What the book says. The revised edition of Smith's own book describes the work: "The search was a long and heavy work, for there were thousands of fragments to be examined, and these were so small, and contained so little of the text, that it was extremely difficult to ascertain their meaning." It then gives the date plainly, Smith "published his discovery to the world at a meeting of the Society of Biblical Archæology, December 3rd, 1872." The flood text turned out to be the eleventh of twelve tablets.
What happened next is a fact about how much it mattered. "The interest excited by Mr. Smith's discovery was naturally very great. Immediately after the meeting of the Society of Biblical Archæology, Mr. E. Arnold, in the name of the proprietors of the 'Daily Telegraph,' asked the fortunate discoverer to reopen, at their cost, the excavations in Assyria in the hope of finding the missing portions of the story of the Deluge." A London newspaper funded an archaeological expedition to Mesopotamia to find the rest of a flood story. Smith went, found more of the tablet, and died in the field in 1876, aged 36.
⚠️ A detail we have NOT verified: contemporary press reports are widely said to place the Prime Minister, W. E. Gladstone, in the audience that night. We have not read those reports, and the Gladstone detail does not appear anywhere in the book we hold. It is recorded here as commonly reported and unverified, which is the honest status to give it.
Sources: George Smith, The Chaldean Account of Genesis, rev. Sayce (c. 1880), the discovery narrative.