Entdeckungen über die Theorie des Klanges — Discoveries in the Theory of Sound — was published in Leipzig by Weidmanns Erben und Reich in 1787. The Internet Archive copy comes from the Getty Research Institute: four preliminary leaves, 77 pages, an errata page, and eleven plates engraved by Johann Stephan Capieux.
The plates are the point. Chladni's method was to strew fine sand on a metal plate and draw a violin bow along its edge; the sand migrated off the moving areas and settled on the nodal lines, and he drew what he saw, systematically, mode after mode. The text is dense Fraktur and hard going even in German, but the figures read straight off the page and still match what a modern plate does.
He demonstrated the effect in Paris in 1808 to an audience that included Napoleon, who set a prize for a mathematical explanation. That prize is a story of its own.