The roots of this classic trick can be seen in “How to vanish a glasse full of Beere”, described by “Hocus Pocus Junior” in The Art of Legerdemain Discovered, 1634, n.p. The author's description is vague on detail. A glass of beer was set over a sixpence on the table. In the act of dipping a finger into the beer it seems the sixpence was somehow secretly picked up on another finger having a sticky wax on it. The performer then cupped his hands around the glass, concealing it. (Either the glass was very short, or the cupped hands were positioned one above the other.) He raised his hands and in this act lapped the glass of beer. The hands were separated to show the glass and sixpence gone; after which the sixpence was immediately produced from the conjurer’s nose and the glass of beer from his pocket.
While this trick is presented as a vanish and reproduction, converting the presentation to a penetration of the tabletop is a small step. It is unknown who conceived the idea of using a napkin or sheet of paper to cover the glass and create a shell around it, which permitted the perception of the vanish or penetration of the glass to be delayed and distanced from the lapping of the glass. Philippe Billot has traced this improvement back to 1845, when the trick was included in the February 1 issue of The New Parley Library, Vol. 2 No. 48, p. 319. Its appearance in a popular periodical for the public suggests the trick was not a well-kept secret by the time and was likely older.
The version using the paper cover, though, was still being performed by professional magicians in the 1890s; e.g., see the Washington Post on February 7, 1891, p. 8, for the description of an unfortunate performance of it by Yank Hoe.
An audio convincer was added by John Northern Hilliard in The Sphinx, Vol. 3 No. 12, Feb. 1905, p. 152. He suggested covering the glass with a newspaper that had been doubled over. Sandwiched between the sheets was a second, secreted half dollar. This allowed the magician to lap the glass, while still being able to later tap the top of the “glass” to hear a clinking sound, further preventing anyone from suspecting that the glass is already gone. Hilliard also includes a feint to create doubt that the coin is still under the glass, giving even more focus on the coin when the glass is raised to lap it.
An interesting variant was marketed by Hamley Bros. in 1907, in which a coin and sugar cube are placed into the glass. When the paper is smashed down, the glass and coin are seen to have vanished, but the sugar cube remains on the table. (See the ad in The Sphinx, Vol. 5 No. 12, Feb. 1907, p. 136.)