This mid-July day has been hot - in the high 90s - and though the bite has gone from the sun as evening rolls along, the muggy Mississippi air still wraps a heavy embrace around us. The clinking of ice in my soda glass is comforting as we relax within a few feet of the mighty river and let a sense of its history enfold us.

Here in Natchez, it is easy to let that happen - one reason this town and nearby Vicksburg have begun drawing increasing numbers of tourists in recent years. The history is fascinating, from Indian times through French, English, and Spanish rule, clear through the Civil War. So are the sights and sounds that go with it.

This is a town of magnificent antebellum homes, slave quarters, and Indian burial mounds; of mementos and memories of a war more brutal than any in history until World War I; of a magnificent river that evokes romantic images from a colorful past by the mere mention of its name.

What a river. It drains two-thirds of the United States. Before the levees were built opposite Natchez, a flood might mean you would have to row 30 miles just to get across. France, Britain, and Spain fought and feuded over it, and after independence a new United States government saw it as so important to its national interest that it pried the region from the grasp of Spain.

History books will tell you about the river and its past, but a real feel for it comes here in Natchez - and nowhere more tellingly than in a restaurant called the Cock o' the Walk, below the Natchez bluffs, with only a narrow road between the front veranda and the yawning expanse of the river.

Some of the credit for this sense of history must go to Weeta Colebank - Mrs. History as some people call her - who is one of the proprietors of Cock o' the Walk. Mrs. Colebank says that a cocked red feather in a hat is the symbol of the restaurant, as it was the symbol of previous cocks o' the walk, the champion brawlers of the Mississippi in the days when brawling was a major form of entertainment among the barge crews. What else was there to do during the long haul back upstream, after the flowing river had brought them so easily to its mouth?

The trade made possible by the river traffic brought much wealth to the region in the days when the Mississippi was the western frontier of the nation and cotton was king, Mrs. Colebank explained. Around 1850, half the millionaires in the United States lived here atop the Natchez bluffs. Today, 600 Natchez homes are in the National Register of Historic Places. There are more of these important buildings per square mile in Natchez than anywhere else in the country.

The architecture is interestingly varied (for instance, one home I saw belonged more to the Swiss or Austrian Alps). There is good reason for this. Many European sea captains who brought manufactured goods (and bricks, as ballast) to this town in exchange for cotton returned to settle here when their careers at sea were over. The descendants of these people are typically American , and their accents typically Southern. But the time was when many of the accents of Europe could be heard in Natchez's quiet streets, and this town was as international as any in the world.

There are magnificent views of the river from the Natchez bluffs, but these bluffs have far more significance to the town than that of providing scenic outlooks. They made possible the founding of Natchez as the first permanent European settlement on the over 3,000-mile-long river. The French, who controlled the Mississippi, considered that the northern stretches in Minnesota were too cold for permanent settlement and the south, around New Orleans, was too swampy. So they opted for the Natchez bluffs in 1716 - though La Salle had already given the site his blessing in 1682, 300 years ago last summer. The French called the place Fort Rosalie. The bluffs made it easy to defend and immune to flooding.

Natchez was once a town of two parts: elegant homes atop the bluffs and the shanties of the riverfront below them. The riverfront was still in its rough-and-tumble heyday when the cyprus frame building that now houses the restaurant was built a century ago.

Now the differentiation has gone. Fully two-thirds of the shantytown has fallen to the relentless erosion of the river, and what is left has been restored and smartened up. There is too much history and atmosphere here along the riverbank to let it fall into decay. Certainly the Cock o' the Walk is popular both for its catfish menu and its place in the preservation of the town's past.

On the night I was there, as I was called in from the riverbank because my table was ready at about 8 o'clock, the red, upright, slightly off-key piano was playing ''I'm Going to Buy a Paper Doll.'' Around 10:30, when I rose to leave, the tune was ''April in Paris.'' And still there was barely an empty chair in the place.

Many of the town's historic sites can be visited on foot. A very different type of monument, on the outskirts of town, is the Grand Village of the Natchez Indians, the result of archaeological investigations in 1930, 1962, 1972, and ' 73. The Natchez, thought to be an offshoot of the Mayans, were the original founders of Natchez. All that is left of them today is the village and the name of the town itself.

Except for one brief shelling, Natchez came through the War Between the States unscarred. Not so neighboring Vicksburg. Though somewhat unionist in sentiment, Vicksburg was besieged and battered the way few others were because of its strategic position on the river. President Lincoln had instructed General Grant to take Vicksburg whatever the cost, because it was ''the key to the Confederacy.''

Today, the 1,858-acre National Military Park is one of the best-maintained military memorials in the US. If you go, be sure to take in the Old Court House Museum. While the park tells of the war through Union eyes, the museum takes a Confederate perspective. As curator Gordon Cotton puts it: ''The winner always gets to write the history; the loser gets his history written about him.''

Vicksburg is far more than a memorial to war and the courage that goes with it. It, too, has graceful antebellum homes - even if a cannonball remains lodged in one of them; great restaurants; Southern hospitality; and the river.

Yes. Always there is the river.