IN THE mid-1980s, some museums tried to meet financial shortfalls by expanding their money-making gift shop and membership offers; they promptly ran into complaints from small businesses that as tax-exempt organizations they constituted unfair competition. Others sought to defray the costs of big exhibitions through corporate backing; they got grumbles, which continue, about scholarly independence and outside control. (The National Archives took considerable heat for joining with Philip Morris Co. to salute the Bill of Rights.) But the biggest outcry, in this city at least, comes when museums try to charge admission. Against this backdrop, it's not too surprising that the Smithsonian's otherwise lighthearted dinosaur show, "Dinamation," whose run the Museum of Natural History has announced it will extend through December, has had only mixed success and that its policy of charging admission continues to draw muttering.

People want a lot from their museums -- they want them truthful, independent, readily accessible and also entertaining and welcoming. And in Washington, they want them free. "Dinamation," whose fees are $4 for adults and $2 for children, would seem at first to be an easy exception to the rule: it isn't really an exhibition at all, but a sort of special effects show, a flashy mechanical recreation of the extinct monsters to thrill children. Designed by a private company, it has been touring museums around the world, with half its admission revenues returned to the company and half going to the host museum. Though it claims to have an educational purpose -- to draw children into the magic of dinosaurs -- it probably benefits from that already well-established mystique more than it feeds it. Now that the museum is trying to reach out to school groups, the stated reason for the extension to December, officials say they are taking pains to improve the accompanying guide materials and to link the visit to the mechanized creatures to a stop in the more substantial dinosaur halls that hold fossils and the like.

The Smithsonian has handled the pay-for-admission issue with considerable caution, and its repeated reassurances that this is not a trend are a gauge of the issue's continuing sensitivity. Attendance still doubles on the alternate Tuesdays that the show is free. Revenues are not especially impressive, and the Smithsonian's half comes nowhere near the kinds of profits that some hoped it would generate. The downside of this is obvious, but one can also detect, and approve, a hint in the voices of officials and visitors alike that it's probably just as well.