As a dairy farmer, Page Nuckols may be somewhat unaccustomed to the intricate world of corporate finance, but as a member of the Board of Supervisors he knows the peculiar arithmetic it takes to calculate the impact of a giant amusement park on a place like Hanover County, Va.

"Now, you got to figure that King's Dominion occupies about 800 acres of this county, said the man who made the motion that brightened the night skies of Doswell with a neon imitation of the Eiffel Tower.

"You put homes there instead -- you're talking half-acre lots -- you're talking 1,600 homes. You figure two children to a home," Page Nuckols said, "and King's Dominion means 3,200 children we'll never have to educate."

But Bruce English of the Hanover County Citizens' Federation looks at King's Dominion differently.

What he sees is a hasty, ill-conceived adventure in development that has raised taxes, thrown the county's sewage treatment plans into chaos, plagued the park's neighbor and threatened local thoroughbreds with nervous breakdowns. What English sees is a "fiasco."

It has been three years since King's Dominion came to Hanover County, while its competitor, Busch Gardens' "The Old Country", settled down the road in James City County near Williamsburg. So far, it seems, the presence of the two "themed" amusement parks has been both bane and blessing to the two largely rural, revenue-starved counties they call home.

For some residents, they are harbingers of future growth, a symbol of development and unimpeded progress. For others, they have been an economic letdown, much less spectacular on the ledger sheets than predictions had led would-be speculators to expect.

And while there are those who feel that these evidence to corporate presence have added a touch of class to the quiet backwaters they inhabit, there are others for whom the new tone comes down to the merely tacky.

"This used to be a pleasant, provincial sort of county," said Katherine Myers, whose home in Hanover was built in 1703. "All of a sudden -- tadah -- we're catapulted into the 20th century.This is the place where [Kentucky Derby winners] Riva Ridge and Secretariat were foaled. They're sort of local heroes to us. We all felt that sort of thing was a whole lot neater than living near an amusement park."

Living within a half-mile of King's Dominion, Myers has grounds for comparison. There are the trumpeting elephants. There are the fat ladies screaming on the roller coaster. There is the smell of the popcorn. There is that "herd of buffalo," as Myers refers to the tourists, staring down at you from the top of the Eiffel Tower."

Worst of all, however, have been the hot air ballons -- tearing off tree-tops, setting fire to soybean fields, landing in the driveway before she has had a chance to park and, in their most heinous offense to date, settling on the badminton court. "I am a very serious badminton player," Myers said. "Have you any idea what it's like to play under those conditions?"

After three years of this sort of thing, Myers has found a rather dramatic analogy to describe King's Dominion's presence in Hanover County. "It's like modern day carpetbagging," she said "They figure, 'those suckers, they need the money. It's what they did to the South 100 years ago and it's no more attractive now than it was then."

But Myers also knows as well that hers is a minority point of view in Hanover County.

"Sometimes," she said, "I feel embarrassed for the county, like it's be ing made a fool of. But to have my my point of view, you have to not need anything. I can say 'raise my damn taxes, I'll pay for my peace and quiet, 'I'm willing to go without a new car or something else.' It's all in what you prize."

And for the officials of counties with growing populations, few sources of revenue and an increasing number of services to provide, a corporate venture that requires little in the way of services and provides a lot in the way of property taxes in a prize worth dreaming of.

James City County manager James Oliver remembers what the dreams were like when the Anheuser-Busch corporation decided to place its largest single capital investment in this forested neighbor to Colonial Williamsburg.

"It was just euphoria," he said. "James City County was going to be the promised land. The county was going to take a quantum jump with this thing called Busch."

The corporation was hardly less ambitious when it came to describing its impact on the community. "An Eagle Has Landed in Colonial Virginia," was the way it was put in gold letters on glossy promotional brochure.

"On May 12, 1607," said the brochure, the first Englishmen set foot on American soil on a stretch of beach on Virginia's James River so blessed by nature they could barely contain their eagerness to share it with others. . . Some 360 years later, August A. Busch III explored the same land. . ."

And brought forth a brewery, a giant amusement park, an exclusive housing development, a planned corporate and light industrial center and $2 million in taxes that accounts for about 20 percent of James City County's operating budget.

Now James Oliver sits surrounded by the fresh paint and modern design of the county government's new office building located on land donated by Busch and surrounded by Busch property and says that "the county is very sensitive to the notion that it not be a kept county. There have been accusations at times that we are too close to Busch."

Instead, Oliver descibes the county's relationship with the corporation as "a mature marriage," one with its share of differences. It is clear, though, observers say that, as in most such relationships, being the breadwinner in the family carries some clout.

