The Dinamation show -- the Smithsonian's experiment in charging admission to an exhibit at a museum on the Mall -- has attracted only moderate attendance and generated a profit of just $171,000 for the institution in its first 3 1/2 months.

Nonetheless, officials say they consider the exhibit a success in terms of educational value and excitement. And they say the show would not have been possible without the fee. Hoping to lure school groups, the Museum of Natural History will keep the dinosaur show through the end of the year instead of ending the exhibit Sept. 3, as planned. (The show will close from Sept. 3 through Sept. 8 for some remodeling.)

Still unclear is how the admission fee ($4 for adults, $2 for children under 12, free for those under 3) is playing with the public. While the contract arranging the show reflects considerable apprehension and strategy-making on this point, the Smithsonian says it has received only about a dozen written complaints. Some discontent may be suggested by the moderate attendance (about 12 percent of those who come to the museum). And the number of visitors to the exhibit soars on the second and fourth Tuesdays of each month, when the museum waives the fee. On those days, officials say, attendance at the exhibit is double that of an average weekday and even beats weekend figures.

Random interviews with visitors suggest that most of those who make the trip aren't especially unhappy about paying to see the robotic beasts, which roar, tend nests and crane their necks in a manner that is more or less convincing (depending on which child you ask).

"Since we come here once every 10 years, we don't get passionate about it," said Herb Hastings, of Roanoke. His son, 4-year-old Noah, clearly thought the show was worth his father's money. "I like dinosaurs and I know a lot about them," he said.

Jane Slemmons, a teacher from Silver Spring, said the admission fee kept her away at first but she changed her mind when a friend visited from out of town. "I'd be upset if they started charging for more programs," she said. Rochelle Baker, of Silver Spring, didn't mind paying at all. "Somebody should have to pay for it," she said.

One woman, who wouldn't give her name, was disappointed. "There's no way I'd do it again," she said. Her 8-year-old daughter agreed: "It was kind of gross."

By the end of July, 402,489 visitors had seen the show. That didn't exactly meet the wildest dreams of Museum of Natural History officials. "It's probably about in the middle of what we had in mind," said acting deputy director Stanwyn Shetler. "Our highest projections might have seen us doing maybe almost twice that number."

Overall, Shetler said, attendance at the Mall museums has declined in recent years. He believes the Dinamation exhibit helped the Natural History Museum stay about even with last summer.

The notion of charging admission is likely to receive a lot of study at the financially strapped Smithsonian -- but the Dinamation show will provide only limited encouragement. The net profit by the end of July, after the show had been open for 3 1/2 months, was $342,000 -- the sum split 50-50 between the Smithsonian and the company that created the exhibit.

The total cost of mounting and running the show through July was $775,500. In a detailed 33-page contract with Dinamation International Corp. of San Juan Capistrano, Calif., which created and owns the robots, the museum agreed that admission fees initially would go toward the cost of setting up the show.

The contract says Dinamation could recover its costs, such as the expense of designing the exhibit, providing materials, shipping and delivering, and producing and setting up the displays. The museum was to be reimbursed for such costs as insurance, site preparation and even long-distance calls associated with the exhibit.

That initial $600,000 outlay has been covered, and the fees now go toward operating costs and profits.

The contract reflects the Smithsonian's awareness of the sensitivity of selling tickets. "One joint goal is to minimize the potential for a negative public reaction to the admission fees," it reads. A section of the contract then goes on to describe the "strategy and guidelines" for dealing with a possible public outcry -- which never materialized.

"The Smithsonian shall coordinate, review and approve in advance all advertising, press releases and media contacts," the contract says. As it happened, the press release on the show casually mentioned the fees without confronting the potential controversy.

If a flap resulted, the Smithsonian expected to emphasize "a need for institutional self-sufficiency and ... the potential for future public/private sector ventures." The campaign would also emphasize the exhibit "as a unique, enjoyable and somewhat exclusive or limited property."

Another big concern for the museum was avoiding the appearance of profiteering. In one sentence, for example, the contract uses the word "profit" when referring to Dinamation and substitutes "an additional source of operating revenue" when talking about the museum.

This concern is also reflected when the contract turns to another ticklish area -- corporate sponsorship. (While the Smithsonian has turned increasingly to private funding, its officials are aware that corporate sponsorship can create questions about the integrity of a presentation.)

In this case, the museum decided not to seek corporate funding for the exhibit. Natural History's concerns about appearances were mixed with practical considerations: The contract points out that seeking corporate money might simply increase profits while draining possible support from other exhibits.

The Smithsonian seems certain to avoid charges of profiteering, since it made just $171,000 through the end of July. At the Smithsonian, two-thirds of the net goes to the Natural History Museum and the balance to the parent Smithsonian Institution.

Natural History will use its profit to cover the $40,000 cost of a free exhibit of dinosaur sculptures made from car parts, to renovate existing collections and exhibits, and to bring in temporary exhibits. The Smithsonian will put its share -- $57,000 to date -- into its unrestricted trust fund. That pays for educational programs, acquisitions, research and special exhibits.

The dinosaur show represented a novel joint venture between the museum and a private firm. At first, the museum considered simply paying a rental fee for the creatures rather than the current cost- and profit-sharing deal. But the museum's costs would have been higher and officials feared they would lose money. "At the moment, because attendance is moderate, I would say we made the right judgment," Shetler said. "There were optimists around at the time who thought this was going to be a terrific moneymaker. Fortunately, we had cool heads that made the determination."

Shetler said the museum was never interested in maximizing profits and considers every dollar over break-even to be a bonus. While the Dinamation firm is in business for profit, Shetler said the company is pleased that its dinosaurs, which have appeared around the country, have the Smithsonian imprimatur. The company accepted the museum's reticence about advertising and promotion. "We don't want to get into crass commercialism or hucksterism," Shetler said.

The exhibit is likely to experience a drop in attendance at the beginning of September, but the museum will try to attract school groups. When the show opened, "most schools were already closing down on field trips," Shetler said. Museum spokeswoman Pamela Baker said officials also hope the show will lure area residents who might have stayed away fearing crowds during tourist season.

Keeping the show open means the museum will incur more expenses. To make room for another exhibit, the museum has to spend about $30,000 to $35,000 moving its box office and a small adjunct interactive exhibit that shows how the robots work and allows children to make rubbings with crayons.

The monthly cost of operating the show is $49,980. The Smithsonian estimates that its profits for the exhibit's extended September-December run will be $100,000 or more.

While Shetler thinks the dinosaurs have perked up the museum -- "People do pay more attention to moving things," he said -- he knows of nothing similar that might be on the horizon at the museum.

"We're not really trying to compete with theme parks," he said. "The country is awash in theme parks."