By a proclamation of the governor, Sunday is a day of prayer for rain across Georgia, but not even divine intervention seems likely to save farmers here from the ravages of the record-breaking drought of 1986.

The story is similar across the searing Southeast, but here in Burke County, the state's largest farming county, the combination of yearlong dryness, mounting debt and low prices is taking shape as a death knell for agriculture.

Veteran Burke County extension agent William H. Craven Jr., ordinarily given to lyrical turn of phrase, delivers a terse and somber prediction: By this time next year, the county's full-time farmer population could be down to 30 from the current 375.

"It's over, there ain't no more," Craven said. "This drought is the longest in duration and the most severe of the century, but it's more than drought. It's low prices from the new farm bill, high interest rates, embargoes, energy costs, the strong dollar, three freezes this spring . . . .

"But our biggest loss is the loss of spirit, determination and desire. There is a complete crumbling of farmer and farm-family spirit," Craven continued. "In my career, which covers seven major droughts, never have I seen the spirits as decimated as they are now."

The literal last straw is visible across the rolling east Georgia hills, where mile upon mile of soybeans, cotton, corn, sorghum, peanuts and hay appear to have been scorched by a celestial flame thrower. The gray earth between the rows is baked to a hard crust. Soil temperatures have hit 140 degrees, making plant growth impossible.

Once verdant pastures, now sepia, lie vacant, their beef cattle denizens having been sent off to slaughter. Farm ponds are drawn down, many streams empty. Rain from the occasional shower evaporates before it can penetrate the soil. Oppressive heat -- the temperature passed 100 degrees on each of the first 21 days of July -- slows human and animal movement.

Agricultural officials say the yearlong drought, with rainfall less than half of normal, has caused more than $1 billion damage to southeastern crops and livestock, with the toll certain to rise as the dimensions of the disaster become clearer. The governors of Georgia, North Carolina and Alabama have asked President Reagan to declare their states disaster areas, which would free up some federal relief aid.

But Agriculture Secretary Richard E. Lyng indicated last week that the region's farmers could not expect additional new assistance from Washington. Lyng promised to speed up claims processing and to cut red tape for the traditional farm disaster aid programs.

The disaster has evoked region-wide cries for direct federal assistance to stricken farmers who cannot afford to take on more debt, even at the lower-interest disaster rates. State Agriculture Commissioner Tommy Irwin has rejected low-interest loans as "a farce" because of tough qualifying rules.

At a meeting Friday in Tifton, where he was on a politically oriented drought inspection tour with Sen. Mack Mattingly (R-Ga.), Lyng was told bluntly by farmer H.C. Richardson that loans wouldn't work. "I already owe more than I can pay back. A loan is not going to do me any good," Richardson said.

Many here regard the administration's response as indifference toward the region in general and toward farmers in particular, which in turn has stirred emotions of bitterness and resignation. Farmers here laughed cynically when Reagan showed up in South Carolina last week to see a small load of midwestern gift hay taken from an Air Force cargo plane.

"It's not just the lack of rain," said Larry Drake, who farms 450 withered acres near here. "Our prices are terrible because of our government's policies. It's all going down the drain. And this is all I know how to do. The reason I stay with it is the hope that things will get better. I don't see it happening."

Drake is uncertain whether he'll be farming next year, but his crop prospects are dismal today. His corn, ordinarily good for 80 to 100 bushels per acre, may produce 20. The heat has dwarfed his soybeans, some are in flower on stunted plants; weeds abound because his herbicides don't work without moisture.

County agent Craven's surveys show this kind of crop damage across Burke County: spring wheat, 55 percent loss, corn, 77 percent loss; oats, 40 percent; sorghum, 84 percent; hay, 80 percent; cotton, 60 percent; peanuts, 40 percent; grazing lands, 75 percent; milk production, 15 percent. Craven esitmates that Burke's approximately $50 million farm income will be halved.

The potential consequences of this widespread devastation hang heavy in the humid air. A farming county that has suffered drought in eight of the last nine crop years is nearing the end of its ability to cope.

Prime farm land that reached $1,000 an acre now sells -- if a buyer can be found -- for several hundred dollars. A county that had only $4.5 million farm debt in 1974 owed at least $125 million a decade later. A county that had 201,000 acres of crops in 1980 is down to 107,000 this year.

"I get the feeling that I'm overly pessimistic, but this county is fast losing its agricultural base," said Wayne Crockett, a farm implement dealer whose business has dwindled rapidly. "Farmers here needed a good crop and average-to-good prices and it looks like they will get neither . . . We're going to lose a lot more farmers.

"I grew up here, grew up in farm equipment," Crockett added. "I never thought I would see Burke County get in this bad shape. It's going to be like a ghost town here. The drought is going to accelerate what's been going on for the last 24 months. A few farmers realize there is a cheap-food policy in Washington, and they are bitter about that."

Ray Delagle, chairman of the Burke County Commission, said he thinks that it will take several years to assess the impact of the drought on local agriculture -- and it will be severe. The only positive economic note here is a Georgia Power Co. nuclear plant project, which has employed thousands of workers and boosted county tax income.

"I don't know if we ever will recover from this," Delagle said. "It's a sad situation . . . farm land prices will fall more, our tax revenues will be cut back. But we already were in a disaster situation before this drought hit."

Delagle, heavily in debt, gave up farming this year after 37 years on a tractor. "I could have gone another year, but I quit to keep my sanity. I couldn't have made it even with good weather. I lived conservatively, I didn't take somebody else's money and frolic on it, but there's no recovery for me," he said.

Beyond the immediate effects of the dryness and heat and dissolution of spirit, observers like Rep. Lindsay Thomas (D-Ga.), who represents this area, see even more portentous developments.

"What I see is a dramatic deterioration in the structure of agriculture. If this is a 10-year drought cycle, as some believe, then we're about at the end," Thomas said. "When this is over, we will see that we have an absolute catastrophe.

"We have already documented in Georgia the phenomenon of drought and how it has played a role in the emergence of two states -- metropolitan Atlanta and the land-based rural counties. By and large, the vast expanse of these counties have never been under these kinds of pressures," Thomas said.

"We are losing a part of the country that has contributed a great deal," Thomas, a former farmer continued. "This combination of drought, prices, pressure to produce, the departure of farmers from the land -- what it has done to the fiber of communities and to people, it just grieves me. These people are devastated by things absolutely beyond their control."

County agent Craven had another thought. "The greatest asset of Burke County was the great number of sons and daughters of the soil who had gone to college, come back to their native country to work in agriculture. We had a bright future," he said.

"But now we're beginning to ask who's going to feed us. One of our fortes was that we had the infrastructure -- railroads, ports, cotton gins, farm suppliers, elevators -- all that we needed. This now is beginning to crumble, and we can't easily or quickly rebuild the infrastructure if it takes until 1988 or 1989 for this new farm program to put us back in business."

And yet, for all this, some harbor slender hope. George Cane, 56, a bankrupt farmer who has lost most of his land, said, "A lot of us feel the government has deserted us. Why are you leaving us?, we ask. We have 70-year-old women and farmers in their 60s who are dispossessed from their land. I think that's morally wrong in this country . . . but this is still the U.S.A. If there's a place where a miracle can happen, this is it."