Here along the snowy ridges and hollows of Pike County, one of the world's richest coal fields, striking miners are secure in what they know:

Armies cannot mine coal Presidential directives cannot mine coal. Courts cannot mine coal. Only coal miners mine coal.

That much the history of tense times in other strikes has taught them. And now, as official Washington ponders ways to end this 75-day-old strike, the United Mine Workers members are secure in their beliefs:

There will be no coal as long as they do not get the contract they want.

But nothing in these remote Appalachian hills ever is as simple as it seems. Here in the UMW's District 30, which covers Pike and other eastern Kentucky counties, coal is as much the miner's burden as the nation's need.

Coal is all these miners can turn to. It is the crop of their land. Yet it turns on them with a vengence - taking their lives in dark underground mines, maiming them and crushing spirits.

Gad Johnson has lived this story. He is 64, gasping from the coal dust in his lungs, bent from the work he began at age 14. He sits in a comfortable living room in a comfortable house on one of the muddiest winding roads in these parts, at Hemphill in Letcher County.

"We are fighting for survival," he says. "If we don't have proper health care and proper food and clothes, we know what it will be because we've experienced it - without our union there is no right in this area.

"Our people are closer, more determined than they've been in a long time. I've never seen such closeness. This contract is not acceptable. As ignorant, as untaught as I am, I could tear that thing apart."

In 1972 when Arnold Miller was elected president of the UMW, Gad Johnson's local at Hemphill was one of the few in the district that supported Miller. Now, at Hemphill, at Jackhorn, at Shelbiana, at Zebulon, at Hatfield and all the other oddly named coal towns, they talk of impeaching their president for failing them.

But Gad Johnson misspeaks himself. He applies to himself that popular conception of the miner as the unlettered, unsophisticated mule of the blue-collar force.

This is not true. Up and down these hollows the miners - unlettered, perhaps - and their wives understand and explain their cares with the fluency that only experience can teach.

They have eyes and ears. They know that their homes and trailer-residences, which dot these bottomlands, sit above and incredible wealth of black mineral whose fruits they share minimally. So as the strike drags on, they use food stamps. They postpone visits to the doctor. The banks and the stores extend them credit and tolerate mortgage delinquencies because the strike will end one day and payments will resume.

Older relatives, in the custom of the of tightly drawn family unit of the Appalachian mountains, share Social Security and black-lung benefits with them. Picketers stop motorists and solicit "relief fund" contributions.

Across this tableau runs a constant strain, a class strain of the "have" against the "have-not." Miners stay to themselves, coal operators stay to themselves.

Miners live in the trailers and the small house down along the roads, many of them winding, unpaved mud ruts that parallel the mountain creeks. Coal operators live in the brick ramblers in the towns and the developments.

Nowhere is this division of have and have-not more evident that here in Pike County, the largest coal-producing county in eastern Kentucky. It is the nerve center of the coal boom that developed after the Arab oil embargo of 1973-74.

Great fortunes are being made here every month, although since Dec. 6 very little coal - that is, coal from the county's non-UMW mines - has been allowed out by the UMW pickets. No one knows for certain, but the claim made widely here is that Pike County has more than 200 millionaires among its 70,000 residents.

All of this comes from coal. It is speculated on, it is mined, it is sold and carried out on huge trucks and long unit trains that move out night and day during ordinary times to the East and the Midwest.

When times are good, everyone thrives. Motels in the county seat, Pikeville, a city of some 5,000 people, are booked weeks in advance by travelers dealing in coal. The city's stores bustle and sell fine merchandise. Franchise food stands around its fringes confirm that Pikeville has joined the mainstream.

Dr. William Hambley, a surgeon who has been Pikeville's unpaid years, describes this situation: "Energy is the noose around the neck of everybody. There had to be changes in energy policy and cost. This area has subsidized the rest of the country with low wage rates and cheap coal."

But as this strike continues in its third month, the economic pace in Pikeville is sowing. Businessmen like Terry Johnson, a young firearms merchant, note the decline in sales and wonder how long it will last.

"This month I'm lost," he says over the counter of TJ's Gun Store, one of four in town. Last month, after a striker was shot, the store's sales increased. Miners wanted guns, which in this county are so common as coal.

The "noose" that Mayor Hambley describes continues to draw tight around Pike County residents and their lives.

Families divide over union sympathy. Coal operators, as they have since the 1920s, sternly resist organizing efforts. Nonunion operators try to move coal, unon picketers try to stop them.

Coal companies hire security guards imagines threats. Railroad police roam the lines of the Chessie System, but are unable to prevent a major railroad bridge out of Kentucky from being dynamited, as occured the other night in Lawrence County to the north. Nor can they stop the derailment of a train, as occurred two nights later near here.

State police sit watchfully in their cruisers outside the nonunion mine sites where the occasionally hold operator will attempt to run coal. UMW picketers glare at them, complain that the police follow them and threaten them.

Nonunion miners often sympathize with UMW counterparts, but fear that they will be fired if they do not cross the picket lines. That happens. They fear the consequences if they cross the lines and then try to emerge without escort.

J. C. Kirk, a strapping, articulate local union official who works for the Island Creek Coal Co. near South Williamson, shakes his head in dismay.

His brother became a coal mine foreman and since that day they have not visited each other. He sees this coal business tear other families assunder.

"The history of the UMW and the companies is a terrible black mark on this country. That bothers me. It is a disgrace. No good. It runs deeper than social functions or religion, where the miners stay apart from the company people," Kirk says.

His buddy, Denny Ray Marcum, the local president from Hatfield, laments the same phenomenon. "My brother makes $15 more a day than I do by working in a nonunion mine. But he knows he'd have nothing without us and the pressure we keep on these companies," Marcum says.

"But when it get to crossing that picket line. Well, buddy, I told my uncle the other day, 'Cross this line and you're whupped.'"

In these times, as families split, others come together, putting aside their entrepreneurial differences. When Ray Bevins of Elkhorn City, a UMW miner for 32 years at a Republic Steel Co. mine, went on strike Dec. 6, the closing of ranks was immediate.

Bevins' two sons-in-law, who operate their own small non-UMW mines, and his son, who works in one of them, shut down their operations voluntarily without saying a word.

"We have no disagreements because we just don't talk about this," Bevins says. "They don't want violence and tey did this to get along with us."

Related to UMW members or not, operators of hundreds of other small nonuion mines in the country followed suit. Discretion - or, as counry store operator Ronald Webb at Shelbiana put it, "just good sense" - takes over.

Kirk sits on the sofa in Marcum's mobile home and talks more about this atmosphere of brothers avoiding brothers and coal men avoiding miners.

"No one can make us mine coal. I know there may be a national emergency, but the miners should not have to take the full blame for the problems - there have been irresponsible people on both sides," Kirk says.

"We want a decent living and decent security, decent medical benefits, decent job protection. The coal miner feels his security is gone with this contract they're negotiating.

"We are all up there for one reason - all of us - to make a living. But the companies treat their miners like kids. They own the mines, but thank the Lord they don't own the men."