The costliest water project in American history, a barge canal through the mid-South, has been pushed toward completion with a spurious economic analysis by the Army Corps of Engineers.

Behind the issue of dubious economics to justify the project is a cast of southern political figures, with names such as Carter, Stennis and Eastland, adding their considerable influence over the project's fate.

The project is the $1.8 billion Tennessee-Tombigbee Waterway, a canal linking the Tennessee River with the Gulf of Mexico and shortening the commercial barge route for most inland shippers of coal, chemicals and other bulk commodities.

Environmentalists and the Louisville & Nashville Railroad are challenging the legality of the project in federal court in Mississippi arguing that the corps is building it wider than authorized by Congress.

But a new look at the controversial Tenn-Tom, as the canal is called, raises points beyond those being argued in the court case -- questions about the justification for the project and the involvement of powerful southern political and corporate figures.

Among the points:

A "confidential" study commissioned by the corps in 1975 to justify huge new cost overruns was based on shipping data shippers say is inaccurate. One company projected as a major canal user has gone out of business. Others say they do not intend to use the Tenn-Tom.

Sen. John C. Stennis (D-Miss.), a leading congressional supporter of the Tenn-Tom, owns about $65,000 in stock in two chemical firms that stand to profit from the waterway -- Mississippi Chemical Corp. and First Mississippi Corp. Stennis has not been available for comment on his interests.

Former senator James O. Eastland (D-Miss.), who retired this year, owns about $100,000 in stock in Mississippi Chemical Corp. Pressure from Eastland led to a special $4 million federal low-interest loan to a small Mississippi railroad that is to hook up with the Tenn-Tom.

The Columbus & Greenville Rail road, a 167-mile line operated by political associates of Eastland, carries all the cottonseed oil from the Greenwood, Miss., farm cooperative in which Eastland has a $15,000 interest. He said he was unaware of that point, and contended that there is no connection between the canal and his interest in Mississippi Chemical Corp.

Owen Cooper of Yazoo City, Miss., a founder and former president of Mississippi Chemical, is a clos personal friend of President Carter. The company plans to use the Tenn-Tom, and has readied a loading-dock site along the canal at Aberdeen, Miss.

Although there is no evidence that the Carter-Cooper friendship affected his decision, the president in 1977 chose not to oppose funding for the Tenn-Tom, despite long-standing opposition to, and controversy over, the canal.

Carter's decision, made when he moved against 18 federal water projects he regarded as economically unsound, was based on the same key economic benefits study produced by the corps.

The corps insists tha shipping data in its study, prepared by A. T. Kearney Management Consultants of Chicago, is confidential and cannot be made public. But portions of the data have become available through other sources, allowing closer examination of the findings. Corps officials have declined to make further comment on the Tenn-Tom because of the litigation in Mississippi.

According to Kathy Fletcher, a White House staff assistant, the only economic-benefit data available to Carter was that provided by the engineers. That same corps data, buttressed by the Kearney report, underwent prior review by the Office of Management and Budget, which did no independent investigation.

Paul Crabtree, an OMB official, explained, "You have to trust (that) an agency you're working with doesn't lie."

Without the favorable findings of the Kearney team, however, the Tennessee-Tombigbee project would not provide the favorable benefit-to-cost ratio that Congress requires before proceeding with a waterways development scheme.

The waterway's economic benefits, it appears, were vastly overrated to cover up a major cost miscalculation that became apparent to the corps in mid-1974, when it discovered the Tenn-Tom would cost almost $500 million more than expected.

Instead of reporting the overrun to Congress, the corps hired Kearney to restudy traffic projections and recalculate the potential benefits that would come from the Tenn-Tom. Kearney's favorable report and word of the higher new costs were then passed on to Capital Hill.

But the rush of barge traffic envisioned by the engineers to win support for the Tenn-Tom will not materialize, according to interviews with potential shippers.

Kearney said that 70 percent of tonnage on the waterway in its first year of operation, expected to be 1986, would be coal from the Ohio and Tennessee Valleys.

But the recent interviews disclose that at least two-thirds of the projected volume of 18.5 million tons would not move on the Tenn-Tom. Thus, two-thirds of the anticipated economic benefits would not materialize.

One major shipper was to have been the Kentucky Energy Development Co. which, Kearney said, would be shipping 2.4 million tons on the Tenn-Tom instead of the Mississippi River because it would save $2.35 a ton.

