played somewhat like Pin the Tail on the Donkey, only you cut paper berries with numbers and blindfolded, try to pin them in the bear's open mouth.

This was not what game manufacturers would call a real natural and Collins suspects his example of this game is unique.

Ceramic vases with teddy bears on them bore the names of various towns - Washington, Hagerstown - and were sold in1904 in souvenir shops for people who insist on knowing where they have been.

A bandana for women is on display, a teddy bear with a tray full of champagne glasses printed on it.

Collins wonders if this is not a bit masculine - a good design for cocktail napkins at a stag party, he speculated - for women to wear on their heads. But there is no telling what fashion may dictate at any particular moment.

A pillow cover shows two teddy bear in a seasaw. Collins thinks it is charming. The owner at first did not wish to part with it.

A china plate shows bears waddling towards the White House, and a book purports to recount adventures of the Roosevelt bears.

The show is small, only one case full of these objects. The lover of American political lore and whoopla will find them ample. Like a case of engraved carnelians from Alexandria.

The museum's shop is selling teddy bears and canvas bags decorated with bear design.

In England there is general shock when it is pointed out the teddy bear is American. They all assume it is English and such bears are held in esteem. One adult male gave a party for his teddy bears in Berkeley Square.

The thing has gone pretty far.

One Englishman who was given a teddy bear fell to musing and invented the Pooh Bear. There is also Paddington Bear, a current English television cuddly and Smokey Bear, who preserved forests from fire.

There are athletic-team bears. Athletes are said to favor teddy bears as mascots.

The Smithsonian has nothing against Pooh or Smokey or athletic teams or Russians but deals, in this little salute to the bear, only with the pure teddy.

One man, with an elegant French name and a passion for French culture and gloire, said of this exhibit that he was damaged in infancy by being given a stuffed toy rabbit.

"All my friends had teddy bears and I had a rabbit. It made a difference."

He has not been right since.The small bear at the museum costs $4.50 and while there's life there's hope.