Having just beaten Bernie Mitton to clinch victory for the United States in the American Zone North Section finals against South Africa on Sunday, Harold Solomon wanted to remind everyone this was the beginning, not the end, of the 1978 U.S. Davis Cup effort.

"Every time you win a match, it's exciting, but this is just a small step," said Solomon, 25.

"What we want to do is go ahead and win the next one and the next one and the next one to win the whole thing. It's ridiculous that we haven't won it since 1972. We have the personnel and there is no reason we shouldn't win it this year."

The recurring problem for the U.S. in recent quests for the oldest and most prized team trophy in tennis has been tapping that deep reservoir of talented personnel and this year promises to be no different.

Solomon has seen the good, the bad, and the ugly. He was a rookie the last time the U.S won the cup against favored Romania in Bucharest in 1972.

He also was present when the current decline - consecutive losses in the American Zone to Colombia, Mexico twice, and Argentina - began. He lost both his singles in a 4-1 loss at Bogota in January, 1974, just weeks after the U.S. had lost the 1973 final to Australia in Cleveland.

"We don't enjoy losing like we have the last five years. I think we're about ready to win the whole thing," he said before heading to Las Vegas, where he is defending his title in the WCT $400,000 Tournament of Champions.

Solomon also realizes, sadly, that the sterling silver punch bowl introduced by Harvardian Dwight F. Davis in 1900 as "the International Lawn Tennis Challenge Trophy" isn't as polished as it used to be.

"The prestige has kind of slipped the last few years," Solomon said. "When I was a junior, I dreamed of playing Davis Cup. Every kid in tennis did. That was kind of the pinnacle. But it really hasn't found a spot in the professional game."

Solomon hopes this is changing, that the dwindling importance of the cup relative to the huge prize money events that crowd the international tennis calender can be reversed by intelligent scheduling that will permit the leading players to be available for any given match.

He hopes a U.S. victory will signal renewed interest in a grand old competition that has lagged because of amateurish and reactionary management, cumbersome scheduling that has clashed rather than blended with the burgeoning progame, and disruptive politics.

Attempts to coordinate the calender and schedule Davis Cup series only during the 17 weeks when there are no $175,000 "Super Grand Prix" tournaments, have been implemented clumsily, without much forethought. But at least a commitment to reform has been made.

"The effort to fix the schedule is a positive step in the right direction," says Tony Trabert, the third-year U.S. captain, who knows too well the frustration of knocking on the top players' doors when recruiting his squad and finding no one home. "Some mistakes may have been made this year, but hopefully they'll be rectified in 1979."

In the meantime, the U.S. recovery operation this year will not be easy.

Now that the U.S. team has put the most politically sensitive problem of the competition behind it by beating South Africa, 4-1, amid demonstrations at Vanderbilt University over the weekend, the next opponent is Chile in the American Zone final at Santiago, Sept. 15-17.

The winner of that will move into the Inter-Zone semifinals against the victor of the European Zone, probably Italy or Spain. But if recent experience has taught the U.S. a lesson, it should be not to look past Chile.

The Chileans, with Jaime Fillol and Hans Gildemeister playing singles and Fillol and Patricio Cornejo in doubles, are a formidable team, especially on their home clay court, as they proved by beating Argentina there over the weekend.

"Darn right I'm worried. This is no cakewalk," says Trabert.

It will be impossible for the U.S. to send a well-prepared team to Santiago.

"That's the week after the U.S. Open, probably the worst week of the year to have a Davis Cup match," said Solomon. Who teamed with Vitas Gerulaitis to sweep the four singles against South Africa.

"Anybody who does well at the Open will be drained, and we'll be going straight from cement to the slowest clay in the world. It's a different ball game."

Even Trabert - who has not officially been named captain for future matches, but seems assured of reappointment for the remainder of 1978 - will be late arriving in Chile.

He is the color commentator for CBS-TV, which is pressing to have the Open final played in prime time on Sunday night, Sept. 10. If it is, Trabert and any players in the final would not arrive in Chile until Tuesday for a match scheduled to begin Friday.

That is not enough time to get acclimated properly for a Davis Cup series on foreign soil. But even fielding a representative team could be a bigger problem.

The leading players are bound to be tired after gearing their summer schedule to peak for the U.S Open.

Some already have commitments, and others will be faced with conflicts. The World Team Tennis playoffs that week will have first call on Gerulaitis, who is under contract to the New York Apples.

The leading doubles teams will be in demand for a $175,000 tournament at The Woodlands, outside Houston, the lone doubles-only event on the Colgate Grand Prix calendar, given that date specifically because so few top players want to compete in singles the week after the Open.

Solomon said that he would play if asked, but only reluctantly because "that would mean I'd be playing seven or eight weeks in a row, and that never works out well."

While Eddie Dibbs is the only man in the U.S. top 10 who has told Trabert he is not interested in playing Davis Cup, Jimmy Connors, America's top-ranked player, has not chosen to play since December, 1975.

Nevertheless, Trabert hopes to enlist him.

Trabert says he spoke to Gloria Connors, Jimmy's mother and manager, about Davis Cup when he got the 1978 schedule last November.

"She said she thought he shouldn't play, that Jimmy ought to start thinking about and taking care of himself," Trabert said.

Connors reportedly earned more than $900,000 playing tennis last year, appearance and endorsement revenue aside. That is the sort of looking after himself that has made the U.S. Davis Cup effort so troubled in recent years.