Perhaps the most telling example of the direction in which the balance of power is tipped came two years ago when the county made a determined effort to convince the Virginia General Assembly to grant it authority to levy a 1 percent admissions tax on Busch Gardens.

A blitz by corporation lobbyists and personal letters to the legislators from "young Augie" Busch, as he is referred to by some local businessmen, defeated the bill; a backdoor attempt to get the same results through a similar bill from Dinwiddie County last year was similarly scrubbed.

But the outward signs of Busch's influence in the county are only infrequently in evidence -- its impact is seen primarily in the growth of the county services and a corresponding increase in the county payroll.

"Until 1969, we didn't even have any zoning," said Stuart Taylor, a farmer from the largely rural northern end of the county who represents these interests on the Board of Supervisors. "Now we got all these so-called services I could do my own self, I don't need them."

But it is service like a planning department, an additional fire station and an expanded library system that Taylor is talking about, services that those in the predominantly residential section of the county where the Busch complex is located consider necessities.

To some extent, complaints about growth of the county government are coupled with deflated expectations of the sudden increase in personal fortunes Busch was to bring about.

"There was a lot less growth than predicted," Oliver said. News of the corporation's coming prompted a lot of land in the vicinity of the project to change hands as fast as deals could be made. But a protracted court battle between the county and local landowners over what could be built there put the land in legal limbo just when "the bloom was on the rose," according to William Bull, a prominent local real estate broker.

By the time Bull and the other plaintiffs had won their case in the state Supreme Court, an inflationary frost had hit the building market and developers' visions for the area went unrealized.

Similarly, Busch's entry into the housing market did more to cramp its competitors' style than to expand their horizons. Several other exclusive residential areas were on the boards for James City County when Busch announed plans for "Kingsmill on the James." Today, it is the only one to survive into maturity. The 1974 recession made development impossible for most speculators -- only the Busch corporation was able to pour enough money into the project to keep it afloat until the economic winds had shifted.

Now, according to Bull, nearly half of the new deeds of residence recorded in James City County last year were recorded in Kingsmill, and the success of Busch's venture into the housing market has seen a 300 percent increase in the number of real estate brokers and agents in the county.

"It's just more people chasing fewer sales," said Bull. "They're all coming in on the name that the Busch corporation has."

Whatever the unfulfilled expectations in development, the Busch presence has wrested some amused chuckles from local businessmen who lived long in the shadow of the massive Colonial Willaimsburg organization. "They sure took some of the sting out of old CW (as the foundation is called locally)," said one Williamsburg businessman. "All of a sudden, they weren't the big boys in town anymore."

It was after all, Colonial Williamsburg that sold Busch the land for its project in the first place and camaraderie, not competition, is the official line between the two tourist-oriented organizations. But it is not at all clear to the officials of CW, Jamestown and Yorktown that, when it comes down to a limited amount of money to spend, they will win the hearts and minds of American tourists.

"As you know," sighed one such official, "Americans are rather inclined to please, humor and gratify their children. And given these very same children's choices now between the Loch Ness Monster and some of our more sober historical sites, I wonder at times if ther's much of a contest."

In what direction James City County will continue to grow remains uncertain. The county is half residential, half rural, and there is at least one large, several-hundred acre parcel ready to be sold once the right sort of enterprise is found for it.

"It would be nice to have the sort thing where everybody has a masters degree," Bull said. "But they're very hard to find."

A fact Hanover County found out for itself. There, much of the opposition voiced by a small but vocal minority centers around the county's decision to reject King's Dominion's offer to build its own sewage treatment plant and to build its own. The plant is operating at one-fourth its capacity at an annual deficit of $50, 000.

Much of the slack will be taken up by 1983 when a newsprint mill scheduled to be built in Hanover reaches full operation. But in the meantime, some residents feel that the amusement park has done nothing but increase their taxes and destroy longrange planning.

Because of King's Dominion, said Bruce English, the Doswell sewage treatment plant was "overbuilt and built in a hurry. I don't know that anything would have been built if it hadn't been for King's Dominion."

And while the local Board of Supervisors did go so far as to turn down a King's Dominion request for nightly fireworks for fear of endangering the mental health of local thoroughbreds, the prevailing sentiment toward King's Dominion, including the hot air balloonists, is overwhelmingly favorable.

"If this county could support 10 more of them. I'd be for it," said Page Nuckels, who contends that the drain on revenues that comes with the county's increasing function as a bedroom community to Richmond makes an enterprise like King's Dominion "a godsend."

But with the kind of growth that the theme parks booth hasten and help to pay for come sophisticated problems. County governments that have only recently begun to shed their rural persons find them difficult to solve, no matter how mature the marriage.

"Sometimes," said James Oliver, "I wish they'd get more involved in Things. It would be nice to know what they think we should do."