In its editions of Sunday, June 19, The Washington Post reported that Amtrak's dues payments to the Association of American Railroads help support the association's lobbying team. In fact, Amtrak has insisted that none of its dues be spent on lobbying activities.

When you're running a corporation as big as U.S. Steel, it's not always easy for the right hand to know what the left hand is doing. That must explain the huge firm's lobbying position of S. 790.

Ohio Barge Line, Inc., a U.S. Steel subsidiary that hauls raw materials and steel along various Midwestern waterways, has contributed more than $5,000 to the lobbying effort against the Senate bill, which would require barges to pay tools for use of inland waterways built or maintained by the federal government.

Meanwhile, the Elgin, Joliet, and Eastern Railroad, another whollyowned subsidiary of U.S. Steel, has contributed undisclosed sums to the Western Railroad Association, the rail industry umbrella group that has spearheaded lobbying in favor of the waterways bill.

U.S. Steel's schizophenia on S.790 may be unusual, but the giant steelmakers involvement in the lobbying fight is definitely not. As the controversial waterways proposal heads toward a final Senate vote - probably sometime this week - some of the biggest fish in America's corporate sea circling the Capitol, looking for a legislative kill.

As with most economic legislation in Congress, the waterways toll plan is being debated largely in terms of its effect on consumers and small business. But also as with most economic legislation, the lobbying is being financed largely by big business.

Under the 1946 Regulation of Lobbying Act, all those involved in the lobby campaign should report how much they are spending on the effort.

In practice, the act is so structured that anyone who wants to can conceal his identity and his expenditure. Thus it is impossible to detail precisely who is spending what on S.790.

But records that are, vailable indicate that railroad interests, which favor the waterway toll, have spent at least $350,000 on the toll legislation and a companion bill that would authorize construction of a major new barge facility on the Mississippi at Alton, III.

Those chipping in to the rail fund include most of the nation's big railroads, conglomerates such as IC Industries (which owns everything from railroads to Midas Mufflers to Dad's Root Beer), and two government funded rail behemoths, Amtrak and Conrail, whose annual dues to the Association of American Railroads help pay for that association's lobbying team.

The railroad spending seems to have been at least matched by the barge industry, which opposes the toll.

The barge business is a curious combination of small, one-or two-boat piloting concerns and huge industrial, mineral, and agricultural firms that maintain large river fleets.

Those big barge shippers have been generous in supporting four different industry groups lobbying against the toll. Contributors include Dow Chemical; Peabody Coal; Cargill, the grain giant; American Electric Power, the nation's largest utility combine; and Mobil, Sun, and Ashland Oil companies.

Once you've raised the money, how do you start lobbying? The two sides in the S.790 flight have adopted opposite approaches to the problem.

The railroad people, on the whole, are working through senators' staffs. Using their own loquacious lobbyist, Robert Bird, and a squadron of environmentalists and economists supported by railroad funds, they have tirelessly carried their message - in personal visits and voluminous literature - to every administrative assistant in the Senate.

The staff strategy is a proven winner, one of the great Senate victories in lobbying lore - the civil rights lobby's defeat of the G. Harrold Carswell Supreme Court nomination - was won by convincing staff members, who convinced their senators, that Carswell was unfit for the court.

But it also has a hitch. While one lobbyist is busily selling a senator's aide, he may find out that his adversary has been working equally hard on the senator himself.

And that, in the case of the waterway toll, is where George A. Smathers comes in. Smathers has been hired by the bargemen to take their case directly to the senators.

George Smathers is a smooth-talking, ingratiating Floridian who served three teams as a Democratic senator and set up shop along "Lobbyists' Row" on K Street N.W., after retiring from Congress in 1968.

With his convincing ways and close friendships among senior Senate Democrats, Smathers' operation has been able to command fees of $2,000 per month and more from major corporate clients.

For the past five years, in fact, Smathers had been paid about $100,000 per year, according to rail executives, by the railroad industry to lobby in support of the waterway toll.

Then, this spring, the highly paid Smathers changed his spots. Smathers was signed up by the barge industry, and immediately began lobbying assiduosly against the toll proposal he had so assiduously supported while he was on the railroad payroll.

The quick turnabout seems not to have impaired Smathers' effectiveness with his old friends in Congress. He and his new associate, former Democratic Rep. James Symington of Missouri, have been calling senators and cornering them in the hallways to spread the bargemen's message.

Indeed, the opponents' direct approach to senators seemed to be working so well that one of the chief supporters of the waterway toll began last week to employ that lobbying tack in addition to the staff strategy.

Secretary of Transportation Brock Adams, who has led the fight for the Carter administration, which supports the toll idea, began placing calls to his friends in the Senate to convince them that S.790 deserved their vote.

Not all the lobbying effort was aimed directly at Capitol Hill. There was also a concerted effort to win the hearts and minds of the news media, on the theory that what was printed about the waterway toll would influence senators' perception of the issue.

Accordingly, a barge industry group two weeks ago hosted some 20 reporters on a free, two-day barge tour of the Ohio River Valley.

And last week senator o both sides of the issue were approaching Washington reporters proposing news stories about the bill that would run a day or two before the Senate vote. Each side's version of the story, of course, supported its view of the toll proposal.

Last week, Sen. Pete Domenici (R-N.M.), the sponsor of the waterway toll bill, and Sen. Russell Long (R-La.), its chief opponent, both suggested that reporters write a news story a day or two before the Senate vote. Each man's version of the proposed story, of course, supported his view of the issue.

Whether all the money and effort would bear fruit remained unclear, however. With the vote just a few days off, Lee Lane, an economist who has been lobbying in favor of the waterway toll, was almost ready to conclude that it had all been in vain.

"The more I talk to people," Lane said, "the more I'm afraid that half the Senate doesn't understand the issue and the other can't make up its mind."