Eadweard Muybridge, ‘Buffalo; Galloping,’ 1887, collotype, Iris and B. Gerald Cantor Center for Visual Arts, Stanford University. (Iris and B. Gerald Cantor Center for Visual Arts, Stanford University, Stanford Family Collections/IRIS AND B. GERALD CANTOR CENTER FOR VISUAL ARTS, STANFORD UNIVERSITY, STANFORD FAMILY COLLECTIONS)

“The Great American Hall of Wonders” is ambitious, and exactly the sort of exhibition that the Smithsonian American Art Museum should be attempting.

It takes on a big subject: the art and iconography and the peculiar mix of the scientific, political and cultural ambition of 19th-century America. It pursues its subject with all means available, including painting, sculpture, scientific patent drawings, advertisements, photographs, letters and journals. And it pursues connections, and contradictions, in American cultural life that are confounding and complicated: our boundless optimism and frightful xenophobia, our love and loathing of all things wild and untamed, our passion for self-improvement and our know-nothing idiocy.

But the exhibition is often disappointing. Claire Perry, a deeply knowledgeable curator, has taken on more than can be managed in a show of modest dimensions, and she has chosen objects that don’t always further her rhetorical aims and all too often lack visual appeal.

Like the museum’s exhibition devoted to George Ault and the art of the 1940s (on view until Sept. 5), the “Hall of Wonders” is elaborated as much in its catalogue as in the visual material on the walls. But unlike the focused and idiosyncratic Ault exhibition, the “Hall of Wonders” isn’t sure what it wants to say. And worse, Perry’s reading of the paintings doesn’t always feel trustworthy. Lots of curators “over read” their material — and a brilliant “over reading” can be thrilling — but Perry simply sees things that aren’t there or are so ambiguous as to be unconvincing.

The “Hall of Wonders” takes its inspiration from an 1822 painting by the American painter and naturalist Charles Willson Peale, who produced iconic images of the Founding Fathers and founded a museum in Philadelphia, where he exhibited an enormous mastodon skeleton, among other wonders. Peale’s 1822 self-portrait, made when he was 81, shows a vigorous silver-haired man, dressed in a sober black coat, pulling up a sumptuously theatrical red curtain. Revealed behind the cloth is a long gallery of zoological treasures and a tantalizing glimpse of the mastodon bones.

Although parts of the canvas are clumsily painted, it is a magnificent image, capturing Peale’s strange mix of showmanship and intellectual gravitas. In 1780, John Adams wrote to his wife that he and his generation would study the arts of government and war in order that their sons could study “mathematics and philosophy, geography, natural history.” And their sons, in turn, would study science so that Adam’s grandsons might have the “right to study painting, poetry, music, architecture, statuary, tapestry and porcelain.” Peale embodied it all, republican severity and self-discipline, and artistic accomplishment, all cohabiting in one very fine old curmudgeon, and all in less than a generation.

It is a very good place to begin an exhibition. Like a giant painting from the same period on display at the National Gallery, Samuel Morse’s “Gallery of the Louvre,” created by the inventor of the telegraph, Peale’s self-portrait emphasizes the mutual dependence of both science and art on keen observation. It shows how fundamental the museum — and the broader impulse to collect, classify and catalogue — was to American intellectual ambition, and it underscores the quaint and endearing belief that the knowledge of the world could be contained, encompassed and digested by a single mind.

Perry is at her best with this material. At one point, she says, Peale “contemplated the idea of exhibiting the embalmed corpses of a select group of Founding Fathers.” He thought better of it. But his painting made explicit reference to their legacy: “The curtain conveys the farewell of the revolutionary old guard — Peale, Jefferson, Adams would be dead before the end of the decade — and sets the stage for the nation’s second act.” Peale hoped it would be an age of invention and experiment.

But from this promising start, the exhibition goes downhill. Few of the other works in the show have the visual appeal and dense interest of the Peale painting. Too often, engravings and reproductions substitute for the paintings themselves. And although Perry is smart about Peale, and erudite on details, she is prone to peculiar interpretations. Sometimes it’s a matter of evidence and argument, as in her reading of Frederic Church’s enormous and enormously influential 1857 painting of Niagara Falls (seen in an uninspiring chromolithograph reproduction). The painting presents the magnificently rendered falls just at the point at which the water tumbles over the precipice, which, Perry argues, “is no coincidence.” Church focuses his painting “at the edge of an abyss” because the United States would plunge into the Civil War four years later.

This could be a magnificent bit of academic “over reading,” and it’s perfectly plausible. But one wants at least one more data point — a letter, a journal entry, a contemporary account — that suggests perhaps someone read the painting that way. But Perry doesn’t offer anything else, no justifying footnote, just the observation that the Dred Scott decision, which reinforced slavery and divided the nation, came down the same year as the painting.

There are also several cases in which Perry simply sees a different image than most people will agree on. In the catalogue, she says that Winslow Homer’s 1871 “Old Mill (The Morning Bell)” represents a female factory worker “commanded by a tolling” that exemplifies “the despotism of the new” industrial order. In fact, the bell is rather small, the scene quiet and the women represented in the distinctly bucolic landscape under no visible duress at all. In Albert Bierstadt’s “The Last of the Buffalo” (from about 1888), Perry describes a “desolate and windswept valley,” where Indians do battle with the last of the great species that once swarmed the continent. But, in fact, it is a rather green and pleasant valley, and if it is windswept, the winds haven’t dispelled what appear to be mists rising off the valley walls. Curiously, a verdant valley is essential to Perry’s basic analysis of the painting, which suggests that with the demise of both Indian and buffalo, the United States was a paradise awaiting the White Man.

Finally, there is an annoying tendency to use trendy-sounding verbiage as a substitute for clear thinking, a mix of sexy populism and academic obscurantism. One “chapter” of the exhibition is devoted to “Democratic Time,” the regulated, industrious and industrial sense of time that is determined by clocks, factory whistles and old adages such as “time is money.” But is there anything innately democratic about it? Spend a day in Beijing. In discussing a painting by the African American artist Robert Duncanson, Perry writes: “In claiming his right to participate in the nation’s most elevated endeavors, the intrepid artist had invented himself.” That’s okay for PBS and Ken Burns, but it’s an empty metaphor and doesn’t belong in a serious essay.

In an introduction to the exhibition, the museum’s director, Betsy Broun, says that the reader’s mind may reel as he “tries to discern some linear thread in the tangle of astounding details and rich amazement of the story.” This is, she argues, a virtue of the unfortunate hodgepodge and disconnected show. It isn’t. “The Great American Hall of Wonders” needs both an editor and a thesis, and it must be accounted a missed opportunity.

“The Great American Hall of Wonders” is on view at the Smithsonian American Art Museum through Jan. 8. Admission is free. For more information, visit americanart.si.edu.