A drought as extensive as this year's sends ripples all through the economy, even into the last place one might expect: a stark turn-of-the-century red brick factory building on the banks of the Missouri River southwest of St. Louis.

The drought in the Midwest means poor corn. Poor corn means undersized or undeveloped cobs. And poor cobs mean trouble for Missouri Meerschaum Co., the world's largest maker of corncob pipes.

Missouri Meerschaum keeps its pipe production figures a deep, dark secret. But the company uses between 7 million and 9 million corncobs a year, grown on contract by area farmers to company specifications, using a large cob, small kernel hybrid developed years ago by University of Missouri scientists.

But the one thing that farmers and science can't control is the weather, and this year Mother Nature has made things, well, rough as a cob for them. The heat and lack of rain have devastated the corn crop, and the folks at Missouri Meerschaum are more than a little edgy about the situation.

"Our yield won't be as good as in some other years," said Bill Deering, the company's day-to-day manager and director of marketing. "The main question is: will we have the quantity we need? Three weeks ago there was deep concern."

Earl Holtgreiwe, the plant manager, added, "It will be touch and go with the cobs this year . . . . You know, a corncob is a corncob, and there's not that much you can do with it."

Holtgreiwe isn't just blowing smoke when he says that. The corncob pipe has come to hold a special romantic spot in American country lore and it has varied only slightly in shape and content since it was invented here in 1869 by Henry Tibbe, a Dutch immigrant woodworker.

Mark Twain, a Missourian who knew his pipes, sized it up pretty well. He said, "If you grow wheat just to get the chaff, you're crazy, but if you grow corn to get the cob, you're smart."

Before there was a Henry Tibbe, farmers and frontiersmen were hollowing out corncobs and using them for pipes. Tibbe took it a step further, coating the cob with a plaster of Paris goo to fill holes left by the kernels, and he had an instant hit on his hands.

Tibbe named his product the Missouri Meerschaum, after the mineral used in making meerschaum pipes, and the name endured. When Tibbe's patent expired other firms got into the business, and by the 1920s this somnolent town of 9,000 was a center of the industry, with a dozen or more companies making cob pipes.

Today, it's down to Missouri Meerschaum and a lone competitor just up the hill, the Buescher Pipe Co., vying for the smoker's favor. Missouri Meerschaum seems to go out of its way to perpetuate itself as a purveyor of Americana.

An air of must and dust pervades Tibbe's ancient brick factory. Old photos, sales posters and exposition certificates hang at off-center angles. Popeye, Gen. Douglas MacArthur, Norman Rockwell and faded advertising placards share honor spots on the dingy walls. Some file cabinets seem to have been there before Tibbe.

The files contain letters from MacArthur and former president Herbert Hoover, with special orders for Missouri Meerschaums. In fact, the company still makes limited numbers of a long-stemmed, deep-bowled model known affectionately as "the Mac"--after the general, naturally.

While there's not all that much to making a pipe (a cob, the plaster, a wooden stem and a plastic mouthpiece), Deering's company is finicky about the way things are done. Farmers who grow the corn, for example, must use special shelling machines provided by the company to avoid scarring the cobs.

And the only real concession to modernity is that the pipe stems are made from New England wood, unlike Tibbe's originals, which used cob stems and reeds pulled from marshes along the Missouri.

"Wood actually performs better than a cob stem," Deering said, "but the fact is, it's very expensive to make a cob stem anymore.

"It's a fun product, an American product, and we take pride in it," said Deering. "Reagan would be proud of us. It's a great kick to come back to the United States after a sales trip to Europe, just to hear the fascination of our Customs people when I tell them what I was doing there.

"But we make a quality product, an honest product," Deering continued. "We are not thought of as a stepchild in the pipe industry. Fact is, in terms of units produced, this is one of the biggest pipe factories in the world."

No one will say so, but Missouri Meerschaum is producing at least 1 million pipes a year, ranging from tiny novelty models to sophisticated, fancy pipes that sell for $14. That continues to amaze Holtgreiwe, who came to work here in 1960.

"To tell the truth, I don't know where all those pipes go. After I was here a couple years, I figured the market for pipes was saturated. But we just keep making and selling them," he said.

Making and selling them, that is, as long as there's a steady flow of top-quality cobs. The company keeps a two-year supply on hand, but the drought of 1983 still is bad news for Missouri Meerschaum. Already they're thinking of increasing their cob-corn plantings next year for insurance.