Late last month, during the peak of the general election campaign, the Virginia Electric & Power Co. sounded the opening gun, sending out an urgent appeal to every one of its 93,000 stockholders, employes and retirees.

"The railroads are fighting hard to maintain their transportation monopoly," wrote Vepco board chairman T. Justin Moore, urging construction of a huge pipeline to move coal to its plants. "Now is the time to let the candidates for the Virginia House of Delegates and the incumbent state senator in your area know how you feel about this issue."

That unabashed pitch for political pressure was only one facet of a full-blown -- and apparently unprecedented -- corporate lobbying campaign by Vepco on behalf of its mammoth coal slurry pipeline project. And as Moore's letter suggests, it is a campaign that is being matched, dollar for dollar, by the state's railroads, which now haul the coal and see Vepco's proposed pipeline as a dangerous competitive threat.

The upshot is a head-on and unsually fierce battle that already has included political campaign contributions, corporate-financed consultants' studies and the retention of a public relations firm and high-priced lobbyists, including the closest political adviser to Gov. Charles S. Robb. Within the past few weeks, many legislators and lobbyists say, the proposed coal slurry pipeline has suddenly emerged as the premier special interest controversy pending before the 1983 General Assembly, scheduled to convene in January.

"This one is going to make the feud between the Hatfields and McCoys seem like a Girl Scout cookie campaign," said Houston Kitts, veteran lobbyist for the United Transportation Union, which represents rail workers and is aligned solidly with the railroads against the pipeline.

Vepco -- in conjunction with the Houston-based Transco Energy Co. -- wants to build a huge, 400-mile pipeline that would pump a slush-like mixture of pea-sized coal and water from the coal mines of southwestern Virginia to the its coal-fired power plants in Hampton Roads. The project, which Vepco estimates would cost $650 million, would reduce coal transportation costs and serve as a shot in the arm for the state's depressed coal industry, its proponents say.

The railroads counter that the pipeline is a potential economic white elephant and environmental disaster. Behind it all, though, is competition: The railroads could lose millions of dollars in business if a pipeline is constructed.

The intensity of the coal slurry pipeline issue offers an unusual opportunity to observe how corporations try to exert influence in Virginia's capital:

Consultants' Studies. Masking one's arguments in scientific objectivity is a sure way to give credence to the cause, and there are more than enough consultants and academics to oblige. Vepco kicked off the slurry fest this summer by bankrolling a $64,000 study by the Virginia Center for Coal and Energy Research at Virginia Polytechnic Institute and State University.

Not surprisingly, the Vepco-financed study came up with a report that said a coal pipeline would save between $5 and $11 per ton in coal transportation costs, for a potential saving of $30 million to $66 million a year.

Last week, the Virginia Railway Association countered with its own study by Teknekron Inc., a Bethesda-based consulting firm. The study, for which the railroads paid between $30,000 and $35,000, predictably shot holes in the Vepco study, indicating that a pipeline could end up costing twice as much as Vepco says it will.

Lobbyists. In addition to the usual stable of utility and railroad lobbyists, both sides are going outside for special help on the coal slurry pipeline issue. Vepco and Transco, which recently formed a consortium called Virginia Coal Slurry Associates, have hired William G. Thomas, the super lobbyist of Richmond and political confidant of Robb.

Vepco and Transco also are financing a group called "Virginians for Competitive Coal Transportation," which hopes to enlist consumer groups, labor and other interests that might favor the pipeline. To head it, they hired Curry Roberts, former political aide to Attorney General Gerald Baliles and finance director for Lt. Gov. Richard J. Davis' losing Senate campaign.

The railroads say they also are negotiating to hire outside special forces, including former legislators and other former state officials. Although no deal has been closed, some politically well-connected lobbyists are already on hand. Charles Davis, a top aide to former Republican Gov. John Dalton, has been retained by CSX, the Richmond-based rail conglomerate.

Campaign contributions. Vepco's political action committee, the Committee for a Responsible Government, was among the most active PAC in the recently concluded campaigns for the House of Delegates, funneling more than $10,000 to 51 legislative candidates. Records show the railroad union workers' PAC, the Transportation Political Education League, gave $4,200 to 14 legislative candidates.

Public pressure. Last month, Vepco instructed its district managers to begin visiting legislators on behalf of coal slurry pipeline legislation. There is talk that next month the utility will enclose appeals in its monthly bills to about a million Virginia customers -- a step Vepco spokesmen won't rule out. The railroads have hired a Richmond public relations firm to present their side of the case and plan to counter Vepco's appeals with mailings to their own stockholders and employes.

Legislators, meanwhile, are enjoying the spectacle. "What two more powerful interest groups in the state can you find at each other's throats?" asks state Del. Warren Stambaugh (D-Arlington.) "It's going to be a fascinating battle, isn't it?"