Kearney reported that the firm was shipping its coal from Graysville, Tenn., to New Orleans and Mobile, the Gulf port where the Tenn-Tom will end.

But there is no multimillion-ton mine in Graysville, and the Kentucky Energy Development Co. is out of business. William Willard, a former partner in the company, said KEDC never had produced 2.4 million tons in Graysville or anywhere else. It never got beyond small trucking status.

Kearney also spotlighted the Alabama Power Co. and a sister corporation, Gulf Power Co., as potentially major users of the Tennessee-Tombig-bee -- more than 8 million tons of coal to move from Shawneetown, Ill., to power-generating plants in Alabama and Florida.

Not so, said Jim Small, fuel supply manager for the power companies. "It's hard to beat the Mississippi's rates on 30- and 40-barge tows," he said. "At this point we have nothing that looks very logical that would come down that direction [on the Tenn-Tom], nor do the barge lines serving us indicate they're interested in making a change."

Another company cited in the Kearney study was the Hawley Fuel Co. of New York, listed as a future shipper of 1.5 million tons of coal from Guntersville, Ala., and Chattanooga, Tenn., to Mobile.

Hawley today owns no mines in those areas, and Frank Nappi, a company vice president, said, "Our situation has changed quite a bit -- we were trying to work into the purchase of an operation in Alabama which never materialized."

Kearney's miscalculations did not involve coal alone. The firm said that Hammermill Paper Co. would abandon the railroads and switch to the Tenn-Tom to save $1.09 on every ton of wood pulp shipped between Selma, Ala., and Erie, Pa.

H. LeRoy Weidner, Hammermill's transportation manager, said that will not occur. The projected savings, he said, would not cover additional charges that would come up in trucking pulp to a barge dock.

He added, "I want to make a point here: nobody has ever come to us and really asked us, 'Would you use the Tenn-Tom?'"

In the view of Kearney, however, the report is valid. Victor Churchward, an official of the firm, said a "sort of a dynamic process" is involved in the development of any waterway project, and that specific company-by-company data were not that essential.

"Now," he continued, "the specific companies that are involved may or may not actually be the specific companies that are involved once the waterway is completed. In other words, some companies would drop out and others would drop in."

Kearney found enough potential shippers to provide the Tenn-Tom with a benefit of $1.10 for every $1 spent in construction and operation of the canal.

Not coincidentally, perhaps, a corps worksheet prepared in June 1975 specifically listed the amount by which benefits would have to be raised to bring the Tenn-Tom back to a favorable benefit-cost ratio.

William Hearrean of the corps' district office at Mobile said in an interview that he had never encountered such a situation -- the corps would not rejigger its calculations. But under oath during a pretrial deposition for the federal suit, Hearrean testified that the worksheet was his, although he couldn't remember preparing it.

In the interview, however, Hearrean said it wouldn't really matter if the Kearney findings did not hold up. "Every time we reanalyze a project we find an entirely different mix, but we have never, to my knowledge, found a project that wasn't feasible," he said.

Since it was approved by Congress in 1946 and given its first funding in 1971, when then-president Richard M. Nixon was openly courting the southern electorate, the Tenn-Tom has been controversial.

The idea behind it is to link the Tombigbee River in Alabama and Mississippi with the Tennessee by a deep canal in northwest Mississippi and a series of 17 locks and dams along the new 260-mile route that would be created.

Great Lakes ports, major shipping points along the upper Mississippi, the Ohio, the Illinois, the Tennessee and the Cumberland Rivers all would have a shorter route to and from the Gulf than via the Mississippi.

Stennis, Eastland and other southern politicians in important congressional committee positions long pushed for completion of the canal, but could not win presidential support for funding until Nixon gave in.

In 1977, when Stennis still chaired the appropriations subcommittee that provided money for the Tenn-Tom, he prevailed upon the General Accounting Office to withhold publication of a report that was critical of the corps' benefit-cost calculations.

Stennis insisted that his only comment to the GAO was that the Tenn-Tom was involved in litigation. GAO then agreed not to issue the report on the same grounds.

A GAO auditor's comments at the bottom of a memo on the matter said, "It seems this decision was made solely to keep from offending Stennis. Where is GAO's impartiality and moral obligation to the American public?"